Amplification or Reduction of Backscattering in a Coherently Amplifying or Absorbing Disordered Chain

TL;DR

This paper investigates how non-hermitian disorder affects localization and resistance in one-dimensional systems, revealing unified behavior in amplification and absorption cases with unique statistical properties.

Contribution

It introduces a unified resistance measure for both amplifying and absorbing disordered chains, highlighting differences from traditional Anderson localization.

Findings

Logarithmic resistance grows linearly with length.

Variance of resistance can be much smaller than in hermitian systems.

Distribution of resistance remains non-Gaussian at large lengths.

Abstract

We study localization properties of a one-dimensional disordered system characterized by a random non-hermitean hamiltonian where both the randomness and the non-hermiticity arises in the local site-potential; its real part being random, and a constant imaginary part implying the presence of either a coherent absorption or amplification at each site. While the two-probe transport properties behave seemingly very differently for the amplifying and the absorbing chains, the logarithmic resistance $u$ = ln$(1+R_4)$ where $R_4$ is the 4-probe resistance gives a unified description of both the cases. It is found that the ensemble-averaged $<u>$ increases linearly with length indicating exponential growth of resistance. While in contrast to the case of Anderson localization (random hermitean matrix), the variance of $u$ could be orders of magnitude smaller in the non-hermitean case, the distribution of $u$ still remains non-Gaussian even in the large length limit.