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Absorption yields an additional exponential decay in open quantum systemswhich can be described by shifting the (scattering) energy E along theimaginary axis, E+i\hbar/2\tau_{a}. Using the random matrix approach, wecalculate analytically the distribution of proper delay times (eigenvalues ofthe time-delay matrix) in chaotic systems with broken time-reversal symmetrythat is valid for an arbitrary number of generally nonequivalent channels andan arbitrary absorption rate 1/\tau_{a}. The relation between the average delaytime and the ``norm-leakage'' decay function is found. Fluctuations above theaverage 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 isestablished at arbitrary absorption that gives us the distribution ofreflection eigenvalues. The particular case of single-channel scattering isexplicitly considered in detail.Comment: 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

Delay times and reflection in chaotic cavities with absorption