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Free fermions and the classical compact groups. (arXiv:1705.05932v1 [math-ph])
来源于:arXiv
We unveil the existence of a precise mapping between the ground state of
non-interacting free fermions in a box with classical (absorbing, reflecting,
and periodic) boundary conditions and the eigenvalue statistics of the
classical compact groups. The associated determinantal point processes can be
extended in two natural directions: i) we consider the full family of
admissible quantum boundary conditions (i.e., self-adjoint extensions) for the
Laplacian on a bounded interval, and the corresponding projection correlation
kernels; ii) we construct the grand canonical extensions at finite temperature
of the projection kernels, interpolating from Poisson to random matrix
eigenvalue statistics. The scaling limits in the bulk and at the edges are
studied in a unified framework, and the question of universality is addressed.
Whether the finite temperature determinantal processes correspond to the
eigenvalue statistics of some matrix models is, a priori, not obvious. We
complete the picture b 查看全文>>