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X-WR-CALNAME:SFB TRR 352
X-ORIGINAL-URL:http://www.trr352.de
X-WR-CALDESC:Events for SFB TRR 352
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TZID:Europe/Berlin
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DTSTART:20220327T010000
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BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230629T143000
DTEND;TZID=Europe/Berlin:20230629T143000
DTSTAMP:20260506T205900
CREATED:20250707T125402Z
LAST-MODIFIED:20250829T134950Z
UID:10000088-1688049000-1688049000@www.trr352.de
SUMMARY:A new approach to Scattering: On the Asymptotic states of Nonlinear Dispersive and Hyperbolic equations with General Data
DESCRIPTION:I will present a new approach to finding the asymptotic states of Nonlinear Wave Equations with general initial data.\nIn 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 results hold for initial data for which the H^1 Sobolev norm (the energy norm) is uniformly bounded in time.\nThis answers the question of Asymptotic Completeness to a large class of equations\, including for the first time\, equations with time dependent potentials.\nThese are joint works with Baoping Liu (Peking Univ) and Xiaoxu Wu (Rutgers).
URL:http://www.trr352.de/event/a-new-approach-to-scattering-on-the-asymptotic-states-of-nonlinear-dispersive-and-hyperbolic-equations-with-general-data/
LOCATION:Room C3N14\, Auf der Morgenstelle 10\, Tübingen\, 72076\, Germany
CATEGORIES:Talks
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230628T161500
DTEND;TZID=Europe/Berlin:20230628T161500
DTSTAMP:20260506T205900
CREATED:20250707T125547Z
LAST-MODIFIED:20250904T103444Z
UID:10000089-1687968900-1687968900@www.trr352.de
SUMMARY:Ground state phase diagram of jellium: what do we think we know?
DESCRIPTION: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 ground state phase diagram and Fermi Liquid properties.
URL:http://www.trr352.de/event/ground-state-phase-diagram-of-jellium-what-do-we-think-we-know/
LOCATION:Room B 349\, Theresienstr. 39\, Munich\, 80333\, Germany
CATEGORIES:Talks
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230622T160000
DTEND;TZID=Europe/Berlin:20230622T160000
DTSTAMP:20260506T205900
CREATED:20250707T125722Z
LAST-MODIFIED:20250829T135115Z
UID:10000090-1687449600-1687449600@www.trr352.de
SUMMARY:Large deviations in Bose-Einstein condensates
DESCRIPTION: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\, bounded one-particle operators with law given by the ground state satisfy large deviation estimates. We derive a lower and an upper bound on the rate function that match up to second order and that are characterized by quantum fluctuations around the condensate.
URL:http://www.trr352.de/event/large-deviations-in-bose-einstein-condensates/
LOCATION:Room C3N14\, Auf der Morgenstelle 10\, Tübingen\, 72076\, Germany
CATEGORIES:Talks
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230613T170000
DTEND;TZID=Europe/Berlin:20230613T170000
DTSTAMP:20260506T205900
CREATED:20250707T125926Z
LAST-MODIFIED:20250904T103455Z
UID:10000091-1686675600-1686675600@www.trr352.de
SUMMARY:Boltzmann-type collision operators for Bogoliubov excitations of Bose-Einstein condensates
DESCRIPTION: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 Yves Pomeau.
URL:http://www.trr352.de/event/boltzmann-type-collision-operators-for-bogoliubov-excitations-of-bose-einstein-condensates/
LOCATION:Room 5608.03.011 (Seminarraum (M1/M7))\, Boltzmannstr. 3\, Garching b. München\, 85748\, Germany
CATEGORIES:Talks
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230613T160000
DTEND;TZID=Europe/Berlin:20230613T160000
DTSTAMP:20260506T205900
CREATED:20250707T130135Z
LAST-MODIFIED:20250707T130135Z
UID:10000092-1686672000-1686672000@www.trr352.de
SUMMARY:Estimation of propagation of chaos via cumulant hierarchies in two example models
DESCRIPTION: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 and the degree of such independence\, i.e.\, theamount of “chaos” in the system. In this talk\, we will consider two\, qualitatively different\, ex-ample cases for which kinetic theory is believed to be applicable: the discrete nonlinear Schrodinger evolution (DNLS) with suitable random\, spatially ho- mogeneous initial data\, and the stochastic Kac model. In both cases\, we set up sui- table random variables and propose methods to control the evolution of their cumu- lant hierarchies. The talk is based on joint work with Aleksis Vuoksenmaa\, and earlier works with Matteo Marcozzi\, Alessia Nota\, and Herbert Spohn.
