Semiclassical field theory approach to quantum chaos

A. V. Andreev, B. D. Simons, O. Agam, B. L. Altshuler

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62 Citations (Scopus)

Abstract

We construct a field theory to describe energy averaged quantum statistical properties of systems which are chaotic in their classical limit. An expression for the generating function of general statistical correlators is presented in the form of a functional supermatrix non-linear σ-model where the effective action involves the evolution operator of the classical dynamics. Low-lying degrees of freedom of the field theory are shown to reflect the irreversible classical dynamics describing relaxation of phase space distributions. The validity of this approach is investigated over a wide range of energy scales. As well as recovering the universal long-time behavior characteristic of random matrix ensembles, this approach accounts correctly for the short-time limit yielding results which agree with the diagonal approximation of periodic orbit theory.

Original languageEnglish
Pages (from-to)536-566
Number of pages31
JournalNuclear Physics B
Volume482
Issue number3
DOIs
Publication statusPublished - 30 Dec 1996
Externally publishedYes

Keywords

  • Quantum chaos
  • Random matrix theory

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