Magnetic-field effects on the motion of a charged particle in a heat bath

In a recent paper, Ford, Lewis, and O'Connell [Phys. Rev. A 37, 4419 (1988)] considered a charged quantum particle moving in an arbitrary potential and linearly coupled to a heat bath, and they showed that the macroscopic equation describing the time development of the particle motion is in the form of a quantum generalized Langevin equation. We generalize these results to include the presence of an external magnetic field. We find that the magnetic field manifests itself in the presence of an additional term in the Langevin equation, which is the quantum generalization of the Lorentz force, but the magnetic field does not affect the memory function nor the random force appearing in the quantum Langevin equation. It follows that the noise-noise autocorrelation function, as well as the nonequal time commutator of the noise, is the same as that in the absence of a magnetic field. The case of a blackbody radiation heat bath is shown to be easily analyzed as a special case of our general formalism.

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