Induced vs Spontaneous Breakdown of S-matrix Unitarity: Probability of No Return in Quantum Chaotic and Disordered Systems

TL;DR

This paper analyzes the probability of no return in wave scattering within disordered quantum systems, deriving formulas for its distribution and linking it to the Anderson transition through S-matrix unitarity breakdown.

Contribution

It provides explicit formulas for the distribution of no-return probability in quantum chaotic and disordered systems, connecting unitarity violation to localization transitions.

Findings

Derived formulas for no-return probability distribution

Linked unitarity violation to Anderson localization transition

Identified signatures of spontaneous S-matrix unitarity breakdown

Abstract

We investigate systematically sample-to sample fluctuations of the probability $\tau$ of no return into a given entrance channel for wave scattering from disordered systems. For zero-dimensional ("quantum chaotic") and quasi one-dimensional systems with broken time-reversal invariance we derive explicit formulas for the distribution of $\tau$, and investigate particular cases. Finally, relating $\tau$ to violation of S-matrix unitarity induced by internal dissipation, we use the same quantity to identify the Anderson delocalisation transition as the phenomenon of spontaneous breakdown of S-matrix unitarity.