In this talk, I will describe some work in progress about relating the low-lying spectrum of the Davies Lindbladian for qLDPC codes to that of Glauber dynamics on a classical model.
Calderbank-Shor-Steane (CSS) codes, such as the toric code, are a widely studied class of quantum error-correcting codes. Understanding the thermalization time of these systems is important not only for error correction but also for applications like Gibbs sampling. We show that CSS codes on a lattice satisfy a modified logarithmic Sobolev inequality and thus thermalize […]
Registration for the TRR 352 Winter School on Mathematical Physics is now open! The event will take place from March 9-13, 2026, at the Georg-von-Vollmar-Akademie in Kochel am See. Invited speakers: Emanuela L. Giacomelli (University of Milan) Vojkan Jaksic (Politecnico di Milano) Benjamin Schlein (University of Zurich) Katharina Schratz (Sorbonne University) Participation is free of […]
A gas of interacting Bosons can be represented using an ensemble of stochastic diffusions – a Brownian loop soup. In this talk, we review the construction of this Feynman representation, its representation of Free Energy and the 1-PRDM. We also introduce some results from the literature in the dilute and other regimes and state some […]
Describing the long-time dynamical behaviour of quantum systems is a long-standing open problem. When the coupling constant \lambda of the interaction is small, the dynamics of the system up to kinetic time t \sim \lambda^{-2} is conjectured to be effectively governed by the Boltzmann-Nordheim kinetic equation. In this talk, I will present a result on […]
We consider a class of Unitary Quantum Walks on arbitrary graphs, parameterized by a family of scattering matrices. After explaining that these Scattering Quantum Walks encompass several known Quantum Walks, we further introduce two classes of Scattering Open Quantum Walks on arbitrary graphs based on that construction, whose asymptotic states we discuss.
We study the dynamical density and current responses of a class of non-interacting, one-dimensional gapless lattice Fermi systems subjected to density-type perturbations slowly varying in space and time, in the infinite-volume and zero-temperature limit. In addition, we analyse the edge density and current responses for quantum Hall lattice systems defined on a cylindrical geometry. We […]
Schedule: 14:30 Welcome 15:00 Talk by Nicos Georgiou (Sussex) 16:00 Coffee break 16:30 Talk by Christian Kühn (TU Munich) 18:00 Option for common dinner Titles and abstracts: Nicos Georgiou: Mean-field limit and parameter estimation for contagion dynamics on higher-order structures Classical models of contagion epidemics have graph based representations where the nodes represent the population and infections occur […]
With the proof of Widom’s conjecture giving new insights on the entanglement properties of the non-relativistic free Fermi gas, it is a natural question whether this situation extends to the relativistic case, where the single-particle Hamiltonian is given by the free Dirac operator. In this talk I give a brief introduction to both the Widom-Sobolev […]
The microscopic laws of quantum mechanics give rise to some of the most fascinating macroscopic phenomena in physics, such as superfluidity and superconductivity. The theoretical description of such phenomena is intimately linked with beautiful mathematics in fields like functional analysis, partial differential equations, or probability. This conference brings together internationally recognised experts in mathematical physics […]
We present the relativistic quantum physics model hierarchy from Dirac-Maxwell to Vlasov/Euler-Poisson that models fast moving charges and their self-consistent electro-magnetic field. Our main interest is (asymptotic) analysis of these nonlinear time-dependent PDE, with focus on the Pauli-Poisswell/Darwin system which is the consistent model at first/second order in 1/c (c = speed of light) that […]
November 17-21, 2025 at Haus Chiemgau, Teisendorf The meeting will begin on Monday at 3 pm and conclude on Friday after lunch. Speakers: Lennart Becker (UT) Yoon Jun Chan (UA) Eddy de Leon (TUM) Jorge Acuña Flores (UT) Paul Pfeiffer (LMU) Sebstian Stengele (TUM) Cornelia Vogel (LMU) Program: November 20: Full-Day Organizers: Florian Haberberger (LMU […]
Repeated compositions of quantum channels arise naturally in many places across quantum: they arise, for example, in the transfer operator approach to quantum spin chains, and also in the repeated interactions description of open quantum dynamics. Assuming the system of interest is subject to some amount of disorder, it is therefore natural that one consider […]
The CRC’s Annual Retreat took place from September 28 to October 1, 2025, at the Georg-von-Vollmar-Akademie in Kochel am See. The retreat was fully dedicated to preparing the application for the next funding period. Every project that will be continued or newly participating was introduced by a project leader. On Wednesday morning, the Best Paper Awards were announced. […]
Quantum mechanics, now about a century old, is a very successful physical theory of matter on a small scale. From its first description until today, it has surprised scientists and laypersons alike by the strange behaviour it attributes to particles, atoms, and molecules. This behaviour can be characterized by the keywords Uncertainty, Superposition, and Entanglement. […]
This talk will provide a basic introduction to the three dimensional Dirac equation that describes an electron interacting with a magnetic field. Over the years a lot of work has gone into constructing zero energy solutions, also known as zero modes, for said equation. In this talk I will explain the importance of zero modes […]
I will review the mathematical analysis behind two classes of new exciting materials: Twisted bilayer graphene (TBG) and twisted semiconductors (TMDs) with an emphasis on their mathematical properties and differences. If time permits I will discuss results on these models under disorder. Joint work with Maciej Zworski, Izak Oltman, Martin Vogel, and Mengxuan Yang.
Conventional quantum tomography assumes a high degree of control over the system in question in order to measure many observables. On the other hand, a classical dynamical system may be reconstructed from a time series of a single observable by means of delay embeddings. Inspired by this, we investigate the possibility of tomography of a […]
Evolutionary deep neural networks have emerged as a rapidly growing field of research. This talk discusses numerical integrators for such and other classes of nonlinear parametrizations u(t) = Φ(θ(t)) where the evolving parameters θ(t) are to be computed. The primary focus is on tackling the challenges posed by the combination of stiff evolution problems and […]
Thanks to their high degree of control and tunability, ultracold atomic gases provide a rich platform for the study of quantum many-body effects. Ultracold gases of highly magnetic atoms exhibit unique interaction properties that lead to striking behaviors, both at the mean-field level and beyond . A decade ago, a universal stabilization mechanism driven by […]
We explore a connection between a weak topology on spaces of probability measures, a classical combinatorial problem in matching, and numerical schemes for the solution of PDEs by neural networks.
