Gaussian Random Matrix Ensembles in Phase Space

A new class of Random Matrix Ensembles is introduced. The Gaussian orthogonal, unitary, and symplectic ensembles GOE, GUE, and GSE, of random matrices are analogous to the classical Gibbs ensemble governed by Boltzmann's distribution in the coordinate space. The proposed new class of Random Mat...

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Bibliographic Details
Published in:arXiv.org 2019-07
Main Author: Duras, Maciej M
Format: Article
Language:English
Subjects:
Distribution functions
Enthalpy
Equations of state
Free energy
Ideal gas
Maximum entropy
Partitions (mathematics)
Potential energy
Online Access:Get full text
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Summary:A new class of Random Matrix Ensembles is introduced. The Gaussian orthogonal, unitary, and symplectic ensembles GOE, GUE, and GSE, of random matrices are analogous to the classical Gibbs ensemble governed by Boltzmann's distribution in the coordinate space. The proposed new class of Random Matrix ensembles is an extension of the above Gaussian ensembles and it is analogous to the canonical Gibbs ensemble governed by Maxwell-Boltzmann's distribution in phase space. The thermodynamical magnitudes of partition function, intrinsic energy, free energy of Helmholtz, free energy of Gibbs, enthalpy, as well as entropy, equation of state, and heat capacities, are derived for the new ensemble. The examples of nonideal gas with quadratic potential energy as well as ideal gas of quantum matrices are provided. The distribution function for the new ensembles is derived from the maximum entropy principle.
ISSN:2331-8422