Quantum Dynamics with Strong Friction: the Quantum Smoluchowski Equation and Beyond

Philip Pechukas, Joachim Ankerhold, Hermann Grabert

The quantum Smoluchowski equation is an equation for the coordinate-diagonal elements of the density operator, and it is identical to the classical Smoluchowski equation. Here, the leading finite-friction correction to the quantum Smoluchowski equation is derived, for the particular case of the overdamped harmonic oscillator. It is in fact a quantum correction, different from the well-known classical correction, and it dominates the classical correction in the strong friction regime.

A. D. Jannussis, P. Filippakis, Th. Filippakis

Joachim Ankerhold, Philip Pechukas, Hermann Grabert

For a quantum system coupled to a heat bath environment the strong friction limit is studied starting from the exact path integral formulation. Generalizing the classical Smoluchowski limit to low temperatures, a time evolution equation for the position distribution is derived and the strong role of quantum fluctuations in this limit is revealed.

B. A. Arbuzov

Stefan Alexander Maier, Joachim Ankerhold

The strong-friction regime at low temperatures is analyzed systematically starting from the formally exact path-integral expression for the reduced dynamics. This quantum Smoluchowski regime allows for a type of semiclassical treatment in the inverse friction strength so that higher-order quantum corrections to the original quantum Smoluchowski equation [J. Ankerhold, P. Pechukas, and H. Grabert, Phys. Rev. Lett. 87, 086802 (2001); J. Ankerhold and H. Grabert, Phys. Rev. Lett. 101, 119903 (2008)] can be derived. Drift and diffusion coefficients are determined by the equilibrium distribution in position and are directly related to the corresponding action of extremal paths and fluctuations around them. It is shown that the inclusion of higher-order corrections reproduces the quantum enhancement above crossover for the decay rate out of a metastable well exactly.

Joachim Ankerhold, Hermann Grabert, Philip Pechukas