Time correlations in a confined magnetized free-electron gas

TL;DR

This paper investigates how a flat wall affects the time-dependent correlation functions of a degenerate quantum electron gas in a magnetic field, revealing faster decay near the wall and independence from wall orientation.

Contribution

It provides a detailed analysis of time correlations in a confined magnetized electron gas, including effects of wall orientation and position, using eigenfunction expansions and Fourier transforms.

Findings

Faster decay of correlations near the wall compared to bulk

Independence of correlation form from wall orientation near the wall

Numerical results support analytical findings

Abstract

The time-dependent pair correlation functions for a degenerate ideal quantum gas of charged particles in a uniform magnetic field are studied on the basis of equilibrium statistics. In particular, the influence of a flat hard wall on the correlations is investigated, both for a perpendicular and a parallel orientation of the wall with respect to the field. The coherent and incoherent parts of the time-dependent structure function in position space are determined from an expansion in terms of the eigenfunctions of the one-particle Hamiltonian. For the bulk of the system, the intermediate scattering function and the dynamical structure factor are derived by taking successive Fourier transforms. In the vicinity of the wall the time-dependent coherent structure function is found to decay faster than in the bulk. For coinciding positions near the wall the form of the structure function turns out to be independent of the orientation of the wall. Numerical results are shown to corroborate these findings.