Projects per year

### 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 |
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Journal | Phys. Rev. B |

DOIs | |

State | Published - Nov 1 2019 |

### Bibliographical note

3 pages, 3 figures### Keywords

- cond-mat.dis-nn

### How much support was provided by MRSEC?

- Primary

### Reporting period for MRSEC

- Period 6

## Projects

- 2 Active

## MRSEC IRG-2: Sustainable Nanocrystal Materials

Kortshagen, U. R., Aydil, E. S., Campbell, S. A., Francis, L. F., Haynes, C. L., Hogan, C., Mkhoyan, A., Shklovskii, B. I. & Wang, X.

9/1/98 → …

Project: Research project