Estimation of group action via non-commutative Fourier transform with special functions
2024-05-03 14:00 (Europe/Berlin) | Room HS3 (MI 00.06.011), Boltzmannstr. 3, Garching Forschungszentrum, 85748, Germany
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 related to compact groups.
Throughout this discussion, we’ll highlight the significance of several special functions in this topic.

Regularization by noise and approximations of singular kinetic SDEs
2024-05-03 15:00 | University of Augsburg, Room 2004 (L1), Universitätsstraße 14, Augsburg, 86159
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 Hamiltonian systems, describe the motion of a particle perturbed by some random external force. The difference of comparing it with usual SDEs is that the noise of the space position vanishes and only appears in the direction of velocity, hence less noise gets involved in the system. In this talk we will discuss about the regularization effect by the degenerate noise for the singular kinetic SDEs from numerical approximation and also particles approximation view point.

Robust construction of the high-dimensional incipient infinite cluster
2024-05-03 15:00 | University of Augsburg, Room 2004 (L1), Universitätsstraße 14, Augsburg, 86159
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 same object, but many natural limiting procedures remain unexplored. For instance, it is an open question whether conditioning on {0 is connected to the boundary of [-n, n]d} produces the IIC as n tends to infinity. We answer this question in the affirmative as a corollary of our theorem, which roughly says “conditioning on any long open connection produces the IIC”, and whose proof does not directly use lace expansion analysis.

Spectral theory for systems of ODEs with rough coefficients
2024-05-06 16:00 | Room B 134, Theresienstr. 39, Munich, 80333, Germany

A duality method for mean-field limits with singular interactions
2024-05-16 16:00 | Seminar room C4H33, An der Morgenstelle 10, Tübingen, 72076, Germany
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 D.Bresch and P.E.Jabin.

Analogue quantum simulation of open quantum systems with accuracy guarantees
2024-06-04 16:15 | Room 5608.02.020 (Seminarraum (M11)), Boltzmannstr. 3, Garching b. München, 85748, Germany

3rd IST Austria Summer School in Analysis and Mathematical Physics
2024-06-10 00:00 - 2024-06-14 23:59 | ISTA, Am Campus 1, Klosterneuburg, 3400, Austria

Reducing the overhead of quantum error correction
2024-06-10 12:00 | Room 5502.01.250 (Hörsaal), Boltzmannstr. 15, Garching b. München, 85748, Germany
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 will discuss two intriguing ideas that can significantly reduce these overheads. The first idea, erasure qubits, relies on an efficient conversion of the dominant noise into erasure errors at known locations, greatly enhancing the performance of QEC protocols. The second idea, single-shot QEC, guarantees that even in the presence of measurement errors one can perform reliable QEC without repeating measurements, incurring only constant time overhead.

On Lieb-Robinson bounds for long-range interacting bosons
2024-06-20 16:00 | Room C3N14, Auf der Morgenstelle 10, Tübingen, 72076, Germany
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 both above and below, then the validity threshold for decay rate of the hopping terms can be improved to $alpha > d+ 2$. The proof is based on the weak LRBs and the thermodynamically stable bounds on particle transport obtained in recent joint works with Lemm, Rubiliani, and Sigal.

Metastability of the contact process on evolving scale-free networks
2024-07-08 15:00 | Room 8101.02.110 (Seminarraum), Parkring 11-13, Garching b. München, 85748, Germany
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.
The talk is based on joint work with Emmanuel Jacob (Lyon) and Amitai Linker (Santiago de Chile).

What is the landscape function?
2024-07-09 14:00 | Room 5610.EG.011 (CIT Sitzungsraum 1), Boltzmannstr. 3, Garching b. München, 85748, Germany
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 will give an introduction to the topic and provide an overview of the progress made in the last decade.

Algebraic description of infinite-volume lattice fermions
2024-07-09 14:00 | Room 5610.EG.011 (CIT Sitzungsraum 1), Boltzmannstr. 3, Garching b. München, 85748, Germany
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 formulate and analyse properties of the bulk of the system, such as the bulk Hall conductivity.

A new bulk Z_2 invariant for interacting phases
2024-07-09 16:15 | Room 5610.EG.011 (CIT Sitzungsraum 1), Boltzmannstr. 3, Garching b. München, 85748, Germany
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 lattices and prove its topological stability. I will show that it generalizes the well -known Fu-Kane-Mele index of topological insulators, thereby proving its stability under large perturbations. This is joint work with Alex Bols and Mahsa Rahnama.

