# Anderson transition in three-dimensional systems with non-Hermitian disorder

Research output: Contribution to journalArticlepeer-review

9 Scopus citations

## Abstract

We study the Anderson transition for three-dimensional (3D) $N \times N \times N$ tightly bound cubic lattices where both real and imaginary parts of onsite energies are independent random variables distributed uniformly between $-W/2$ and $W/2$. Such a non-Hermitian analog of the Anderson model is used to describe random-laser medium with local loss and amplification. We employ eigenvalue statistics to search for the Anderson transition. For 25\% smallest-modulus complex eigenvalues we find the average ratio $r$ of distances to the first and the second nearest neighbor as a function of $W$. For a given $N$ the function $r(W)$ crosses from $0.72$ to 2/3 with a growing $W$ demonstrating a transition from delocalized to localized states. When plotted at different $N$ all $r(W)$ cross at $W_c = 6.0 \pm 0.1$ (in units of nearest neighbor overlap integral) clearly demonstrating the 3D Anderson transition. We find that in the non-Hermitian 2D Anderson model, the transition is replaced by a crossover.
Original language Undefined/Unknown Phys. Rev. B https://doi.org/10.1103/PhysRevB.101.014204 Published - Nov 1 2019

### Bibliographical note

3 pages, 3 figures

## Keywords

• cond-mat.dis-nn

• Primary

## Reporting period for MRSEC

• Period 6
• ### MRSEC IRG-2: Sustainable Nanocrystal Materials

9/1/98 → …

Project: Research project

• ### University of Minnesota MRSEC (DMR-1420013)

Lodge, T.

11/1/1410/31/20

Project: Research project