Dissipative effects on the localization of a charged oscillator in a magnetic field

We consider the effect of dissipation on a charged, quantum harmonic oscillator coupled to a heat bath, in the presence of an external magnetic field. General conclusions about the equal-time position autocorrelation functions can be reached by using only those properties of the generalized susceptibility tensor imposed by fundamental physical principles. Explicit calculations are made for an Ohmic heat bath at zero temperature, enabling us to show that (unlike the problem without the magnetic field where dissipation always leads to enhanced localization) when the magnetic field is stronger than a certain critical value, weak dissipation actually delocalizes the oscillation of the charged particle.

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