Classifying loops of symmetry-protected states
2024-07-10 16:00 | Room C3N14, Auf der Morgenstelle 10, Tübingen, 72076, Germany
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 explore its further topological properties. Specifically, I will be interested in what can be identified with its fundamental group; Physically, this is about classifying cycles of physical processes, or pumps. I will
present a classification of such loops of invertible state that have a local symmetry, which can be proved to be complete. This is joint work with Wojciech De Roeck, Martin Fraas and Tijl Jappens.

Augmenting Spectral Methods with Normalizing Flows and Application to Computing Molecular Excited States
2024-07-11 12:15 | Room 03.10.011, Boltzmannstr. 3, Garching Forschungszentrum, 85748, Germany
(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 blocks for a variety of variational techniques to solve nuclear Schrödinger equations. Despite their many favourable approximation properties, these methods suffer from the curse of dimensionality and have slow convergence rates for highly-oscillatory functions. This limits their applicability in a wide variety of fields. Moreover, their effectiveness is highly dependent on the initial choice of the basis.
In this talk I propose increasing the expressivity of (pseudo)spectral methods by composing a chosen orthonormal basis with an optimizable measurable mapping. This gives rise to an induced sequence. I characterize necessary and sufficient conditions for this sequence to inherit the completeness of the underlying orthonormal basis. Here, it is shown that the invertibility of the mapping is a necessary condition. Subsequently, I discuss the approximation of Schwartz functions in the linear span of Hermite functions that are composed with invertible mappings. To this end, I derive convergence guarantees and characterise the convergence order. Finally, I show numerical simulations for computing the vibrational spectra of polyatomic molecules. In these simulations, the invertible mapping was modelled using a normalizing flow, i.e., an invertible neural network to augment the expressivity of a given basis. Comparisons against the use of standard bases demonstrate orders-of-magnitude increased accuracy when using normalizing flows.

Branching Brownian motion, branching random walks, and the Fisher-KPP equation in spatially random environment
2024-07-15 15:00 | Room B 349, Theresienstr. 39, Munich, 80333, Germany
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 to the F-KPP equation. We will discuss some recent result on extensions of the above models to spatially random branching rates and random nonlinearities. Interestingly, the introduction of such inhomogeneities leads to a richer and much more nuanced picture when compared to the homogeneous setting.

Fluctuations in the dilute Curie-Weiss model
2024-07-15 15:00 | Room B 349, Theresienstr. 39, Munich, 80333, Germany
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 Ising model). We analyze CLTs for the these quantities and give several critical values for p at which these fluctuations change. This is joint work with Zakhar Kabluchko and Kristina Schubert.

Introduction to Modelling Molecular Observables and Spectral Responses
2024-07-18 12:15 | Room 03.10.011, Boltzmannstr. 3, Garching Forschungszentrum, 85748, Germany
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.

Summer School on Current Topics in Mathematical Physics
2024-07-22 00:00 - 2024-07-26 23:59 | University of Zurich, Rämistrasse 71, Zürich, 8006, Switzerland

Solid Math 2024
2024-07-30 00:00 - 2024-08-01 23:59 | University of Tübingen, Geschwister-Scholl-Platz, Tübingen, 72074, Germany

Annual Retreat
2024-10-06 00:00 - 2024-10-10 23:59 | Explorer Hotel Garmisch, Frickenstraße 22, Farchant, 82490, Germany
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 had the opportunity to explore the beautiful surroundings of the Alps.
On Wednesday morning, we recognized outstanding contributions to our field. M. Christiansen received the award for the best postdoctoral research paper, while D. Sulz and A. Lauritsen were honored for their exceptional PhD research papers.
We appreciate everyone’s participation and look forward to another successful year of research ahead.
Program
Program Annual Retreat 2024

Poster
A1_Meng_Siedentop
A2_Pfeiffer
A3_Chan
A4_Triay
A5_Phan
A6_Lauritsen
A7_Warzel
A8_Lemm
A9_Müller
B1_Schlein
B5_Lasser_Mendl_Schwarze
B6_König
B8_Teufel

