Nonmonotonic confining potential and eigenvalue density transition for generalized random matrix model

Swapnil Yadav, Kazi Alam, K. A. Muttalib, and Dong Wang
Phys. Rev. E 103, 042137 – Published 27 April 2021

Abstract

We consider several limiting cases of the joint probability distribution for a random matrix ensemble with an additional interaction term controlled by an exponent γ (called the γ ensembles). The effective potential, which is essentially the single-particle confining potential for an equivalent ensemble with γ=1 (called the Muttalib-Borodin ensemble), is a crucial quantity defined in solution to the Riemann-Hilbert problem associated with the γ ensembles. It enables us to numerically compute the eigenvalue density of γ ensembles for all γ>0. We show that one important effect of the two-particle interaction parameter γ is to generate or enhance the nonmonotonicity in the effective single-particle potential. For suitable choices of the initial single-particle potentials, reducing γ can lead to a large nonmonotonicity in the effective potential, which in turn leads to significant changes in the density of eigenvalues. For a disordered conductor, this corresponds to a systematic decrease in the conductance with increasing disorder. This suggests that appropriate models of γ ensembles can be used as a possible framework to study the effects of disorder on the distribution of conductances.

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  • Received 20 October 2020
  • Revised 15 February 2021
  • Accepted 5 April 2021

DOI:https://doi.org/10.1103/PhysRevE.103.042137

©2021 American Physical Society

Physics Subject Headings (PhySH)

Statistical Physics & ThermodynamicsCondensed Matter, Materials & Applied PhysicsNonlinear Dynamics

Authors & Affiliations

Swapnil Yadav1,*, Kazi Alam1, K. A. Muttalib1, and Dong Wang2

  • 1Department of Physics, University of Florida, Gainesville, Florida 32611-8440, USA
  • 2Department of Mathematics, National University of Singapore, Singapore 119076

  • *Corresponding author: yadavswap@gmail.com

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Issue

Vol. 103, Iss. 4 — April 2021

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