We prove a fluid limit for the coarsening phase of the condensing zero-range process on a finite number of sites. When time and occupation per site are linearly rescaled by the total number of particles, the evolution of the process is described by a piecewise linear trajectory in the simplex indexed by the sites. The […]
On Thursday, May 08, 2025, at 12:15 pm, Prof. Dr. Shi Jin (Shanghai Jiao Tong University) will give a talk on “Quantum Computation of partial differential equations and related problems” at TUM, Boltzmannstr. 3, 85748 Garching Forschungszentrum, room 03.06.011. Abstract: Quantum computers have the potential to gain algebraic and even up to exponential speed up compared with its classical counterparts, and can lead to […]
Quantum computing with discrete variable (DV, qubit) hardware is approaching the large scales necessary for computations beyond the reach of classical computers. Separately, hardware containing native continuous-variable (CV, oscillator) systems has received attention as an alternative approach, yet the universal control of such systems is non-trivial. In this talk, I will highlight novel quantum algorithms, […]
In this talk we consider discrete Gaussian free fields with ergodic random conductances on ℤd, d ≥ 2, where the conductances are possibly unbounded but satisfy a moment condition. As our main result, we show that, for almost every realisation of the environment, the rescaled field converges in law towards a continuous Gaussian field. We […]
Let X be a simple random walk in Znd with d≥3 and let tcov be the expected time it takes for X to visit all vertices of the torus. In joint work with Prévost and Rodriguez we study the set Lα of points that have not been visited by time αtcov and prove that it exhibits a phase transition: there exists α∗ so that for all α>α∗ and all ϵ>0 there […]
Program: 11:00 am – Dr. Larry Read, LMU München: Proof of the oval conjecture (Part 1) lunch 1:30 pm – Matthias Baur, M.Sc., Universität Stuttgart: Proof of the oval conjecture (Part 2) coffee and discussion
In relativity, nothing can travel faster than the speed of light. But there are often emergent speed limits, such as the speed of sound, that limit practical information transfer. In quantum many-body lattice models, the existence of this emergent speed limit was first proved by Lieb and Robinson in 1972. Over 50 years later, their […]
In this talk, we address the full discretization of Friedrichs’ systems with a two-field structure, such as Maxwell’s equations or the acoustic wave equation in div-grad form. We follow a method of lines approach, where we first discretize in space via the discontinuous Galerkin method. Subsequently, we consider different second-order schemes for time integration, namely […]
State-sum constructions have numerous applications in both mathematics and physics. In mathematics, they yield invariants for knots and manifolds and serve as a powerful organizing principle in representation theory. To illustrate this principle, we discuss equivariant Frobenius-Schur indicators. In the context of physics, we explain how state-sum models offer a conceptual framework for tensor network […]
In this talk, we consider irreversible translation-invariant interacting particle systems on the d-dimensional hypercubic lattice with finite local state space, which admit at least one Gibbs measure as a time-stationary measure. Under some mild degeneracy conditions on the rates and the specification we prove, that zero relative entropy loss of a translation-invariant measure implies, that […]
We consider a system of closed random walk trajectories interacting by mutual repulsion. This probabilistic model is motivated by its connections to statistical mechanics models, such as the Bose gas, the double dimer model, or the spin O(N) model. We prove the occurrence of macroscopic loops in dimension d>2 (joint with A. Quitmann, 2022) and […]
It is a remarkable property of random matrices, that their resolvents tend to concentrate around a deterministic matrix as the dimension of the matrix tends to infinity, even for a small imaginary part of the involved spectral parameter. These estimates are called local laws and they are the cornerstone in most of the recent results […]
January 21-24, 2025 at Christkönigshaus, Stuttgart Speakers: Jonas Peteranderl (LMU) Sara Terveer (LMU) François Visconti (LMU) Paul Gondolf (Tub) Yifei Li (Tub) Tom Wessel (Tub) Pablo Costa Rico (TUM) Corlie Rall (TUM) Anouar Kouraich (TUM) Beatriz Dias (TUM) Yifan Jia (Copenhagen) Program: Organizers: Alberto Brollo (TUM) Emanuela Giacomelli (LMU Munich) Florian […]
Fix some graph or uniform hypergraph F and then consider the following simple process: start with a large complete (hyper)graph Kn on n vertices and iteratively remove (the edge set of) copies of F as long as possible; each selection is made uniformly among all present copies of F at that time. This process is […]
Phase transitions are natural phenomena in which a small change in an external parameter, like temperature or pressure, causes a dramatic change in the qualitative structure of the object. To study this, many scientists (such as Nobel laureates Pauling and Flory) proposed the abstract framework of lattice models. The focus of this talk is on […]
Of great interest in plasma physics is to determine whether excited charged particles in a non-equilibrium state will relax to neutrality or transition to a nontrivial coherent state. Due to the long range interaction between particles, the self-consistent generating electric field oscillates in time and disperses in space like a Klein-Gordon wave, known in the […]
Bardeen-Cooper-Schrieffer (BCS) theory is a successful model of superconductivity. In this talk, I will begin by providing an overview of how BCS theory connects with other models of superconductivity, highlighting major open questions and recent developments in the field. Second, I will explain recent results on the critical temperature in the presence of a boundary […]
Quantum systems typically reach thermal equilibrium when in weak contact with a large external bath. Understanding the speed of this thermalisation is a challenging problem, especially in the context of quantum many-body systems where direct calculations are intractable. The usual way of bounding the speed of this process is by estimating the spectral gap of […]
Competitive games of complete information famously always have Nash equilibria, but it is well-known that correlation (“advice”) can yield new equilibria, sometimes with preferable collective properties (social welfare, fairness, …). While it is known that quantum correlations in the form of entanglement do not imply further correlated equilibria, this situation changes when going to so-called […]
Quantum Signal Processing (QSP) is an algorithmic process by which one represents a signal $f: \to (-1,1)$ as the upper left entry of a product of $SU(2)$ matrices parametrized by the input variable $x \in $ and some ”phase factors” $\{\psi_k\}_{k \geq 0}$ depending on $f$. We show that, after a change of variables, QSP […]
Quantum walks (QWs) can be viewed as quantum analogs of classical random walks. Mathematically, a QW is described as a unitary, local operator acting on a grid and can be written as a product of shift and coin operators. We highlight differences to classical random walks and stress their connection to quantum algorithms (see Grover’s […]
We study the generalised Lloyd model, that is, a random Schrödinger operator on the lattice Zd of the form H = −∆ + λV, λ > 0, with Vi = ∑j Tij Wj where Wj ∼ Cauchy(0, 1) are iid random variables. If all coeffi- cients Tij are non-negative one can find an exact formula […]
The CRC’s Annual Retreat was held from October 6–10, 2024, at the Explorer Hotel Garmisch in Farchant. Nearly 60 members, including both established researchers and early-career scientists, gathered for a productive few days. Each morning, project teams presented brief talks and posters, providing valuable insights into their research. The afternoons featured engaging discussions, and participants […]
This talk will provide a partial overview of how to model molecular observables and spectral responses. We shall start with the essential quantum mechanical concepts and formalisms that are used in theoretical chemistry and molecular physics. This will be followed by an illustration of the tools that are involved in numerical simulations in this context.
