Exact results for a charged, harmonically trapped quantum gas at arbitrary temperature and magnetic field strength

TL;DR

This paper derives exact analytical expressions for the density matrix of a charged, harmonically trapped quantum gas in two dimensions under any temperature and magnetic field, offering new insights into magnetic effects on quantum systems.

Contribution

It provides the first exact formulas for the density matrix at arbitrary temperature and magnetic field, including a novel factorization of the Bloch density matrix.

Findings

Exact density matrix expressions for all temperatures and magnetic fields.

A new factorization method separating zero-field and field-dependent parts.

Extension potential to other dimensions and anisotropic confinements.

Abstract

An analytical expression for the first-order density matrix of a charged, two-dimensional, harmonically confined quantum gas, in the presence of a constant magnetic field is derived. In contrast to previous results available in the literature, our expressions are exact for any temperature and magnetic field strength. We also present a novel factorization of the Bloch density matrix in the form of a simple product with a clean separation of the zero-field and field-dependent parts. This factorization provides an alternative way of analytically investigating the effects of the magnetic field on the system, and also permits the extension of our analysis to other dimensions, and/or anisotropic confinement.