Classical Langevin dynamics of a charged particle moving on a sphere and diamagnetism: A surprise

¹  Raman Research Institute - Bangalore 560 080, India
²  Jawaharlal Nehru Centre for Advanced Scientific Research - Bangalore 560 064, India
³  CCMT, Department of Physics, Indian Institute of Science - Bangalore 560 012, India

Corresponding authors: nkumar@rri.res.in vijayk@physics.iisc.ernet.in

Received: 4 March 2009
Accepted: 10 March 2009

Abstract

It is generally known that the orbital diamagnetism of a classical system of charged particles in thermal equilibrium is identically zero —the Bohr-van Leeuwen theorem. Physically, this null result derives from the exact cancellation of the orbital diamagnetic moment associated with the complete cyclotron orbits of the charged particles by the paramagnetic moment subtended by the incomplete orbits skipping the boundary in the opposite sense. Motivated by this crucial but subtle role of the boundary, we have simulated here the case of a finite but unbounded system, namely that of a charged particle moving on the surface of a sphere in the presence of an externally applied uniform magnetic field. Following a real space-time approach based on the classical Langevin equation, we have computed the orbital magnetic moment that now indeed turns out to be non-zero and has the diamagnetic sign. To the best of our knowledge, this is the first report of the possibility of finite classical diamagnetism in principle, and it is due to the avoided cancellation.