Issue
EPL
Volume 87, Number 1, July 2009
Article Number 17002
Number of page(s) 3
Section Condensed Matter: Electronic Structure, Electrical, Magnetic and Optical Properties
DOI http://dx.doi.org/10.1209/0295-5075/87/17002
Published online 15 July 2009
EPL, 87 (2009) 17002
DOI: 10.1209/0295-5075/87/17002

On the Bohr-van Leeuwen theorem, the non-existence of classical magnetism in thermal equilibrium

T. A. Kaplan and S. D. Mahanti

Department of Physics and Astronomy and Institute for Quantum Sciences, Michigan State University East Lansing, MI 48824, USA

kaplan@pa.msu.edu

received on 17 June 2009; accepted in final form by G. A. Sawatzky on 25 June 2009; published July 2009
published online 15 July 2009

Abstract
We point out that the classical Langevin equation for a charged particle moving on a ring in a constant magnetic field perpendicular to the ring leads at long times to thermal equilibrium and to zero magnetic moment, consistent with the Bohr-van Leeuwen theorem. This fact is a counter-example to the recent claim that the Langevin equation leads to a non-zero diamagnetic moment in thermal equilibrium when the particle moves in a finite but unbounded space.

PACS
75.20.-g - Diamagnetism, paramagnetism, and superparamagnetism.
05.40.-a - Fluctuation phenomena, random processes, noise, and Brownian motion.
71.10.Ca - Electron gas, Fermi gas.

© EPLA 2009