Mini-Workshop on Condensed Matter Physics
2024-10-10 00:00 - 2024-10-12 23:59 | Explorer Hotel Garmisch and LMU Munich

DOS of Random Schrödinger Operators with negatively correlated Cauchy Distribution
2024-10-22 16:00 | Room 5608.03.011 (Seminarraum (M1/M7)), Boltzmannstr. 3, Garching b. München, 85748, Germany
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 for the density of states (DOS) with the help of supersymmetry (SUSY). However, the case of negative coefficients remains largely unexplored. To illustrate the complexities involved, we study a simple model where only two lattice sites are negatively correlated. This model was already considered in a recent work of Disertori and Lager (MPAG2020), but here we develop a novel approach based on the regularisation of the distribu- tion of V . We derive the leading order expression for the DOS and recover the asymptote for the correction as the correlation strength is sent to zero. Finally, I present my progress in extending these results to a model of infinitely many pairs of negative correlation which are well separated and placed periodically in Zd.

Quantum Walks: Their basic properties and dynamical localization
2024-11-05 16:15 | Room 5608.03.011 (Seminarraum (M1/M7)), Boltzmannstr. 3, Garching b. München, 85748, Germany
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 algorithm). If the QW is assumed to be translation invariant, applying the Fourier transform yields a multiplication operator, whose bandstructure we briefly study. After equipping the underlying lattice with random phases, we turn to dynamical localization. This means that the probability to move from one lattice site to another decreases on average exponentially in the distance, independently of how many steps the QW may take. We sketch the proof of dynamical localization on the hexagonal lattice in the regime of strong disorder, which uses a finite volume method.

Weyl asymptotics for Lipschitz domains
2024-11-05 18:00 | Room A 027, Theresienstr. 37, Munich, 80333, Germany

Eigenvalue estimates for Laplace and Schrödinger operators
2024-11-07 00:00 - 2024-11-08 23:59 | University of Stuttgart, Seminarraum des IADM 8.122, Pfaffenwaldring 57, Stuttgart, 70569, Germany

How to represent a function in a quantum computer
2024-11-07 16:00 | Room C3N14, Auf der Morgenstelle 10, Tübingen, 72076, Germany
Quantum Signal Processing (QSP) is an algorithmic process by which one represents a signal $f: [0,1] to (-1,1)$ as the upper left entry of a product of $SU(2)$ matrices parametrized by the input variable $x in [0,1]$ and some ”phase factors” ${psi_k}_{k geq 0}$ depending on $f$. We show that, after a change of variables, QSP is actually the SU(2)-valued nonlinear Fourier transform, and the phase factors ${psi_k}_k$ correspond to the nonlinear Fourier coefficients. By exploiting a nonlinear Plancherel identity and using some basic spectral theory, we then show that a QSP representation exists for every $f$ satisfying the log integrability condition [ intlimits_{0} ^1 log (1-f(x)^2) frac{dx}{sqrt{1-x^2}} > – infty \, . ]

Lagrange, Euler, Hooke, and Cauchy
2024-11-13 18:00 | Room A 027, Theresienstr. 37, Munich, 80333, Germany

Around Segal Axioms for QFT: construction and interpretations
2024-11-13 19:00 | Room A 027, Theresienstr. 37, Munich, 80333, Germany

Quantum Advantage in Games of Incomplete Information
2024-11-19 16:15 | Room 5601.EG.001 (Magistrale), Boltzmannstr. 3, Garching b. München, 85748, Germany
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 Bayesian games of incomplete information, where each player has to react to a privately known type, while being ignorant about the type of the other players.
In fact, when all players in the game share the same payoff function, this reproduces the “nonlocal games” studied in quantum mechanics since Bell, in which case the CHSH inequality separates classical from quantum correlation and quantum from no-signalling.
In the talk, I will review, how classical correlations, shared quantum states and no-signalling correlations can create a hierarchy of sets of classically correlated, quantum and belief-invariant equilibria of conflict-of-interest games, all containing the set of Nash equilibria. I will show a simple and easy-to-analyze construction of such games based on quantum pseudo-telepathy games, which show the quantum advantage of larger social welfare and of fairer distribution of payoff.
[Based on work with V. Auletta, D. Ferraioli, A. Rai and G. Scarpa, arXiv:1605.07896, and with M. Cerda (BSc thesis, UAB 2021).]
