Parametric Correlations of Phase Shifts and Statistics of Time Delays in Quantum Chaotic Scattering: Crossover between Unitary and Orthogonal Symmetries

TL;DR

This paper investigates the universal statistical behavior of phase shifts and time delays in quantum chaotic scattering systems during the transition from unitary to orthogonal symmetry, revealing a specific power-law distribution in weakly open systems.

Contribution

It provides a detailed analysis of the crossover regime between different symmetry classes, highlighting the parametric correlations of phase shifts and time delays.

Findings

Time delay distribution follows a τ^{-3/2} power law in weakly open systems.

Universal statistical properties are characterized across symmetry crossover regimes.

Results apply to systems with partial time-reversal symmetry breaking.

Abstract

We analyse universal statistical properties of phase shifts and time delays for open chaotic systems in the crossover regime of partly broken time-reversal invariance. In particular, we find that the distribution of the time delay shows $\tau^{-3/2}$ behavior for weakly open systems of any symmetry.