Universal intensity statistics of multifractal resonance states

TL;DR

This paper proposes a universal exponential distribution for the intensity statistics of resonance states in chaotic quantum systems with escape, supported by numerical analysis of various models.

Contribution

It introduces a conjecture that the intensity statistics follow a universal exponential distribution scaled by a multifractal mean, validated through numerical simulations.

Findings

Intensity statistics follow an exponential distribution after scaling.

Numerical evidence from standard map, baker map, and random matrix models supports the conjecture.

The scaling depends on the system and decay rate of resonance states.

Abstract

We conjecture that in chaotic quantum systems with escape the intensity statistics for resonance states universally follows an exponential distribution. This requires a scaling by the multifractal mean intensity which depends on the system and the decay rate of the resonance state. We numerically support the conjecture by studying the phase-space Husimi function and the position representation of resonance states of the chaotic standard map, the baker map, and a random matrix model, each with partial escape.