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 dynamics. Employing a semiclassical theory based on the Gutzwiller trace formula, we show that for large parametric changes the density correlation function, after rescaling, becomes universal and coincides with the leading asymptotic term obtained from random matrix theory. The essential advantage of the semiclassical approach is to provide a simple recipe for the calculation of the nonuniversal scaling parameter from elements of the underlying classical dynamics specific to the system. We also discuss recent improvements of the semiclassical theory, which 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.