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DTSTART;TZID=Europe/Berlin:20260702T161500
DTEND;TZID=Europe/Berlin:20260702T161500
DTSTAMP:20260916T155720
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:http://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
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BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20260707T160000
DTEND;TZID=Europe/Berlin:20260707T160000
DTSTAMP:20260916T155720
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:http://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:20260916T155720
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:http://www.trr352.de/event/positive-hankel-operators/
LOCATION:Room A 027\, Theresienstr. 37\, Munich\, 80333\, Germany
CATEGORIES:Talks
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BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20260721T161500
DTEND;TZID=Europe/Berlin:20260721T161500
DTSTAMP:20260916T155720
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:http://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
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