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Equipartition principle for Wigner matrices

Part of: Equilibrium statistical mechanics Probability theory on algebraic and topological structures

Published online by Cambridge University Press:  27 May 2021

Zhigang Bao ,
László Erdős  and
Kevin Schnelli
Zhigang Bao
Affiliation:
Hong Kong University of Science and Technology, Hong Kong, China; E-mail: [email protected]
László Erdős
Affiliation:
IST Austria, Klosterneuburg, Austria; E-mail: [email protected]
Kevin Schnelli
Affiliation:
KTH Royal Institute of Technology, Stockholm, Sweden; E-mail: [email protected]

Abstract

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We prove that the energy of any eigenvector of a sum of several independent large Wigner matrices is equally distributed among these matrices with very high precision. This shows a particularly strong microcanonical form of the equipartition principle for quantum systems whose components are modelled by Wigner matrices.

MSC classification

Primary: 60B20: Random matrices (probabilistic aspects; for algebraic aspects see )
Secondary: 82B10: Quantum equilibrium statistical mechanics (general)
Type
Mathematical Physics
Information
Forum of Mathematics, Sigma , Volume 9 , 2021 , e44
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s), 2021. Published by Cambridge University Press

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