Classical Orbital Paramagnetism in Non-equilibrium Steady State

We report the results of our numerical simulation of classical-dissipative dynamics of a charged particle subjected to a non-Markovian stochastic forcing. We find that the system develops a steady-state orbital magnetic moment in the presence of a static magnetic field. Very significantly, the sign of the orbital magnetic moment turns out to be paramagnetic for our choice of parameters, varied over a wide range. This is shown specifically for the case of classical dynamics driven by a Kubo–Anderson type non-Markovian noise. Natural spatial boundary condition was imposed through (1) a soft (harmonic) confining potential, and (2) a hard potential, approximating a reflecting wall. There was no noticeable qualitative difference. What appears to be crucial to the orbital magnetic effect noticed here is the non-Markovian property of the driving noise chosen. Experimental realization of this effect on the laboratory scale, and its possible implications are briefly discussed. We would like to emphasize that the above steady-state classical orbital paramagnetic moment complements, rather than contradicts the Bohr–van Leeuwen (BvL) theorem on the absence of classical orbital diamagnetism in thermodynamic equilibrium.