SEMICLASSICAL LIMIT OF UNIVERSAL PARAMETRIC DENSITY CORRELATIONS

This paper is devoted to a critical study of parametric level density fluctuations of systems whose classical counterparts present chaotic d ynamics. Employing a semiclassical theory based on the Gutzwiller trac e formula, we show that for large parametric changes the density corre lation function, after rescaling, becomes universal and coincides with the leading asymptotic term obtained from random matrix theory. The e ssential advantage of the semiclassical approach is to provide a simpl e recipe for the calculation of the nonuniversal scaling parameter fro m elements of the underlying classical dynamics specific to the system . We also discuss recent improvements of the semiclassical theory, whi ch introduce a requantization of the smoothed level density. With this method, we calculate the universal density correlations as a function of a time-reversal symmetry breaking parameter. [S1063-651X(98)09211- 3].