New approach to deriving the Fokker-Planck equation in the Wigner representation

摘要

We exploit the so-called characteristic operator method to derive the Fokker-Planck equation in the Wigner representation. We introduce the characteristic operator of the Wigner representation and establish a set of fundamental differential equations for the action of the creation and annihilation operators on it. As an example, we show the derivation process of the Fokker-Planck equation for the damped harmonic oscillator in the Wigner representation by using the characteristic operator approach. This method provides us with a new convenient approach to deriving the phase-space Fokker-Planck equation in the Wigner representation.

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