Delay times and reflection in chaotic cavities with absorption

TL;DR

This paper analytically investigates how absorption affects delay times and reflection in chaotic quantum cavities using random matrix theory, revealing suppression of large delay time fluctuations and deriving distributions of delay and reflection eigenvalues.

Contribution

It provides a comprehensive analytical framework for delay time and reflection distributions in chaotic systems with absorption, extending previous models to arbitrary channels and absorption rates.

Findings

Absorption introduces exponential decay and suppresses large delay time fluctuations.

Derived analytical distributions for delay times and reflection eigenvalues.

Established relation between delay times, reflection, and absorption in chaotic cavities.

Abstract

Absorption yields an additional exponential decay in open quantum systems which can be described by shifting the (scattering) energy E along the imaginary axis, E+i\hbar/2\tau_{a}. Using the random matrix approach, we calculate analytically the distribution of proper delay times (eigenvalues of the time-delay matrix) in chaotic systems with broken time-reversal symmetry that is valid for an arbitrary number of generally nonequivalent channels and an arbitrary absorption rate 1/\tau_{a}. The relation between the average delay time and the ``norm-leakage'' decay function is found. Fluctuations above the average at large values of delay times are strongly suppressed by absorption. The relation of the time-delay matrix to the reflection matrix S^{\dagger}S is established at arbitrary absorption that gives us the distribution of reflection eigenvalues. The particular case of single-channel scattering is explicitly considered in detail.