Quantum Corrections to the Momentum Relaxation Time of a Brownian Particle

The long-time, heavy-mass limit of the quantum-mechanical momentum autocorrelation function of a massive particle immersed in a bath of light particles is considered. An expression for the momentum relaxation time is obtained. It is found that the symmetrized and canonical correlation functions yield identical results in this limit. The momentum relaxation time, which is the inverse of the friction constant of the quantum Fokker–Planck equation, is expanded in powers of Planck's constant to obtain the first quantum correction to the classical result. Quantum corrections for canonical correlation functions are discussed.