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BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20260609T160000
DTEND;TZID=Europe/Berlin:20260609T160000
DTSTAMP:20260916T155520
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:http://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
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BEGIN:VEVENT
DTSTART;TZID=Europe/Berlin:20260611T161500
DTEND;TZID=Europe/Berlin:20260611T161500
DTSTAMP:20260916T155520
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:http://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:20260916T155520
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:http://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:20260916T155520
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:http://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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