The dilute Curie-Weiss model is the Ising model on a (dense) Erdös-Rényi graph G(N,p). It was introduced by Bovier and Gayrard in 1990s. There the authors showed that on the level of laws of large numbers the magnetization as well as the free energy behave as they do in the usual Curie-Weiss model (i.e. mean-field […]
Branching Brownian motion, branching random walks, and the F-KPP equation have been the subject of intensive research during the last couple of decades. By means of Feynman-Kac and McKean formulas, the understanding of the maximal particles of the former two Markov processes is related to insights into the position of the front of the solution […]
(Pseudo)spectral methods are popular for solving a wide variety of differential equations and generic optimization problems. Due to favourable approximation properties, such as rapid convergence for smooth functions, they are particularly popular and effective for solving time-independent Schrödinger equations. For example, in the domain of molecular quantum physics, spectral and pseudospectral methods are the building […]
The classification of states of quantum lattice systems is a well -defined mathematical endeavour which started with the discovery of the quantum Hall effect. In this talk, I will discuss the topology of a simple cl ass, the so-called invertible states, which I will define. It is by definition a connected set, and we shall […]
The stability of topological indices of condensed matter systems in the p resence of interactions is not expected to hold universally. In this colloquium, I will first discuss the mathematical setup of the classification of interacting phases. I will then focus on a new Z_2 – valued index for time-reversal invariant interacting fermions on infinite […]
The operator-algebraic description of quantum mechanical systems can be used to mathematically deal with systems, where the usual Hilbert space description becomes inconvenient or breaks down. In this talk I will discuss how, using this formalism, one can describe a system of interacting lattice fermions directly in the infinite-volume limit. This will allow us to […]
For many problems in quantum mechanics it is important to have a good grasp of the operators modelling the system. The landscape function was introduced as a tool to compute spectral quantities of such operators. Numerical experiments led to many conjectures on what the landscape function should be able to capture. In this talk I […]
We study the contact process on scale-free inhomogeneous random graphs evolving according to a stationary dynamics, where the neighbourhood of each vertex is updated with a rate depending on its strength. We identify the full phase diagram of metastability exponents in dependence on the tail exponent of the degree distribution and the rate of updating. […]
We prove a thermodynamically stable Lieb-Robinson bound (LRB) for bosons with long-range interaction on lattices. The condition is that the initial state admits (i) uniformly bounded density from above and (ii) no particle in the region separating the initial supports of the observables entering the LRB. Furthermore, if the initial state has controlled density from […]
Fault-tolerant protocols and quantum error correction (QEC) are essential to building reliable quantum computers from imperfect components that are vulnerable to errors. Optimizing the resource and time overheads needed to implement QEC is one of the most pressing challenges that will facilitate a transition from NISQ to the fault tolerance era. In this talk, I […]
We introduce a new approach to justify mean-field limits for first- and second-order particle systems with singular interactions. It is based on a duality approach combined with the analysis of linearized dual correlations, and it allows to cover for the first time arbitrary square-integrable interaction forces at possibly vanishing temperature. This is joint work with […]
In Bernoulli percolation, the incipient infinite cluster (IIC) is a version of the “open cluster of the origin at criticality conditioned to be infinite”. Since this event should have probability 0 on Zd, the IIC is constructed via a limiting procedure. For d > 6, several constructions have been given and shown to produce the […]
Regularisation by noise in the context of stochastic differential equations (SDEs) with coefficients of low regularity, known as singular SDEs, refers to the beneficial effect produced by noise so that the singularity from the coefficients is smoothed out yielding well-behaved equations. Kinetic SDEs, also sometimes called second order SDEs, as one typical type of stochastic […]
In this seminar, we will discuss the estimation of group action using the non-commutative Fourier transform. We’ll explore an interesting relationship between the non-commutative Fourier transform and this estimation problem. Next, we’ll optimize our estimation method by leveraging this connection under various conditions, including energy constraints. Finally, we’ll apply the obtained results to uncertainty relations […]
In this talk, I will try to motivate the subject of constructive quantum field theory which was born in the 70’s as an attempt to give rigorous constructions of quantum field theory models on Minkowski space and also describe scaling limits of spin systems. We will focus on some examples which give a taste of […]
The talk reviews the state of affairs in the mathematically rigorous foundations of the special-relativistic Vlasov-Maxwell equations. The progress is made possible by a recent formulation of a well-posed Lorentz co-variant initial value problem for the joint evolution of charged point particles and their electromagnetic Maxwell fields in a Bopp–Land ́e–Thomas–Podolsky (BLTP) vacuum.
In the setting of lattice gauge theories with finite (possibly non-Abelian) gauge groups at weak coupling, we prove exponential decay of correlations for a wide class of gauge invariant functions, which in particular includes arbitrary functions of Wilson loop observables. Based on joint work with Sky Cao.
