On the distribution of the total energy of a system of non-interacting fermions: Random matrix and semiclassical estimates

We consider a single particle spectrum as given by the eigenvalues of the Wigner-Dyson ensembles of random matrices, and fill consecutive single particle levels with n fermions. Assuming that the fermions are non-interacting, we show that the distribution of the total energy is Gaussian and its vari...

Descripción completa

Guardado en:

Detalles Bibliográficos
Autores principales:	Bohigas, O., Lebœuf, P., Sánchez, M.J.
Formato:	JOUR
Materias:	Fermions Random matrix Semiclassical
Acceso en línea:	http://hdl.handle.net/20.500.12110/paper_01672789_v131_n1-4_p186_Bohigas
Aporte de:	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires

id	todo:paper_01672789_v131_n1-4_p186_Bohigas
record_format	dspace
spelling	todo:paper_01672789_v131_n1-4_p186_Bohigas2023-10-03T15:04:35Z On the distribution of the total energy of a system of non-interacting fermions: Random matrix and semiclassical estimates Bohigas, O. Lebœuf, P. Sánchez, M.J. Fermions Random matrix Semiclassical We consider a single particle spectrum as given by the eigenvalues of the Wigner-Dyson ensembles of random matrices, and fill consecutive single particle levels with n fermions. Assuming that the fermions are non-interacting, we show that the distribution of the total energy is Gaussian and its variance grows as n 2 log n in the large-n limit. Next to leading order corrections are also computed. Some related quantities are discussed, in particular the nearest neighbor spacing autocorrelation function. Canonical and grand canonical approaches are considered and compared in detail. A semiclassical formula describing, as a function of n, a non-universal behavior of the variance of the total energy starting at a critical number of particles is also obtained. It is illustrated with the particular case of single particle energies given by the imaginary part of the zeros of the Riemann zeta function on the critical line. © 1999 Elsevier Science B.V. All rights reserved. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_01672789_v131_n1-4_p186_Bohigas
institution	Universidad de Buenos Aires
institution_str	I-28
repository_str	R-134
collection	Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic	Fermions Random matrix Semiclassical
spellingShingle	Fermions Random matrix Semiclassical Bohigas, O. Lebœuf, P. Sánchez, M.J. On the distribution of the total energy of a system of non-interacting fermions: Random matrix and semiclassical estimates
topic_facet	Fermions Random matrix Semiclassical
description	We consider a single particle spectrum as given by the eigenvalues of the Wigner-Dyson ensembles of random matrices, and fill consecutive single particle levels with n fermions. Assuming that the fermions are non-interacting, we show that the distribution of the total energy is Gaussian and its variance grows as n 2 log n in the large-n limit. Next to leading order corrections are also computed. Some related quantities are discussed, in particular the nearest neighbor spacing autocorrelation function. Canonical and grand canonical approaches are considered and compared in detail. A semiclassical formula describing, as a function of n, a non-universal behavior of the variance of the total energy starting at a critical number of particles is also obtained. It is illustrated with the particular case of single particle energies given by the imaginary part of the zeros of the Riemann zeta function on the critical line. © 1999 Elsevier Science B.V. All rights reserved.
format	JOUR
author	Bohigas, O. Lebœuf, P. Sánchez, M.J.
author_facet	Bohigas, O. Lebœuf, P. Sánchez, M.J.
author_sort	Bohigas, O.
title	On the distribution of the total energy of a system of non-interacting fermions: Random matrix and semiclassical estimates
title_short	On the distribution of the total energy of a system of non-interacting fermions: Random matrix and semiclassical estimates
title_full	On the distribution of the total energy of a system of non-interacting fermions: Random matrix and semiclassical estimates
title_fullStr	On the distribution of the total energy of a system of non-interacting fermions: Random matrix and semiclassical estimates
title_full_unstemmed	On the distribution of the total energy of a system of non-interacting fermions: Random matrix and semiclassical estimates
title_sort	on the distribution of the total energy of a system of non-interacting fermions: random matrix and semiclassical estimates
url	http://hdl.handle.net/20.500.12110/paper_01672789_v131_n1-4_p186_Bohigas
work_keys_str_mv	AT bohigaso onthedistributionofthetotalenergyofasystemofnoninteractingfermionsrandommatrixandsemiclassicalestimates AT lebœufp onthedistributionofthetotalenergyofasystemofnoninteractingfermionsrandommatrixandsemiclassicalestimates AT sanchezmj onthedistributionofthetotalenergyofasystemofnoninteractingfermionsrandommatrixandsemiclassicalestimates
_version_	1782030085511970816

On the distribution of the total energy of a system of non-interacting fermions: Random matrix and semiclassical estimates

Ejemplares similares