On the Bohr-van Leeuwen theorem, the non-existence of classical magnetism in thermal equilibriumT. A. Kaplan and S. D. Mahanti
Department of Physics and Astronomy and Institute for Quantum Sciences, Michigan State University East Lansing, MI 48824, USA
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
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.
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