URL:http://www.trr352.de/event/estimation-of-propagation-of-chaos-via-cumulant-hierarchies-in-two-example-models/
LOCATION:Room 5608.03.011 (Seminarraum (M1/M7))\, Boltzmannstr. 3\, Garching b. München\, 85748\, Germany
CATEGORIES:Talks
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230609T161500
DTEND;TZID=Europe/Berlin:20230609T161500
DTSTAMP:20260506T205900
CREATED:20250707T130400Z
LAST-MODIFIED:20250904T103511Z
UID:10000093-1686327300-1686327300@www.trr352.de
SUMMARY:Light cones for open quantum systems
DESCRIPTION: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 of the von Neumann-Lindblad equation is approximately localized inside an energy- dependent light cone. We also obtain an explicit upper bound for the slope of this light cone. Joint work with S. Breteaux\, J. Faupin\, D.H. Ou Yang\, I.M. Sigal\, and J. Zhang.
URL:http://www.trr352.de/event/light-cones-for-open-quantum-systems/
LOCATION:Room 5607.01.023 (Seminarraum)\, Boltzmannstr. 3\, Garching b. München\, 85748\, Germany
CATEGORIES:Talks
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230530T160000
DTEND;TZID=Europe/Berlin:20230530T160000
DTSTAMP:20260506T205900
CREATED:20250707T130709Z
LAST-MODIFIED:20250829T135211Z
UID:10000094-1685462400-1685462400@www.trr352.de
SUMMARY:Vacuum solutions in the theory of electroweak interactions
DESCRIPTION: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 the magnetic field have the symmetry of a lattice and which have lower energy locally than the homogeneous (gauge-translationally invariant) solutions. The stability of these solutions is an open problem.
URL:http://www.trr352.de/event/vacuum-solutions-in-the-theory-of-electroweak-interactions/
LOCATION:Room C3N16\, An der Morgenstelle 10\, Tübingen\, 72076\, Germany
CATEGORIES:Talks
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230530T143000
DTEND;TZID=Europe/Berlin:20230530T143000
DTSTAMP:20260506T205900
CREATED:20250707T130900Z
LAST-MODIFIED:20250829T135232Z
UID:10000095-1685457000-1685457000@www.trr352.de
SUMMARY:Bulk-edge correspondence for unbounded Dirac-Landau operators
DESCRIPTION: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 functions of the bulk and edge operators. One of these corollaries leads to the so-called Streda formula: if the bulk operator has an isolated compact spectral island\, then the integrated density of states of the corresponding bulk spectral projection varies linearly with the magnetic field as long as the gaps between the spectral island and the rest of the spectrum are not closed\, and the slope of this variation is given by the Chern character of the projection. The same bulk Chern character is related to the number of edge states which appear in the gaps of the bulk operator. This is joint work with M. Moscolari and K. Sørensen.
