Decay Rate Statistics of Unstable Classically Chaotic Systems

TL;DR

This paper investigates the statistical properties of decay rates in unstable chaotic systems, revealing how complex interference affects decay laws beyond simple exponential behavior, using random matrix theory.

Contribution

It introduces a new decay rates distribution function and analyzes its properties within the random matrix framework, especially for systems lacking time reversal symmetry.

Findings

Decay rates distribution function differs from traditional decay width statistics.

Decay law deviations from exponential are characterized by the new distribution.

Analytical results obtained for systems without time reversal symmetry.

Abstract

Decay law of a complicated unstable state formed in a high energy collision is described by the Fourier transform of the two-point correlation function of the scattering matrix. Although each constituent resonance state decays exponentially the decay of a state composed of a large number of such interfering resonances is not, generally, exponential. We introduce the decay rates distribution function by representing the decay law in the form of the mean-weighted decay exponent. In the framework of the random matrix approach we investigate the properties of the new distribution function and its relation to the more conventional statistics of the decay widths. The latter is not in fact conclusive as concerns the evolution during the time shorter than the characteristic Heisenberg time. Exact analytical consideration is presented for the case of systems without time reversal symmetry.