Séminaires du jeudi 15 mars

Séminaire du LPTMS: Samuel Belliard *** séminaire exceptionnel ***

11:00:00

Modified Bethe Ansatz for models without U(1) symmetry

Samuel Belliard (IPhT, CEA, Saclay)

I will present a modified version of the algebraic Bethe ansatz (MABA) that allows to characterize the eigenvalues and the eigenstates of spins chains without U(1) symmetry.  In the case of the XXX Heisenberg spins chain on the circle with a twisted boundary condition, the Bethe vectors and associated eigenvalues will be constructed and the correlation function problem will be discussed. This method also works for the XXX and XXZ Heisenberg spins chains on the segment.

 

Séminaire du LPTMS: Bertrand Lacroix-à-chez-Toine *** séminaire exceptionnel ***

11:30:00

Extreme value statistics in a gas of 2D charged particles

Bertrand Lacroix-à-chez-Toine (LPTMS, Université Paris-Sud)

  We study a system of N charged particles in two dimensions with Coulomb logarithmic repulsion and confined in an external symmetric potential. At the inverse temperature of interest β = 2, the positions of the charges form a 2D determinantal point process. In the case of a quadratic potential, there is a mapping between the positions of these charges and the eigenvalues of complex Ginibre matrices. We focus on the extremal statistics of the positions of the charges and in particular we highlight a new universal regime (with respect to a large class of confining potentials) which had been overlooked before [1]. It allows to solve a puzzle of matching between the typical regime of fluctuations [2] and the large deviation regime [3]. Finally we also considered potentials that deviates from this universality class and computed the extremal statistics in these cases.
  • [1] B. Lacroix-A-Chez-Toine, A. Grabsch, S. N. Majumdar, G. Schehr, Extremes of 2d Coulomb gas: universal intermediate deviation regime, J. Stat. Mech. P013203, (2018).
  • [2] B. Rider, J. Phys. A 36(12), 3401 (2003).
  • [3] F. D. Cunden, F. Mezzadri, P. Vivo, J. Stat. Phys. 164(5), 1062-1081 (2016).