Although many-body quantum simulations have greatly benefited from high-perfor- mance computing facilities, large molecular systems continue to pose formidable challenges. Mixed quantum-classical models, such as Born-Oppenheimer molecular dynamics or Ehren- fest dynamics, have been proposed to overcome the computational costs of fully quantum ap- proaches. However, current mixed quantum-classical models typically suffer from long- standing […]
The Fröhlich polaron models a charged quantum particle interactiong with a polar cystal. Since the moving particle has to drag along a ‘cloud’ of polarization, it appears heavier than it would be without the interaction. An old conjecture of Landau and Pekar states that this so-called effective mass scales as the fourth power of the […]
It is known through classical works of Kac, Salem, Zygmund, Erdös and Gal that lacunary sums behave in several ways like sums of independent random variables, satisfying, for instance, a central limit theorem or a law of the iterated logarithm. We present some recent results on their large deviation behavior, which show that on this […]
In this talk – based on a joint work with J. Lampart, N. Leopold, and D. Mitrouskas – I will talk about the mean field limit of the renormalized Nelson model, in which a large number of bosonic particles is weakly coupled with a large number of coherent excitations of the scalar field. We prove […]
The meeting of the junior members of TRR 352 took place from December 13-15, 2023, at the Haus der bayerischen Landwirtschaft in Herrsching/Ammersee. Program Titles & Abstracts Speakers: Alberto Brollo (TUM) Florian Haberberger (LMU Munich) Paul Hege (Tübingen University) Viet Hoang (Tübingen University) Zahra Khanian (TUM) Peter Madsen (LMU Munich) Larry Read (LMU Munich) Diane Saint Aubin (Zurich […]
We consider a random walk in a truncated cone K_N , which is obtained by slicing cone K by a hyperplane at a growing level of order N. We study the behaviour of the Green function in this truncated cone as N increases. Using these results we also obtain the asymptotic behaviour of the harmonic […]
In this talk, we investigate random convex interfaces which are generated as convex hulls of random point sets. We are interested in their asymptotic behavior when the size of the input goes to infinity. In a first part, we mainly identify average and maximal fluctuations in the radial and longitudinal directions through precise convergence results. […]
Interacting Bose gas at zero temperature is often described by the Bogoliubov approximation. It involves quasiparticles, called phonons, with a rather curious dispersion relation responsible for superfluidity. The Fermi Golden Rule predicts that the lifetime of phonons is proportional to the 5th inverse power of momentum. This was first computed by Beliaev and goes under […]
In 2001 Bolthausen, den Hollander and van den Berg obtained the asymptotics of the probability that the volume of a Wiener sausage at time t is smaller than expected by a fixed muliplicative constant. This asymptotics was given by a variational formula and they conjectured that the best strategy to achieve such a large deviation […]
The Abelian sandpile model on a graph G is a Markov chain whose state space is a subset of the set of functions with integer values defined on the vertices of G. The set of recurrent states of this Markov chain is called the sandpile group and the Abelian sandpile model can be then viewed […]
First CRC meeting in the Bavarian Alps From October 11 to 15, 2023, the kick-off meeting of our CRC took place in Farchant near Garmisch. Around 60 participants came together to spend a few days in the beautiful surroundings of the Bavarian Alps. The project leaders had the opportunity to present their projects and report […]
The KPZ fixed point is conjectured to be the universal space-time scaling limit of the models belonging to the KPZ universality class and it was rigorously constructed by Matetski, Quastel and Remenik (Acta Math., 2021) as a scaling limit of TASEP (Totally Asymmetric Simple Exclusion Process) with arbitrary initial configuration. We set up a new, […]
We introduce a currently hot topic in probability theory, the theory of scaling limits for random fields of gradients in all dimensions. The random fields are a class of model systems arising in the studies of random interfaces, random geometry, Euclidean field theory, the theory of regularity structures, and elasticity theory. After explaining how non-convex […]
I will present a new approach to finding the asymptotic states of Nonlinear Wave Equations with general initial data. In particular, we show for a large class of equations, that all asymptotic states are linear combinations of free wave, localized parts (solitons, breathers..) and a possibility of self-similar solutions as well in some cases. These […]
The homogeneous electron gas (jellium) where electrons interact with each other and with a positive background charge is one of the simplest model system in condensed matter physics. Still, the precise determination of the zero temperature phase diagram remains challenging. In the talk I will review some recent progress from a computational perspective concerning the […]
We consider the ground state of a Bose gas of N particles on the three-dimensional unit torus in the mean-field regime that is known to exhibit Bose-Einstein condensation. Bounded one-particle operators with law given through the interacting Bose gas’ ground state correspond to dependent random variables. We prove that in the limit N to infinity, […]
In this talk, we describe the kinetic equation for the Bogoliubov excitations of the Bose-Einstein Condensate. We find three collisional processes: One of them describes the 1↔2 interactions between the condensate and the excited atoms. The other two describe the 2↔2 and 1↔3 interactions between the excited atoms themselves. This is a joint work with […]
Propagation and generation of “chaos” is an important ingredient in rigorous control of applicability of kinetic theory, in general. Chaos can here be understood as sufficient statistical independence of random variables related to the “kinetic” obser- vables of the system. Cumulant hierarchy of these random variables thus often gives a way of controlling the evolution […]
We consider Markovian open quantum dynamics (MOQD) in continuous space. We show that, up to small-probability tails, the supports of quantum states evolving under such dynamics propagate with finite speed in any finite-energy subspace. More precisely, we prove that if the initial quantum state is localized in space, then any finite-energy part of the solution […]
In this talk I will describe the vacuum sector of the Weinberg-Salam (WS) model of electroweak forces. In the vacuum sector the WS model yields the U(2)-Yang-Mills-Higgs equations. We show that at large constant magnetic fields the translational symmetry of the equations is broken spontaneously. Namely, there are solutions, which in the plane orthogonal to […]
We consider two-dimensional unbounded magnetic Dirac operators, either defined on the whole plane, or with infinite mass boundary conditions on a half-plane. Our main results use techniques from elliptic PDEs and integral operators, while their topological consequences are presented as corollaries of some more general identities involving magnetic derivatives of local traces of fast decaying […]
Unraveling the origin of unconventional superconductivity is one of the driving forces behind quantum simulations with Fermions in optical lattices. In these strongly correlated materials, the necessary pairing of charge carriers is often assumed to be related to the interplay of antiferromagnetic correlations and dopant motion. Despite impressive recent progress in the numerical treatment of […]
We consider the infrared problem in translation-invariant Nelson-type models describing a single quantum mechanical particle linearly coupled to a field of scalar bosons at fixed total momentum. Physical examples include the non- and semi-relativistic Nelson models. If the bosons are massless, then the model is infrared divergent and the infimum of the spectrum is not […]
The correspondence principle, as stated by Niels Bohr in 1923, is at the root of the traditional results in semi-classical analysis. It offers a natural insight into the world of semi- classical pseudodifferential operators, Egorov Theorem, coherent states, Wigner measures, etc… The aim of this talk will be to present this general setting and explain […]
Schrödinger’s equation is a beautiful piece of mathematics. It f its on just one line and is supposed to accurately describe the behavior of most atoms and molecules of our world. But it is essentially impossible to simulate accurately, due to its very high dimensionality. In this talk I will explain how physicists and chemists […]
Recent progress in the development of quantum technologies has enabled the direct investigation of dynamics of increasingly complex quantum many-body systems. This motivates the study of the complexity of classical algorithms for this problem in order to benchmark quantum simulators and to delineate the regime of quantum advantage. Here we present classical algorithms for approximating […]
A mathematical understanding of the mechanism of metallic ferromagnetism still needs to be completed. In this talk, the following three fundamental theorems on metallic ferromagnetism will be first outlined: the Marshall-Lieb-Mattis theorem, the Lieb theorem, and the stability theorem of Lieb ferrimagnetism. Next, I will outline a mathematical framework within which these theorems can be […]
We introduce a classical algorithm to approximate the free energy of local, translation-invariant, one-dimensional quantum systems in the thermodynamic limit of infinite chain size. While the ground state problem (i.e., the free energy at temperature T=0) for these systems is expected to be computationally hard even for quantum computers, our algorithm runs for any fixed […]
In this talk, I will describe some work in progress about relating the low-lying spectrum of the Davies Lindbladian for qLDPC codes to that of Glauber dynamics on a classical model.
