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X-WR-CALDESC:Events for SFB TRR 352
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BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20260609T160000
DTEND;TZID=Europe/Berlin:20260609T160000
DTSTAMP:20261031T185710
CREATED:20260617T062627Z
LAST-MODIFIED:20260617T062627Z
UID:10000149-1781020800-1781020800@www.trr352.de
SUMMARY:Three-body Hamiltonian for abelian anyons with zero-range interactions
DESCRIPTION:Anyons are 2d identical quantum particles with an intermediate exchange symmetry characterized by representations of the braid group. In the abelian case\, they can be modeled through the so-called magnetic representation\, namely as a system of bosons with an Aharonov-Bohm flux attached to each particle. In this talk\, I will discuss the construction of self-adjoint Hamiltonians\, different from the Friedrichs realization\, for a system of three abelian anyons. I will focus in particular on the Ter-Martirosyan-Skornyakov extensions. This family of Hamiltonians turns out to be parametrized by a suitable boundary operator; I will present a complete classification of its self-adjoint realizations and compute the negative spectrum for the specific case of interest. These results shed light on the possible occurrence of Thomas instability in the three-anyon model. Joint work with Michele Correggi (PoliMi) and Davide Fermi (PoliMi)
URL:https://www.trr352.de/event/three-body-hamiltonian-for-abelian-anyons-with-zero-range-interactions/
LOCATION:Room A 027\, Theresienstr. 37\, Munich\, 80333\, Germany
CATEGORIES:Talks
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20260611T161500
DTEND;TZID=Europe/Berlin:20260611T161500
DTSTAMP:20261031T185710
CREATED:20260617T062037Z
LAST-MODIFIED:20260617T062037Z
UID:10000148-1781194500-1781194500@www.trr352.de
SUMMARY:Birth of a gap: critical phenomena in the normal matrix model
DESCRIPTION:We investigate a family of radially symmetric Coulomb gas systems at inverse\ntemperature \ncoming from the normal matrix model. The family is characterised by the\nproperty that the density of the equilibrium measure vanishes on a ring at\nradius \, which lies strictly inside the droplet. The large n expansion of\nthe free energy is obtained up to a novel term. Next\, we perform a scaling\nlimit of the correlation kernel at the scale and obtain a new limiting\nkernel in the bulk\, which differs from the well-known Ginibre kernel. \nJoint work with Matthias Allard based on arXiv:2509.24529
URL:https://www.trr352.de/event/birth-of-a-gap-critical-phenomena-in-the-normal-matrix-model/
LOCATION:5604.02.011 (Seminarraum)\, Boltzmannstr. 3\, Garching b. München\, 85748
CATEGORIES:Talks
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20260616T161500
DTEND;TZID=Europe/Berlin:20260616T161500
DTSTAMP:20261031T185710
CREATED:20260606T204650Z
LAST-MODIFIED:20260606T204650Z
UID:10000143-1781626500-1781626500@www.trr352.de
SUMMARY:On deriving a kinetic equation from many-body quantum dynamics
DESCRIPTION:Effectively describing the long-time dynamical behavior of quantum systems is a long-standing open problem. When the coupling constant λ of the interaction is small\, the dynamics of the system up to kinetic time t ~ λ -2 is conjectured to be effectively governed by the Boltzmann-Nordheim kinetic equation. In this talk\, we consider a system of weakly interacting lattice fermions at thermal equilibrium\, and I will describe how the two-point time correlation function of the system depends on the equilibrium solution of the Boltzmann-Nordheim equation. We approach the problem using a perturbation expansion and represent the appearing terms by Feynman diagrams. \nThis is joint work with Phan Thành Nam\, Herbert Spohn\, and Minh-Binh Tran.
