Density Expansion for the Mobility in a Quantum Lorentz Model

TL;DR

This paper develops a second-order density expansion for electron mobility in a quantum Lorentz model with hard-sphere scatterers, providing theoretical insights to guide future experiments to detect subtle logarithmic effects.

Contribution

It derives the second-order analytic correction and discusses its experimental detectability, extending the classical Boltzmann result for electron mobility in a realistic gas environment.

Findings

Logarithmic term in density expansion is consistent with experimental data.

Second-order correction derived analytically for the quantum Lorentz model.

Guidance provided for future experiments to observe the logarithmic density dependence.

Abstract

We consider the mobility of electrons in an environment of static hard-sphere scatterers, which provides a realistic description of electrons in Helium gas. A systematic expansion in the scatterer density is carried to second order relative to the Boltzmann result, and the analytic contribution at this order is derived, together with the known logarithmic term in the density expansion. It is shown that existing experimental data are consistent with the existence of the logarithmic term in the density expansion, but more precise experiments are needed in order to unambiguously detect it. We show that our calculations provide the necessary theoretical information for such an experiment, and give a detailed discussion of a suitable parameter range.