Calderbank-Shor-Steane (CSS) codes, such as the toric code, are a widely studied class of quantum error-correcting codes. Understanding the thermalization time of these systems is important not only for error correction but also for applications like Gibbs sampling. We show that CSS codes on a lattice satisfy a modified logarithmic Sobolev inequality and thus thermalize […]
Registration for the TRR 352 Winter School on Mathematical Physics is now open! The event will take place from March 9-13, 2026, at the Georg-von-Vollmar-Akademie in Kochel am See. Invited speakers: Emanuela L. Giacomelli (University of Milan) Vojkan Jaksic (Politecnico di Milano) Benjamin Schlein (University of Zurich) Katharina Schratz (Sorbonne University) Participation is free of […]
A gas of interacting Bosons can be represented using an ensemble of stochastic diffusions – a Brownian loop soup. In this talk, we review the construction of this Feynman representation, its representation of Free Energy and the 1-PRDM. We also introduce some results from the literature in the dilute and other regimes and state some […]
Describing the long-time dynamical behaviour of quantum systems is a long-standing open problem. When the coupling constant \lambda of the interaction is small, the dynamics of the system up to kinetic time t \sim \lambda^{-2} is conjectured to be effectively governed by the Boltzmann-Nordheim kinetic equation. In this talk, I will present a result on […]
We consider a class of Unitary Quantum Walks on arbitrary graphs, parameterized by a family of scattering matrices. After explaining that these Scattering Quantum Walks encompass several known Quantum Walks, we further introduce two classes of Scattering Open Quantum Walks on arbitrary graphs based on that construction, whose asymptotic states we discuss.
We study the dynamical density and current responses of a class of non-interacting, one-dimensional gapless lattice Fermi systems subjected to density-type perturbations slowly varying in space and time, in the infinite-volume and zero-temperature limit. In addition, we analyse the edge density and current responses for quantum Hall lattice systems defined on a cylindrical geometry. We […]
Schedule: 14:30 Welcome 15:00 Talk by Nicos Georgiou (Sussex) 16:00 Coffee break 16:30 Talk by Christian Kühn (TU Munich) 18:00 Option for common dinner Titles and abstracts: Nicos Georgiou: Mean-field limit and parameter estimation for contagion dynamics on higher-order structures Classical models of contagion epidemics have graph based representations where the nodes represent the population and infections occur […]
With the proof of Widom’s conjecture giving new insights on the entanglement properties of the non-relativistic free Fermi gas, it is a natural question whether this situation extends to the relativistic case, where the single-particle Hamiltonian is given by the free Dirac operator. In this talk I give a brief introduction to both the Widom-Sobolev […]
The microscopic laws of quantum mechanics give rise to some of the most fascinating macroscopic phenomena in physics, such as superfluidity and superconductivity. The theoretical description of such phenomena is intimately linked with beautiful mathematics in fields like functional analysis, partial differential equations, or probability. This conference brings together internationally recognised experts in mathematical physics […]
We present the relativistic quantum physics model hierarchy from Dirac-Maxwell to Vlasov/Euler-Poisson that models fast moving charges and their self-consistent electro-magnetic field. Our main interest is (asymptotic) analysis of these nonlinear time-dependent PDE, with focus on the Pauli-Poisswell/Darwin system which is the consistent model at first/second order in 1/c (c = speed of light) that […]
November 17-21, 2025 at Haus Chiemgau, Teisendorf The meeting will begin on Monday at 3 pm and conclude on Friday after lunch. Speakers: Lennart Becker (UT) Yoon Jun Chan (UA) Eddy de Leon (TUM) Jorge Acuña Flores (UT) Paul Pfeiffer (LMU) Sebstian Stengele (TUM) Cornelia Vogel (LMU) Program: November 20: Full-Day Organizers: Florian Haberberger (LMU […]
Repeated compositions of quantum channels arise naturally in many places across quantum: they arise, for example, in the transfer operator approach to quantum spin chains, and also in the repeated interactions description of open quantum dynamics. Assuming the system of interest is subject to some amount of disorder, it is therefore natural that one consider […]
The CRC’s Annual Retreat took place from September 28 to October 1, 2025, at the Georg-von-Vollmar-Akademie in Kochel am See. The retreat was fully dedicated to preparing the application for the next funding period. Every project that will be continued or newly participating was introduced by a project leader. On Wednesday morning, the Best Paper Awards were announced. […]
Quantum mechanics, now about a century old, is a very successful physical theory of matter on a small scale. From its first description until today, it has surprised scientists and laypersons alike by the strange behaviour it attributes to particles, atoms, and molecules. This behaviour can be characterized by the keywords Uncertainty, Superposition, and Entanglement. […]
This talk will provide a basic introduction to the three dimensional Dirac equation that describes an electron interacting with a magnetic field. Over the years a lot of work has gone into constructing zero energy solutions, also known as zero modes, for said equation. In this talk I will explain the importance of zero modes […]
I will review the mathematical analysis behind two classes of new exciting materials: Twisted bilayer graphene (TBG) and twisted semiconductors (TMDs) with an emphasis on their mathematical properties and differences. If time permits I will discuss results on these models under disorder. Joint work with Maciej Zworski, Izak Oltman, Martin Vogel, and Mengxuan Yang.
Conventional quantum tomography assumes a high degree of control over the system in question in order to measure many observables. On the other hand, a classical dynamical system may be reconstructed from a time series of a single observable by means of delay embeddings. Inspired by this, we investigate the possibility of tomography of a […]
Evolutionary deep neural networks have emerged as a rapidly growing field of research. This talk discusses numerical integrators for such and other classes of nonlinear parametrizations u(t) = Φ(θ(t)) where the evolving parameters θ(t) are to be computed. The primary focus is on tackling the challenges posed by the combination of stiff evolution problems and […]
Thanks to their high degree of control and tunability, ultracold atomic gases provide a rich platform for the study of quantum many-body effects. Ultracold gases of highly magnetic atoms exhibit unique interaction properties that lead to striking behaviors, both at the mean-field level and beyond . A decade ago, a universal stabilization mechanism driven by […]
We explore a connection between a weak topology on spaces of probability measures, a classical combinatorial problem in matching, and numerical schemes for the solution of PDEs by neural networks.