URL:http://www.trr352.de/event/bulk-edge-correspondence-for-unbounded-dirac-landau-operators/
LOCATION:Room C3N16\, An der Morgenstelle 10\, Tübingen\, 72076\, Germany
CATEGORIES:Talks
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230526T141500
DTEND;TZID=Europe/Berlin:20230526T141500
DTSTAMP:20260506T205900
CREATED:20250707T131434Z
LAST-MODIFIED:20250829T135309Z
UID:10000096-1685110500-1685110500@www.trr352.de
SUMMARY:Observation of hole ordering mediated by antiferromagnetic correlations in mixed-dimensional Hubbard models
DESCRIPTION: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 the Hubbard model[1\,2\,9]\, many open questions remain in particular about the pseudo-gap regime and the relation of striped phases to superconductivity. \nWith our Lithium-6 quantum gas microscope\, we can image strongly correlated many-body Fermi systems with full spin and density resolution and study individual holes’ local distribution and spin environment [3\,4]. In addition\, the microscope and a new phase-stable superlattice enable us to engineer large classes of Hubbard-like Hamiltonians with control on the level of individual sites. \nIn antiferromagnets with weak doping\, individual holes form magnetic polarons whose motion is strongly reduced due to the magnetic background. Pairs of dopants can overcome the frustrating effect but we find strong competition between this magnetically mediated hole-hole attraction and repulsion due to Pauli blocking [5\,6]. The binding energy for hole pairing in normal two-dimensional Hubbard models is thus strongly reduced below the magnetic energy scale J. \nHowever\, in a mixed-dimensional system [7]\, where we restrict the hole motion to one dimension while keeping the spin order two-dimensional\, we directly image tightly bound pairs of holes and find binding energies on the order of the spin exchange energy J [5]. Upon increased doping\, we observe repulsion between hole pairs in one spatial direction and currently investigate the formation of stripes [8]\, which we expect to form already at our current experimental temperatures in the mixD configuration. Such stripes form the ground state of the normal Hubbard model [1] and recent numerical results show that with a diagonal hopping term\, they support the emergence of d-wave superconductivity [9].
URL:http://www.trr352.de/event/observation-of-hole-ordering-mediated-by-antiferromagnetic-correlations-in-mixed-dimensional-hubbard-models/
LOCATION:Room B 349\, Theresienstr. 39\, Munich\, 80333\, Germany
CATEGORIES:Talks
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230516T160000
DTEND;TZID=Europe/Berlin:20230516T160000
DTSTAMP:20260506T205900
CREATED:20250707T131600Z
LAST-MODIFIED:20250829T135335Z
UID:10000097-1684252800-1684252800@www.trr352.de
SUMMARY:Non-Perturbative Results on the Mass Shell in Nelson-Type Models
DESCRIPTION: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 an eigenvalue for any total momentum\, i.e.\, no ground state exists. Applying an appropriate dressing transformation\, dependent on the total momentum\, one obtains an infrared-renormalized representation of the model\, which exhibits a ground state. Previously\, this situation has been investigated using perturba tive methods\, i.e.\, for small total momenta and (possibly dependent on the total momentum) small coupling constants. In this talk\, we discuss non-perturbative proofs both for the absence of ground states in the usual Fock space representation of Nelson-type models (for all total momenta) and the existence of ground states in the non-equivalent representation (for almost all physically relevant total momenta). We emphasize that our results hold for all values of the coupling constants\, due to the non-perturbative nature of their proofs. The talk is based on joint work with Thomas Norman Dam\, David Hasler and Oliver Siebert.
URL:http://www.trr352.de/event/non-perturbative-results-on-the-mass-shell-in-nelson-type-models/
LOCATION:Seminar room C4H33\, An der Morgenstelle 10\, Tübingen\, 72076\, Germany
CATEGORIES:Talks
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230510T170000
DTEND;TZID=Europe/Berlin:20230510T170000
DTSTAMP:20260506T205900
CREATED:20250707T133855Z
LAST-MODIFIED:20250829T140726Z
UID:10000108-1683738000-1683738000@www.trr352.de
SUMMARY:Some avatars of the correspondence principle in semi-classical analysis
DESCRIPTION: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 how recent re- sults of semi-classical analysis express in that frame.
URL:http://www.trr352.de/event/some-avatars-of-the-correspondence-principle-in-semi-classical-analysis/
LOCATION:Room 5301.EG.001 (Auditorium)\, Lichtenbergstr. 2a\, Garching b. München\, 85748\, Germany
CATEGORIES:Colloquia
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230504T163000
DTEND;TZID=Europe/Berlin:20230504T163000
DTSTAMP:20260506T205900
CREATED:20250707T134018Z
LAST-MODIFIED:20250829T140755Z
UID:10000109-1683217800-1683217800@www.trr352.de
SUMMARY:Chemists and physicists have found how to approximate Schrödinger's equation;here is how mathematicians can contribut
DESCRIPTION: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 have overcome this problem in an impressive way\, within a framework called “Density Functional Theory”. I will discuss the role that mathematical results have historically played in this revolution and then present more recent results.
