Bohr-van Leeuwen theorem in non-commutative space

TL;DR

This paper investigates the Bohr-van Leeuwen theorem in non-commutative space, revealing that the theorem generally does not hold and leading to non-zero magnetization in classical charged particle systems.

Contribution

It demonstrates that non-commutative geometry causes the Bohr-van Leeuwen theorem to break down, providing new insights into classical magnetization in such spaces.

Findings

Bohr-van Leeuwen theorem is generally violated in non-commutative space.

Classical partition function yields non-zero magnetization in non-commutative space.

Non-commutative geometry affects classical magnetic properties.

Abstract

Bohr-van Leeuwen theorem has been studied in non-commutative space where the space coordinates do not commute. It has been found that in non-commutative space Bohr-van Leeuwen theorem, in general, is not satisfied and a classical treatment of the partition function of charged particles in a magnetic field gives rise to non zero magnetization.