Quantum effects in the Brownian motion of a particle in a double well potential in the overdamped limit.
Citation:Coffey WT, Kalmykov YP, Titov SV, Cleary L, Quantum effects in the Brownian motion of a particle in a double well potential in the overdamped limit., The Journal of chemical physics, 131, 8, 2009, 084101
Quantum effects in the Brownian motion of a particle in a double well potential in the overdamped limit.pdf (Published (publisher's copy) - Peer Reviewed) 275.7Kb
Quantum effects in the noninertial Brownian motion of a particle in a double well potential are treated via a semiclassical Smoluchowski equation for the time evolution of the reduced Wigner distribution function in configuration space allowing one to evaluate the position correlation function, its characteristic relaxation times, and dynamic susceptibility using matrix continued fractions and finite integral representations in the manner of the classical Smoluchowski equation treatment. Reliable approximate analytic solutions based on the exponential separation of the time scales of the fast intrawell and slow overbarrier relaxation processes are given. Moreover, the effective and the longest relaxation times of the position correlation function yield accurate predictions of both the low and high frequency relaxation behavior. The low frequency part of the dynamic susceptibility associated with the Kramers escape rate behaves as a single Lorentzian with characteristic frequency given by the quantum-mechanical reaction rate solution of the Kramers problem. As a particular example, quantum effects in the stochastic resonance are estimated.
Type of material:Journal Article
Series/Report no:The Journal of chemical physics
Availability:Full text available
Keywords:Electronic & Electrical Engineering, Electronic & Electrical Engineering, Electronic & Electrical Engineering