We prove a fluid limit for the coarsening phase of the condensing zero-range process on a finite number of sites. When time and occupation per site are linearly rescaled by the total number of particles, the evolution of the process is described by a piecewise linear trajectory in the simplex indexed by the sites. The […]
On Thursday, May 08, 2025, at 12:15 pm, Prof. Dr. Shi Jin (Shanghai Jiao Tong University) will give a talk on “Quantum Computation of partial differential equations and related problems” at TUM, Boltzmannstr. 3, 85748 Garching Forschungszentrum, room 03.06.011. Abstract: Quantum computers have the potential to gain algebraic and even up to exponential speed up compared with its classical counterparts, and can lead to […]
Quantum computing with discrete variable (DV, qubit) hardware is approaching the large scales necessary for computations beyond the reach of classical computers. Separately, hardware containing native continuous-variable (CV, oscillator) systems has received attention as an alternative approach, yet the universal control of such systems is non-trivial. In this talk, I will highlight novel quantum algorithms, […]
In this talk we consider discrete Gaussian free fields with ergodic random conductances on ℤd, d ≥ 2, where the conductances are possibly unbounded but satisfy a moment condition. As our main result, we show that, for almost every realisation of the environment, the rescaled field converges in law towards a continuous Gaussian field. We […]
Let X be a simple random walk in Znd with d≥3 and let tcov be the expected time it takes for X to visit all vertices of the torus. In joint work with Prévost and Rodriguez we study the set Lα of points that have not been visited by time αtcov and prove that it exhibits a phase transition: there exists α∗ so that for all α>α∗ and all ϵ>0 there […]
Program: 11:00 am – Dr. Larry Read, LMU München: Proof of the oval conjecture (Part 1) lunch 1:30 pm – Matthias Baur, M.Sc., Universität Stuttgart: Proof of the oval conjecture (Part 2) coffee and discussion
In relativity, nothing can travel faster than the speed of light. But there are often emergent speed limits, such as the speed of sound, that limit practical information transfer. In quantum many-body lattice models, the existence of this emergent speed limit was first proved by Lieb and Robinson in 1972. Over 50 years later, their […]
In this talk, we address the full discretization of Friedrichs’ systems with a two-field structure, such as Maxwell’s equations or the acoustic wave equation in div-grad form. We follow a method of lines approach, where we first discretize in space via the discontinuous Galerkin method. Subsequently, we consider different second-order schemes for time integration, namely […]
State-sum constructions have numerous applications in both mathematics and physics. In mathematics, they yield invariants for knots and manifolds and serve as a powerful organizing principle in representation theory. To illustrate this principle, we discuss equivariant Frobenius-Schur indicators. In the context of physics, we explain how state-sum models offer a conceptual framework for tensor network […]
In this talk, we consider irreversible translation-invariant interacting particle systems on the d-dimensional hypercubic lattice with finite local state space, which admit at least one Gibbs measure as a time-stationary measure. Under some mild degeneracy conditions on the rates and the specification we prove, that zero relative entropy loss of a translation-invariant measure implies, that […]
We consider a system of closed random walk trajectories interacting by mutual repulsion. This probabilistic model is motivated by its connections to statistical mechanics models, such as the Bose gas, the double dimer model, or the spin O(N) model. We prove the occurrence of macroscopic loops in dimension d>2 (joint with A. Quitmann, 2022) and […]
It is a remarkable property of random matrices, that their resolvents tend to concentrate around a deterministic matrix as the dimension of the matrix tends to infinity, even for a small imaginary part of the involved spectral parameter. These estimates are called local laws and they are the cornerstone in most of the recent results […]
January 21-24, 2025 at Christkönigshaus, Stuttgart Speakers: Jonas Peteranderl (LMU) Sara Terveer (LMU) François Visconti (LMU) Paul Gondolf (Tub) Yifei Li (Tub) Tom Wessel (Tub) Pablo Costa Rico (TUM) Corlie Rall (TUM) Anouar Kouraich (TUM) Beatriz Dias (TUM) Yifan Jia (Copenhagen) Program: Organizers: Alberto Brollo (TUM) Emanuela Giacomelli (LMU Munich) Florian […]
Fix some graph or uniform hypergraph F and then consider the following simple process: start with a large complete (hyper)graph Kn on n vertices and iteratively remove (the edge set of) copies of F as long as possible; each selection is made uniformly among all present copies of F at that time. This process is […]
Phase transitions are natural phenomena in which a small change in an external parameter, like temperature or pressure, causes a dramatic change in the qualitative structure of the object. To study this, many scientists (such as Nobel laureates Pauling and Flory) proposed the abstract framework of lattice models. The focus of this talk is on […]
Of great interest in plasma physics is to determine whether excited charged particles in a non-equilibrium state will relax to neutrality or transition to a nontrivial coherent state. Due to the long range interaction between particles, the self-consistent generating electric field oscillates in time and disperses in space like a Klein-Gordon wave, known in the […]
Bardeen-Cooper-Schrieffer (BCS) theory is a successful model of superconductivity. In this talk, I will begin by providing an overview of how BCS theory connects with other models of superconductivity, highlighting major open questions and recent developments in the field. Second, I will explain recent results on the critical temperature in the presence of a boundary […]
Quantum systems typically reach thermal equilibrium when in weak contact with a large external bath. Understanding the speed of this thermalisation is a challenging problem, especially in the context of quantum many-body systems where direct calculations are intractable. The usual way of bounding the speed of this process is by estimating the spectral gap of […]
Competitive games of complete information famously always have Nash equilibria, but it is well-known that correlation (“advice”) can yield new equilibria, sometimes with preferable collective properties (social welfare, fairness, …). While it is known that quantum correlations in the form of entanglement do not imply further correlated equilibria, this situation changes when going to so-called […]
Quantum Signal Processing (QSP) is an algorithmic process by which one represents a signal $f: \to (-1,1)$ as the upper left entry of a product of $SU(2)$ matrices parametrized by the input variable $x \in $ and some ”phase factors” $\{\psi_k\}_{k \geq 0}$ depending on $f$. We show that, after a change of variables, QSP […]
Quantum walks (QWs) can be viewed as quantum analogs of classical random walks. Mathematically, a QW is described as a unitary, local operator acting on a grid and can be written as a product of shift and coin operators. We highlight differences to classical random walks and stress their connection to quantum algorithms (see Grover’s […]
We study the generalised Lloyd model, that is, a random Schrödinger operator on the lattice Zd of the form H = −∆ + λV, λ > 0, with Vi = ∑j Tij Wj where Wj ∼ Cauchy(0, 1) are iid random variables. If all coeffi- cients Tij are non-negative one can find an exact formula […]
The CRC’s Annual Retreat was held from October 6–10, 2024, at the Explorer Hotel Garmisch in Farchant. Nearly 60 members, including both established researchers and early-career scientists, gathered for a productive few days. Each morning, project teams presented brief talks and posters, providing valuable insights into their research. The afternoons featured engaging discussions, and participants […]
This talk will provide a partial overview of how to model molecular observables and spectral responses. We shall start with the essential quantum mechanical concepts and formalisms that are used in theoretical chemistry and molecular physics. This will be followed by an illustration of the tools that are involved in numerical simulations in this context.