URL:https://www.trr352.de/event/on-deriving-a-kinetic-equation-from-many-body-quantum-dynamics/
LOCATION:5606.02.011 (Konferenzraum)\, Boltzmannstr. 3\, Garching b. München\, 85748\, Germany
CATEGORIES:Talks
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20260630T150000
DTEND;TZID=Europe/Berlin:20260630T150000
DTSTAMP:20261031T185710
CREATED:20260626T073706Z
LAST-MODIFIED:20260626T073706Z
UID:10000153-1782831600-1782831600@www.trr352.de
SUMMARY:The index of a pair of pure states and the quantum Hall effect
DESCRIPTION:The index of a pair of projections on a Hilbert space was introduced in 1973 by Brown-Douglas-Filmore and connected to the integer quantum Hall effect by Avron-Seiler-Simon in 1994. For two orthogonal projections P\,Q such that P-Q is compact\, index(P\,Q)=dimimP∩kerQ-dimimQ∩kerP. It is manifestly an integer\, and enjoys norm and compactness stability\, much like the related Fredholm index. Such indices played a pivotal role in describing the quantization and stability properties in the quantum Hall effect; ASS94 related the Hall conductance to the index of a Fermi projection P and its Laughlin-flux-inserted projection U*PU. What becomes of this story in the presence of interactions? To describe infinitely-many interacting electrons in infinite-volume\, the Hilbert space is replaced by a unital C-* algebra A (a CAR algebra)\, but there is no obvious notion of a Fredholm index. We introduce a new notion\, the index of a pair of pure states (on A)\, prove its quantization\, invariance and stability properties\, and relate it to the (possibly fractional) Hall conductance. We comment that Kitaev’s invertible states always have integer conductance. Joint with Bachmann and Tauber.
URL:https://www.trr352.de/event/the-index-of-a-pair-of-pure-states-and-the-quantum-hall-effect/
LOCATION:Room 5612.EG.019 (CIT Sitzungsraum 2)\, Boltzmannstr. 3\, Garching b. München\, 85748\, Germany
CATEGORIES:Talks
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BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20260702T161500
DTEND;TZID=Europe/Berlin:20260702T161500
DTSTAMP:20261031T185710
CREATED:20260722T095653Z
LAST-MODIFIED:20260722T100231Z
UID:10000159-1783008900-1783008900@www.trr352.de
SUMMARY:A Spectral Transition in the Stability Theory of the 1-D Soler Model
DESCRIPTION:In this talk I will present recent spectral results related to the stability theory of standing waves ψ(t\,x) = e−iωtφ(x) for the one-dimensional Soler model\, a nonlinear Dirac equation\, with power nonlinearity.\n \n\n  f(s) = s|s|p−1\, p > 0.\n \n\n  The analysis is motivated by the so-called gap property arising in the stability theory of nonlinear Schrödinger equations. More precisely\, we study the spectral structure of the Dirac operators obtained by linearization around standing waves\, focusing on the existence of eigenvalues inside the spectral gap and resonances at the thresholds of the essential spectrum.\n \n\n  I will describe a sharp spectral transition in the nonlinearity at the critical exponent p = 1: threshold resonances present in the Gross–Neveu case generate eigenvalues inside the spectral gap for 0 < p < 1\, whereas no threshold resonances occur for p > 1.
