Random matrix theory of singular values of rectangular complex matrices I: Exact formula of one-body distribution function in fixed-trace ensemble

The fixed-trace ensemble of random complex matrices is the fundamental model that excellently describes the entanglement in the quantum states realized in a coupled system by its strongly chaotic dynamical evolution [see H. Kubotani, S. Adachi, M. Toda, Phys. Rev. Lett. 100 (2008) 240501]. The fixed...

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Bibliographic Details
Published in:	Annals of physics Vol. 324; no. 11; pp. 2278 - 2358
Main Authors:	Adachi, Satoshi, Toda, Mikito, Kubotani, Hiroto
Format:	Journal Article
Language:	English
Published:	New York Elsevier Inc 01.11.2009 Elsevier BV
Subjects:	CHAOS THEORY CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS DISTRIBUTION FUNCTIONS EIGENVALUES ENERGY LEVELS Fixed-trace ensemble INTEGRALS MATHEMATICAL EVOLUTION MATRICES Matrix Physics PROBABILITY Quantum chaos QUANTUM ENTANGLEMENT QUANTUM MECHANICS Quantum theory Random matrix theory RANDOMNESS Schmidt decomposition Selberg integral Selberg–Kaneko integral Selberg integral 03.65.Yz Random matrix theory Quantum entanglement 03.67.Mn Fixed-trace ensemble 03.65.Ud Quantum chaos 05.45.Mt Schmidt decomposition Selberg–Kaneko integral
ISSN:	0003-4916, 1096-035X
Online Access:	Get full text
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