URL:http://www.trr352.de/event/chemists-and-physicists-have-found-how-to-approximate-schrodingers-equationhere-is-how-mathematicians-can-contribut/
LOCATION:Room A 027\, Theresienstr. 37\, Munich\, 80333\, Germany
CATEGORIES:Colloquia
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230427T160000
DTEND;TZID=Europe/Berlin:20230427T160000
DTSTAMP:20260506T205900
CREATED:20250707T131849Z
LAST-MODIFIED:20250829T135502Z
UID:10000099-1682611200-1682611200@www.trr352.de
SUMMARY:Classical simulation of short-time quantum dynamics
DESCRIPTION: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 the dynamics of local observables and nonlocal quantities such as the Loschmidt echo\, where the evolution is governed by a local Hamiltonian. For short times\, their computational cost scales polynomially with the system size and the inverse of the approximation error. In the case of local observables\, the proposed algorithm has a better dependence on the approximation error than algorithms based on the Lieb–Robinson bound. Our results use cluster expansion techniques adapted to the dynamical setting\, for which we give a novel proof of their convergence. This has important physical consequences besides our efficient algorithms. In particular\, we establish a novel quantum speed limit\, a bound on dynamical phase transitions\, and a concentration bound for product states evolved for short times. Joint work with Dominik S. Wild (arXiv:2210.11490)
URL:http://www.trr352.de/event/classical-simulation-of-short-time-quantum-dynamics/
LOCATION:Seminar room C4H33\, An der Morgenstelle 10\, Tübingen\, 72076\, Germany
CATEGORIES:Talks
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230427T160000
DTEND;TZID=Europe/Berlin:20230427T160000
DTSTAMP:20260506T205900
CREATED:20250707T131722Z
LAST-MODIFIED:20250829T135428Z
UID:10000098-1682611200-1682611200@www.trr352.de
SUMMARY:Magnetic properties of ground states in many-electron systems
DESCRIPTION: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 unified. The theory is formulated using the standard forms of von Neumann algebras.
URL:http://www.trr352.de/event/magnetic-properties-of-ground-states-in-many-electron-systems/
LOCATION:Room C3N14\, Auf der Morgenstelle 10\, Tübingen\, 72076\, Germany
CATEGORIES:Talks
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20230413T143000
DTEND;TZID=Europe/Berlin:20230413T143000
DTSTAMP:20260506T205900
CREATED:20250707T132030Z
LAST-MODIFIED:20250829T135526Z
UID:10000100-1681396200-1681396200@www.trr352.de
SUMMARY:A subpolynomial-time algorithm for the free energy of one-dimensional quantum systems in the thermodynamic limit
DESCRIPTION: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 temperature T>0 in subpolynomial time\, i.e.\, in time O(1/E^c) for any constant c>0 where E is the additive approximation error. Previously\, the best known algorithm had a runtime that is polynomial in 1/E where the degree of the polynomial is exponential in the inverse temperature 1/T. Our algorithm is also particularly simple as it reduces to the computation of the spectral radius of a linear map. This linear map has an interpretation as a noncommutative transfer matrix and has been studied previously to prove results on the analyticity of the free energy and the decay of correlations. We also show that the corresponding eigenvector of this map gives an approximation of the marginal of the Gibbs state and thereby allows for the computation of various thermodynamic properties of the quantum system.
URL:http://www.trr352.de/event/a-subpolynomial-time-algorithm-for-the-free-energy-of-one-dimensional-quantum-systems-in-the-thermodynamic-limit/
LOCATION:Seminar room C4H33\, An der Morgenstelle 10\, Tübingen\, 72076\, Germany
CATEGORIES:Talks
END:VEVENT
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