URL:https://www.trr352.de/event/a-spectral-transition-in-the-stability-theory-of-the-1-d-soler-model/
LOCATION:Room A 027\, Theresienstr. 37\, Munich\, 80333\, Germany
CATEGORIES:Talks
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20260707T160000
DTEND;TZID=Europe/Berlin:20260707T160000
DTSTAMP:20261031T185710
CREATED:20260712T223845Z
LAST-MODIFIED:20260712T223845Z
UID:10000155-1783440000-1783440000@www.trr352.de
SUMMARY:Rapid mixing in long-range Lindbladians and static properties of their fixed points
DESCRIPTION:The classification of mixed-state phases requires criteria beyond two-point correlation functions\, such as the decay of the mutual information (MI) and the conditional mutual information(CMI)\, with the latter encapsulated in the notion of Markov length. In this talk\, we show how such static properties of the fixed point of a Lindbladian follow from natural dynamical features of its generator: rapid mixing and frustration-freeness. We focus on systems with long-range interactions\, and prove i)that local Lindbladians satisfying\n(global) rapid mixing and frustration-freeness have fixed-points whose CMI decays with the shielding distance\, and ii) that (local) rapid mixing together with primitivity and regularity implies global decay of MI. For long-range interactions both quantities decay polynomially rather than exponentially\, in contrast to the finite- and short-range regimes where exponential decay (a finite Markov length) is expected within a phase. We further show that Gibbs states of long-range\, non-commuting Hamiltonians satisfy a local Markov property at any temperature.
URL:https://www.trr352.de/event/rapid-mixing-in-long-range-lindbladians-and-static-properties-of-their-fixed-points/
LOCATION:Room 5608.02.020 (Seminarraum (M11))\, Boltzmannstr. 3\, Garching b. München\, 85748\, Germany
CATEGORIES:Talks
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20260715T161500
DTEND;TZID=Europe/Berlin:20260715T161500
DTSTAMP:20261031T185710
CREATED:20260720T205939Z
LAST-MODIFIED:20260720T205939Z
UID:10000157-1784132100-1784132100@www.trr352.de
SUMMARY:Positive Hankel operators
DESCRIPTION:I will discuss some aspects of spectral theory of positive semi-definite Hankel operators\, realised as integral operators on the positive semi-axis with integral kernels of the form h(x+y). I will focus on some remarkable similarities between spectral theory of Hankel operators in this class and spectral theory of one-dimensional Schrodinger operators.
URL:https://www.trr352.de/event/positive-hankel-operators/
LOCATION:Room A 027\, Theresienstr. 37\, Munich\, 80333\, Germany
CATEGORIES:Talks
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20260721T161500
DTEND;TZID=Europe/Berlin:20260721T161500
DTSTAMP:20261031T185710
CREATED:20260720T210224Z
LAST-MODIFIED:20260720T210224Z
UID:10000158-1784650500-1784650500@www.trr352.de
SUMMARY:Topology of the Ritz energy landscape
DESCRIPTION:Motivated by questions from quantum chemistry and spectral optimization\, this talk explores the topology of the Ritz energy landscape. Ritz values are the eigenvalues of a larger matrix (or operator) B compressed to a smaller trial subspace S. We can view the k-th Ritz value as a real-valued function (“Ritz energy landscape”) on the manifold of all possible\ns-dimensional trial subspaces\, the Grassmannian Gr(n\,s). \nWe show that the k-th Ritz value (for any k) is a perfect Morse function\, once the definition of “perfection” is suitably adjusted. A Morse function is called perfect if it describes the topology of its domain in the most efficient way possible\, meaning the number of its critical points of each type exactly matches the corresponding Betti number of the space. While the k-th eigenvalue is Lipschitz rather than smooth and while its critical points are not isolated — and not even Morse-Bott — its critical point count is nevertheless well-defined and reflects the topology of the Grassmannian in a minimal\, perfect way. \nThe proof proceeds by introducing a suitable perturbation which ensures that points of non-smoothness are not critical (by a theorem of Zelenko and the presenter) and that the critical points that remain are isolated. We also show that the notion of perfection we introduce (“homological perfection”) is closed under such perturbations. \nBased on joint work with Mark Goresky (IAS).
