Instanton Calculus of Lifshitz Tails

TL;DR

This paper resolves discrepancies in the asymptotic density of states for particles in random potentials and clarifies the role of instantons using a novel derivation method.

Contribution

It provides a new derivation employing a Lagrange multiplier field to clarify the physical interpretation of instantons in Lifshitz tail calculations.

Findings

Resolved previous disagreements on density of states asymptotics.

Clarified the physical role of instantons in the problem.

Introduced a new derivation method using a Lagrange multiplier field.

Abstract

For noninteracting particles moving in a Gaussian random potential, there exists a disagreement in the literature on the asymptotic expression for the density of states in the tail of the band. We resolve this discrepancy. Further we illuminate the physical facet of instantons appearing in replica and supersymmetric derivations with another derivation employing a Lagrange multiplier field.