## 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 language | American English |
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Pages (from-to) | 536-566 |

Number of pages | 31 |

Journal | Nuclear Physics B |

Volume | 482 |

Issue number | 3 |

DOIs | |

State | Published - 30 Dec 1996 |

Externally published | Yes |

### Bibliographical note

Funding Information:We are grateful to K.B. Efetov, D.E. Khmel'nitskii, A.I. Larkin, I.V. Lerner, B.A. Muzykantskii, A.M. Polyakov, D. Ruelle, Ya.G. Sinai, N. Taniguchi, and M.R. Zirnbauer for stimulating discussions. This work was supported in part by JSEP No. DAAL 03-89-0001, and by the National Science Foundation under Grant Nos. DMR 92-14480 and PHY94-07194. We acknowledge the hospitality of the ITP in Santa Barbara where part of this work was performed. O.A. also acknowledges the support of the Rothschild Fellowship.

## Keywords

- Quantum chaos
- Random matrix theory