URL:https://www.trr352.de/event/topology-of-the-ritz-energy-landscape/
LOCATION:Room 5608.02.020 (Seminarraum (M11))\, Boltzmannstr. 3\, Garching b. München\, 85748\, Germany
CATEGORIES:Talks
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20261021T161500
DTEND;TZID=Europe/Berlin:20261021T161500
DTSTAMP:20261031T185710
CREATED:20261015T162438Z
LAST-MODIFIED:20261015T162448Z
UID:10000162-1792599300-1792599300@www.trr352.de
SUMMARY:Regularity of Quantum Trajectories and Randomized Measurements
DESCRIPTION:Quantum trajectories are Markov chains that model the evolution of quantum systems subjected to repeated indirect measurements. The classification of their invariant measures relies heavily on a purification assumption that\, while standard\, is difficult to check for a given instrument. Moreover\, little is known about the invariant measures themselves\, like their support or continuity properties.\nWith Sascha Lill and Cornelia Vogel we recently investigated these questions when the measurements are randomized. Namely\, at each time step\, the observable measured on the probe used for the indirect measurement is chosen randomly and independently. Considering this randomization\, we give sufficient conditions for purification to hold\, the invariant measure’s support is the full set of pure states and the invariant measure is absolutely continuous with respect to the uniform measure. Along the way we introduce a new notion of irreducibility for quantum channels we dub multiplicative primitiveness. We provide examples where it holds and some where it does not. That especially shows that\, for some quantum channels\, whatever the measurement used on the probes\, some pure states will never be approximated by the quantum trajectory.\nI will present these results and related open questions.
URL:https://www.trr352.de/event/regularity-of-quantum-trajectories-and-randomized-measurements/
LOCATION:A027\, Theresienstr. 37\, Munich\, Germany
CATEGORIES:Talks
END:VEVENT
BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20261030T143000
DTEND;TZID=Europe/Berlin:20261030T183000
DTSTAMP:20261031T185710
CREATED:20261028T141754Z
LAST-MODIFIED:20261028T141903Z
UID:10000164-1793370600-1793385000@www.trr352.de
SUMMARY:Probability Colloquium Augsburg-Munich
DESCRIPTION:Speakers: \n\nAmol Aggarwal (Stanford)\nJohannes Alt (Bonn)\n\nSchedule: \n\n14:30   Welcome\n15:00   Talk Amol Aggarwal\n16:00   Refreshment break\n16:30   Talk Johannes Alt\n18:30   Option for common dinner\n \nTitles and abstracts: \nAmol Aggarwal: Asymptotics for the Maximal Representation of the Symmetric Group \nWe analyze the behavior of the largest dimension of an irreducible representation of the symmetric group S_N\, as N tends to infinity\, showing that it behaves as (N!)^{1/2} * e^{-(d+o(1)) N^{1/2}}\, for some constant d>0. The proof is based on viewing these dimensions as discrete variants of random matrix integrals or Coulomb gases\, and setting up and analyzing a variational principle for their local statistics. \nJohannes Alt: Random Graphs: From Spectra to Quantum Dynamics \nWe study the Erdős-Rényi graph\, a common random graph model with intricate behaviours. \nFirst\, I establish a transition in the eigenvector structure of its adjacency matrix. For large enough expected degree\, all eigenvectors are delocalized\, i.e. their mass spreads out approximately uniformly over all vertices. When the expected degree is small enough\, localized eigenvectors emerge. More precisely\, the mass of each eigenvector with large eigenvalue is concentrated in a ball around a unique vertex and decays exponentially in the graph distance from this vertex. \nSecond\, I determine the Schrödinger time evolution of a free quantum particle hopping on the Erdős-Rényi graph through refined spectral information. \nThird\, I demonstrate that for the corresponding directed Erdős-Rényi graph\, all eigenvectors\, with eigenvalue away from zero\, are delocalized. This is in contrast to the undirected setting in the first part. \nThe talk is based on joint works with Raphael Ducatez\, Antti Knowles and Sarah Timhadjelt.
URL:https://www.trr352.de/event/probability-colloquium-augsburg-munich-3/
LOCATION:University of Augsburg\, Room 2004 (L1)\, Universitätsstraße 14\, Augsburg\, 86159
CATEGORIES:Talks
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