Delay times and reflection in chaotic cavities with absorption
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.
Cite
@article{arxiv.cond-mat/0303083,
title = {Delay times and reflection in chaotic cavities with absorption},
author = {D. V. Savin and H. -J. Sommers},
journal= {arXiv preprint arXiv:cond-mat/0303083},
year = {2007}
}
Comments
5 pages, 3 figures; final version to appear in PRE (relation to reflection extended, new material with Fig.3 added, experiment cond-mat/0305090 discussed)