Quantum Smoluchowski equation: A systematic study

Abstract

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 [PRL 87, 086802 (2001), PRL 101, 11903 (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.

15 pages, 4 figures

References in corpus (3)

• Demon-free quantum Brownian motors
• Quantum Smoluchowski equation for driven systems
• Comment on 'Semiclassical Klein-Kramers and Smoluchowski equations for the Brownian motion of a particle in an external potential'

Cited by in corpus (12)

• Synchronization in a semiclassical Kuramoto model
• Quantum Brownian Motion with Inhomogeneous Damping and Diffusion
• Quantum entropy production in phase space
• Low-Temperature Quantum Fokker-Planck and Smoluchowski Equations and Their Extension to Multistate Systems
• Quantum fluctuation theorems in the strong damping limit
• Beating the House: Fast Simulation of Dissipative Quantum Systems with Ensemble Rank Truncation
• On the Small Mass Limit of Quantum Brownian Motion with Inhomogeneous Damping and Diffusion
• Semiclassical theory of energy diffusive escape in a Duffing oscillator
• Low-temperature quantum fluctuations in overdamped ratchets
• Current-flux characteristics in mesoscopic nonsuperconducting rings
• Non-Markovian quantum Brownian motion: a non-Hamiltonian approach
• Current characteristics of mesoscopic rings in quantum Smoluchowski regime