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 various correlators, averaged over the energy, is presented in the form of a functional supermatrix nonlinear σ-model. The effective action involves 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-time limit yielding results which agree with the diagonal approximation of periodic orbit theory. As an explicit example we consider the disordered Lorentz gas. Various regimes of the two-point correlation function, from the ballistic chaotic regime to the diffusive one, are explored and characterized.