Long-time tails in quantum Brownian motion

R. Jung, G.-L. Ingold und H. Grabert

Phys. Rev. A 32, 2510–2512 (1985) DOI: 10.1103/PhysRevA.32.2510

The authors address the problem of quantum Brownian motion at low temperatures and with arbitrarily strong damping. For a harmonically bound particle the zero-temperature correlation functions are shown to display long-time tails. At finite temperatures a power-law decay at intermediate times is followed by an exponential decay with time constant ℏ/2πkBT. The case of free Brownian motion is treated, and some general conclusions for nonlinear systems are drawn.