Projects per year
Abstract
We study the Anderson transition for threedimensional (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 nonHermitian analog of the Anderson model is used to describe randomlaser medium with local loss and amplification. We employ eigenvalue statistics to search for the Anderson transition. For 25\% smallestmodulus 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 nonHermitian 2D Anderson model, the transition is replaced by a crossover.
Original language  Undefined/Unknown 

Journal  Phys. Rev. B 
DOIs  
State  Published  Nov 1 2019 
Bibliographical note
3 pages, 3 figuresKeywords
 condmat.disnn
MRSEC Support
 Primary
Projects
 2 Finished

University of Minnesota MRSEC (DMR1420013)
Lodge, T. P. (PI)
11/1/14 → 10/31/20
Project: Research project

MRSEC IRG2: Sustainable Nanocrystal Materials
Kortshagen, U. R. (Coordinator), Aydil, E. S. (Senior Investigator), Campbell, S. A. (Senior Investigator), Francis, L. F. (Senior Investigator), Haynes, C. L. (Senior Investigator), Hogan, C. (Senior Investigator), Mkhoyan, A. (Senior Investigator), Shklovskii, B. I. (Senior Investigator) & Wang, X. (Senior Investigator)
11/1/14 → 10/31/20
Project: Research project