Localization Bounds for an Electron Gas

TL;DR

This paper proves exponential decay of the two-point function in a Fermi gas, providing insights into localization phenomena relevant for quantum Hall systems, using fractional moments of the Green function.

Contribution

It establishes exponential decay bounds for a Fermi gas across all temperatures and in the ground state, extending localization analysis to this context.

Findings

Exponential decay of the two-point function in a Fermi gas.

Implications for the Integral Quantum Hall Effect.

Applicability across all temperatures and ground state.

Abstract

Mathematical analysis of the Anderson localization has been facilitated by the use of suitable fractional moments of the Green function. Related methods permit now a readily accessible derivation of a number of physical manifestations of localization, in regimes of strong disorder, extreme energies, or weak disorder away from the unperturbed spectrum. The present work establishes on this basis exponential decay for the modulus of the two--point function, at all temperatures as well as in the ground state, for a Fermi gas within the one-particle approximation. Different implications, in particular for the Integral Quantum Hall Effect, are reviewed.