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DTSTART;TZID=Europe/Berlin:20251210T170000
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DTSTAMP:20260503T231452
CREATED:20260117T132305Z
LAST-MODIFIED:20260117T132305Z
UID:10000129-1765386000-1765386000@www.trr352.de
SUMMARY:The Widom-Sobolev formula for the free Dirac operator
DESCRIPTION: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. \nIn this talk I give a brief introduction to both the Widom-Sobolev formula as well as the free Dirac operator\, and give an answer to the question above. I also talk about the strategy of the proof of this result\, in particular I show how it can be reduced to an application of another result from my PhD thesis\, a Widom-Sobolev formula for more general matrix-valued symbols. \nThe presented results were obtained in collaboration with Peter Müller.
URL:http://www.trr352.de/event/the-widom-sobolev-formula-for-the-free-dirac-operator/
LOCATION:Room B 349\, Theresienstr. 39\, Munich\, 80333\, Germany
CATEGORIES:Junior Coffee Breaks
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DTSTART;TZID=Europe/Berlin:20251215T160000
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CREATED:20260117T132056Z
LAST-MODIFIED:20260117T132056Z
UID:10000128-1765814400-1765814400@www.trr352.de
SUMMARY:Validity of Kubo formula for 1d and quasi-1d lattice fermionic systems
DESCRIPTION: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. \nWe establish the validity of linear response for these observables\, thereby providing a justification of Kubo’s formula. The latter is computed explicitly in terms of the spectral properties at the Fermi points and the profile of the perturbation. \nThe proof of linear response validity on the relevant time scales is based on a detailed analysis of the imaginary-time Duhamel expansion. A crucial ingredient is a cancellation mechanism in the scaling limit of higher-order correlation functions that describe the nonlinear part of the response. \nJoint work with Marcello Porta.
URL:http://www.trr352.de/event/validity-of-kubo-formula-for-1d-and-quasi-1d-lattice-fermionic-systems/
LOCATION:Seminar Room\, 4th floor\, Auf der Morgenstelle 10\, Tübingen\, 72076\, Germany
CATEGORIES:Junior Coffee Breaks
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