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Free Fermions and the Classical Compact Groups

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 natura...

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Autores principales: Cunden, Fabio Deelan, Mezzadri, Francesco, O’Connell, Neil
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2018
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6560678/
https://www.ncbi.nlm.nih.gov/pubmed/31258183
http://dx.doi.org/10.1007/s10955-018-2029-6
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author Cunden, Fabio Deelan
Mezzadri, Francesco
O’Connell, Neil
author_facet Cunden, Fabio Deelan
Mezzadri, Francesco
O’Connell, Neil
author_sort Cunden, Fabio Deelan
collection PubMed
description 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 free fermions with classical boundary conditions.
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spelling pubmed-65606782019-06-26 Free Fermions and the Classical Compact Groups Cunden, Fabio Deelan Mezzadri, Francesco O’Connell, Neil J Stat Phys Article 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 free fermions with classical boundary conditions. Springer US 2018-04-20 2018 /pmc/articles/PMC6560678/ /pubmed/31258183 http://dx.doi.org/10.1007/s10955-018-2029-6 Text en © The Author(s) 2018 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Article
Cunden, Fabio Deelan
Mezzadri, Francesco
O’Connell, Neil
Free Fermions and the Classical Compact Groups
title Free Fermions and the Classical Compact Groups
title_full Free Fermions and the Classical Compact Groups
title_fullStr Free Fermions and the Classical Compact Groups
title_full_unstemmed Free Fermions and the Classical Compact Groups
title_short Free Fermions and the Classical Compact Groups
title_sort free fermions and the classical compact groups
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC6560678/
https://www.ncbi.nlm.nih.gov/pubmed/31258183
http://dx.doi.org/10.1007/s10955-018-2029-6
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