Free fermions and the classical compact groups
| Autor: | Neil O'Connell, Francesco Mezzadri, Fabio Deelan Cunden |
|---|---|
| Rok vydání: | 2017 |
| Předmět: |
Group heat kernel
Pure mathematics FOS: Physical sciences 01 natural sciences Point process Article 010305 fluids & plasmas Non-interacting fermions Random matrix theory and extensions 0103 physical sciences FOS: Mathematics Quantum boundary conditions Boundary value problem 010306 general physics Condensed Matter - Statistical Mechanics Mathematical Physics Eigenvalues and eigenvectors Haar measure Mathematics Statistical Mechanics (cond-mat.stat-mech) Probability (math.PR) Statistical and Nonlinear Physics Fermion Mathematical Physics (math-ph) Non-intersecting paths Determinantal processes Bounded function Laplace operator Random matrix Mathematics - Probability |
| Zdroj: | Journal of Statistical Physics Cunden, F D, Mezzadri, F & O’Connell, N 2018, ' Free Fermions and the Classical Compact Groups ', Journal of Statistical Physics, vol. 171, no. 5, pp. 768-801 . https://doi.org/10.1007/s10955-018-2029-6 |
| DOI: | 10.48550/arxiv.1705.05932 |
| Popis: | There is a close connection between the ground state of non-interacting 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 by constructing a finite temperature extension of the Haar measure on the classical compact groups. The eigenvalue statistics of the resulting grand canonical matrix models (of random size) corresponds exactly to the grand canonical measure of non-interacting free fermions with classical boundary conditions. Comment: 35 pages, 5 figures. Final version |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|