The dilute Curie-Weiss model is the Ising model on a (dense) Erdös-Rényi graph G(N,p). It was introduced by Bovier and Gayrard in 1990s. There the authors showed that on the level of laws of large numbers the magnetization as well as the free energy behave as they do in the usual Curie-Weiss model (i.e. mean-field […]
Branching Brownian motion, branching random walks, and the F-KPP equation have been the subject of intensive research during the last couple of decades. By means of Feynman-Kac and McKean formulas, the understanding of the maximal particles of the former two Markov processes is related to insights into the position of the front of the solution […]
(Pseudo)spectral methods are popular for solving a wide variety of differential equations and generic optimization problems. Due to favourable approximation properties, such as rapid convergence for smooth functions, they are particularly popular and effective for solving time-independent Schrödinger equations. For example, in the domain of molecular quantum physics, spectral and pseudospectral methods are the building […]
The classification of states of quantum lattice systems is a well -defined mathematical endeavour which started with the discovery of the quantum Hall effect. In this talk, I will discuss the topology of a simple cl ass, the so-called invertible states, which I will define. It is by definition a connected set, and we shall […]
The stability of topological indices of condensed matter systems in the p resence of interactions is not expected to hold universally. In this colloquium, I will first discuss the mathematical setup of the classification of interacting phases. I will then focus on a new Z_2 – valued index for time-reversal invariant interacting fermions on infinite […]
The operator-algebraic description of quantum mechanical systems can be used to mathematically deal with systems, where the usual Hilbert space description becomes inconvenient or breaks down. In this talk I will discuss how, using this formalism, one can describe a system of interacting lattice fermions directly in the infinite-volume limit. This will allow us to […]
For many problems in quantum mechanics it is important to have a good grasp of the operators modelling the system. The landscape function was introduced as a tool to compute spectral quantities of such operators. Numerical experiments led to many conjectures on what the landscape function should be able to capture. In this talk I […]
We study the contact process on scale-free inhomogeneous random graphs evolving according to a stationary dynamics, where the neighbourhood of each vertex is updated with a rate depending on its strength. We identify the full phase diagram of metastability exponents in dependence on the tail exponent of the degree distribution and the rate of updating. […]
We prove a thermodynamically stable Lieb-Robinson bound (LRB) for bosons with long-range interaction on lattices. The condition is that the initial state admits (i) uniformly bounded density from above and (ii) no particle in the region separating the initial supports of the observables entering the LRB. Furthermore, if the initial state has controlled density from […]
Fault-tolerant protocols and quantum error correction (QEC) are essential to building reliable quantum computers from imperfect components that are vulnerable to errors. Optimizing the resource and time overheads needed to implement QEC is one of the most pressing challenges that will facilitate a transition from NISQ to the fault tolerance era. In this talk, I […]
We introduce a new approach to justify mean-field limits for first- and second-order particle systems with singular interactions. It is based on a duality approach combined with the analysis of linearized dual correlations, and it allows to cover for the first time arbitrary square-integrable interaction forces at possibly vanishing temperature. This is joint work with […]
In Bernoulli percolation, the incipient infinite cluster (IIC) is a version of the “open cluster of the origin at criticality conditioned to be infinite”. Since this event should have probability 0 on Zd, the IIC is constructed via a limiting procedure. For d > 6, several constructions have been given and shown to produce the […]
Regularisation by noise in the context of stochastic differential equations (SDEs) with coefficients of low regularity, known as singular SDEs, refers to the beneficial effect produced by noise so that the singularity from the coefficients is smoothed out yielding well-behaved equations. Kinetic SDEs, also sometimes called second order SDEs, as one typical type of stochastic […]
In this seminar, we will discuss the estimation of group action using the non-commutative Fourier transform. We’ll explore an interesting relationship between the non-commutative Fourier transform and this estimation problem. Next, we’ll optimize our estimation method by leveraging this connection under various conditions, including energy constraints. Finally, we’ll apply the obtained results to uncertainty relations […]
In this talk, I will try to motivate the subject of constructive quantum field theory which was born in the 70’s as an attempt to give rigorous constructions of quantum field theory models on Minkowski space and also describe scaling limits of spin systems. We will focus on some examples which give a taste of […]
The talk reviews the state of affairs in the mathematically rigorous foundations of the special-relativistic Vlasov-Maxwell equations. The progress is made possible by a recent formulation of a well-posed Lorentz co-variant initial value problem for the joint evolution of charged point particles and their electromagnetic Maxwell fields in a Bopp–Land ́e–Thomas–Podolsky (BLTP) vacuum.
In the setting of lattice gauge theories with finite (possibly non-Abelian) gauge groups at weak coupling, we prove exponential decay of correlations for a wide class of gauge invariant functions, which in particular includes arbitrary functions of Wilson loop observables. Based on joint work with Sky Cao.
