Quantum Stochastic Absorption

Abstract

We report a detailed and systematic study of wave propagation through a stochastic absorbing random medium. Stochastic absorption is modeled by introducing an attenuation constant per unit length $α$ in the free propagation region of the one-dimensional disordered chain of delta function scatterers. The average value of the logarithm of transmission coefficient decreases linearly with the length of the sample. The localization length is given by $ξ~ = ~ ξ_w ξ_α/ (ξ_w + ξ_α)$, where $ξ_w$ and $ξ_α$ are the localization lengths in the presence of only disorder and of only absorption respectively. Absorption does not introduce any additional reflection in the limit of large $α$, i.e., reflection shows a monotonic decrease with $α$ and tends to zero in the limit of $α\to\infty$, in contrast to the behavior observed in case of coherent absorption. The stationary distribution of reflection coefficient agrees well with the analytical results obtained within random phase approximation (RPA) in a larger parameter space. We also emphasize the major differences between the results of stochastic and coherent absorption.