QUANTUM CHAOS - A FIELD-THEORY APPROACH

We review the recent developments of the field theoretic approach to ' quantum chaos'. Within this approach, the generating function of vario us correlators, averaged over the energy, is presented in the form of a functional supermatrix nonlinear sigma-model. The effective action i nvolves the generator of evolution operator of irreversible classical dynamics. The low-lying degrees of freedom are, therefore, the Perron- Frobenius modes describing relaxation of phase space distributions. As well as recovering the universal long-time behavior characteristic of random matrix ensembles, this approach also accounts for the short-ti me limit yielding results which agree with the diagonal approximation of periodic orbit theory. As an explicit example we consider the disor dered Lorentz gas. Various regimes of the two-point correlation functi on, from the ballistic chaotic regime to the diffusive one, are explor ed and characterized. (C) 1997 Elsevier Science Ltd.