Although many-body quantum simulations have greatly benefited from high-perfor- mance computing facilities, large molecular systems continue to pose formidable challenges. Mixed quantum-classical models, such as Born-Oppenheimer molecular dynamics or Ehren- fest dynamics, have been proposed to overcome the computational costs of fully quantum ap- proaches. However, current mixed quantum-classical models typically suffer from long- standing […]
The Fröhlich polaron models a charged quantum particle interactiong with a polar cystal. Since the moving particle has to drag along a ‘cloud’ of polarization, it appears heavier than it would be without the interaction. An old conjecture of Landau and Pekar states that this so-called effective mass scales as the fourth power of the […]
It is known through classical works of Kac, Salem, Zygmund, Erdös and Gal that lacunary sums behave in several ways like sums of independent random variables, satisfying, for instance, a central limit theorem or a law of the iterated logarithm. We present some recent results on their large deviation behavior, which show that on this […]
In this talk – based on a joint work with J. Lampart, N. Leopold, and D. Mitrouskas – I will talk about the mean field limit of the renormalized Nelson model, in which a large number of bosonic particles is weakly coupled with a large number of coherent excitations of the scalar field. We prove […]
The meeting of the junior members of TRR 352 took place from December 13-15, 2023, at the Haus der bayerischen Landwirtschaft in Herrsching/Ammersee. Program Titles & Abstracts Speakers: Alberto Brollo (TUM) Florian Haberberger (LMU Munich) Paul Hege (Tübingen University) Viet Hoang (Tübingen University) Zahra Khanian (TUM) Peter Madsen (LMU Munich) Larry Read (LMU Munich) Diane Saint Aubin (Zurich […]
We consider a random walk in a truncated cone K_N , which is obtained by slicing cone K by a hyperplane at a growing level of order N. We study the behaviour of the Green function in this truncated cone as N increases. Using these results we also obtain the asymptotic behaviour of the harmonic […]
In this talk, we investigate random convex interfaces which are generated as convex hulls of random point sets. We are interested in their asymptotic behavior when the size of the input goes to infinity. In a first part, we mainly identify average and maximal fluctuations in the radial and longitudinal directions through precise convergence results. […]
Interacting Bose gas at zero temperature is often described by the Bogoliubov approximation. It involves quasiparticles, called phonons, with a rather curious dispersion relation responsible for superfluidity. The Fermi Golden Rule predicts that the lifetime of phonons is proportional to the 5th inverse power of momentum. This was first computed by Beliaev and goes under […]
In 2001 Bolthausen, den Hollander and van den Berg obtained the asymptotics of the probability that the volume of a Wiener sausage at time t is smaller than expected by a fixed muliplicative constant. This asymptotics was given by a variational formula and they conjectured that the best strategy to achieve such a large deviation […]
The Abelian sandpile model on a graph G is a Markov chain whose state space is a subset of the set of functions with integer values defined on the vertices of G. The set of recurrent states of this Markov chain is called the sandpile group and the Abelian sandpile model can be then viewed […]
First CRC meeting in the Bavarian Alps From October 11 to 15, 2023, the kick-off meeting of our CRC took place in Farchant near Garmisch. Around 60 participants came together to spend a few days in the beautiful surroundings of the Bavarian Alps. The project leaders had the opportunity to present their projects and report […]
The KPZ fixed point is conjectured to be the universal space-time scaling limit of the models belonging to the KPZ universality class and it was rigorously constructed by Matetski, Quastel and Remenik (Acta Math., 2021) as a scaling limit of TASEP (Totally Asymmetric Simple Exclusion Process) with arbitrary initial configuration. We set up a new, […]
We introduce a currently hot topic in probability theory, the theory of scaling limits for random fields of gradients in all dimensions. The random fields are a class of model systems arising in the studies of random interfaces, random geometry, Euclidean field theory, the theory of regularity structures, and elasticity theory. After explaining how non-convex […]
I will present a new approach to finding the asymptotic states of Nonlinear Wave Equations with general initial data. In particular, we show for a large class of equations, that all asymptotic states are linear combinations of free wave, localized parts (solitons, breathers..) and a possibility of self-similar solutions as well in some cases. These […]
The homogeneous electron gas (jellium) where electrons interact with each other and with a positive background charge is one of the simplest model system in condensed matter physics. Still, the precise determination of the zero temperature phase diagram remains challenging. In the talk I will review some recent progress from a computational perspective concerning the […]
We consider the ground state of a Bose gas of N particles on the three-dimensional unit torus in the mean-field regime that is known to exhibit Bose-Einstein condensation. Bounded one-particle operators with law given through the interacting Bose gas’ ground state correspond to dependent random variables. We prove that in the limit N to infinity, […]
In this talk, we describe the kinetic equation for the Bogoliubov excitations of the Bose-Einstein Condensate. We find three collisional processes: One of them describes the 1↔2 interactions between the condensate and the excited atoms. The other two describe the 2↔2 and 1↔3 interactions between the excited atoms themselves. This is a joint work with […]
Propagation and generation of “chaos” is an important ingredient in rigorous control of applicability of kinetic theory, in general. Chaos can here be understood as sufficient statistical independence of random variables related to the “kinetic” obser- vables of the system. Cumulant hierarchy of these random variables thus often gives a way of controlling the evolution […]
We consider Markovian open quantum dynamics (MOQD) in continuous space. We show that, up to small-probability tails, the supports of quantum states evolving under such dynamics propagate with finite speed in any finite-energy subspace. More precisely, we prove that if the initial quantum state is localized in space, then any finite-energy part of the solution […]
In this talk I will describe the vacuum sector of the Weinberg-Salam (WS) model of electroweak forces. In the vacuum sector the WS model yields the U(2)-Yang-Mills-Higgs equations. We show that at large constant magnetic fields the translational symmetry of the equations is broken spontaneously. Namely, there are solutions, which in the plane orthogonal to […]
We consider two-dimensional unbounded magnetic Dirac operators, either defined on the whole plane, or with infinite mass boundary conditions on a half-plane. Our main results use techniques from elliptic PDEs and integral operators, while their topological consequences are presented as corollaries of some more general identities involving magnetic derivatives of local traces of fast decaying […]
Unraveling the origin of unconventional superconductivity is one of the driving forces behind quantum simulations with Fermions in optical lattices. In these strongly correlated materials, the necessary pairing of charge carriers is often assumed to be related to the interplay of antiferromagnetic correlations and dopant motion. Despite impressive recent progress in the numerical treatment of […]
We consider the infrared problem in translation-invariant Nelson-type models describing a single quantum mechanical particle linearly coupled to a field of scalar bosons at fixed total momentum. Physical examples include the non- and semi-relativistic Nelson models. If the bosons are massless, then the model is infrared divergent and the infimum of the spectrum is not […]
The correspondence principle, as stated by Niels Bohr in 1923, is at the root of the traditional results in semi-classical analysis. It offers a natural insight into the world of semi- classical pseudodifferential operators, Egorov Theorem, coherent states, Wigner measures, etc… The aim of this talk will be to present this general setting and explain […]
Schrödinger’s equation is a beautiful piece of mathematics. It f its on just one line and is supposed to accurately describe the behavior of most atoms and molecules of our world. But it is essentially impossible to simulate accurately, due to its very high dimensionality. In this talk I will explain how physicists and chemists […]
Recent progress in the development of quantum technologies has enabled the direct investigation of dynamics of increasingly complex quantum many-body systems. This motivates the study of the complexity of classical algorithms for this problem in order to benchmark quantum simulators and to delineate the regime of quantum advantage. Here we present classical algorithms for approximating […]
A mathematical understanding of the mechanism of metallic ferromagnetism still needs to be completed. In this talk, the following three fundamental theorems on metallic ferromagnetism will be first outlined: the Marshall-Lieb-Mattis theorem, the Lieb theorem, and the stability theorem of Lieb ferrimagnetism. Next, I will outline a mathematical framework within which these theorems can be […]
We introduce a classical algorithm to approximate the free energy of local, translation-invariant, one-dimensional quantum systems in the thermodynamic limit of infinite chain size. While the ground state problem (i.e., the free energy at temperature T=0) for these systems is expected to be computationally hard even for quantum computers, our algorithm runs for any fixed […]
