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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
How much support was provided by MRSEC?
 Primary
Reporting period for MRSEC
 Period 6

MRSEC IRG2: 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
