Classical orbital magnetic moment in a dissipative stochastic system

Area of Science:

• Physics
• Statistical Mechanics
• Condensed Matter Physics

Background:

• Classical charged particles in magnetic fields exhibit complex dynamics.
• Langevin dynamics describes systems with dissipation and noise.
• The fluctuation-dissipation relation is key to understanding equilibrium states.

Purpose of the Study:

• To analytically investigate the dissipative-stochastic dynamics of a charged particle in a biharmonic potential and magnetic field.
• To examine the orbital magnetic moment generated by the particle under non-equilibrium conditions.
• To explore the influence of deviations from the standard fluctuation-dissipation relation on magnetic properties.

Main Methods:

• Analytical treatment of dissipative-stochastic dynamics.
• Analysis of a charged classical particle in a biharmonic potential and perpendicular magnetic field.
• Introduction of a parameter (η) to modify the fluctuation-dissipation relation.

Main Results:

• A steady state is achieved in the long-time limit.
• The charged particle generates a finite orbital magnetic moment.
• The magnetic moment exhibits a crossover from paramagnetic to diamagnetic behavior as η varies.
• The moment is zero at equilibrium (η=1).
• The magnitude of the orbital magnetic moment is non-monotonic with respect to the applied magnetic field, approaching zero at both small and large field limits.

Conclusions:

• The study demonstrates the generation of a classical orbital magnetic moment in a non-equilibrium steady state.
• The findings offer insights into classical orbital diamagnetism, potentially challenging the classical Bohr-van Leeuwen theorem.
• The results suggest possibilities for experimental realization.