Quantum phase space function formulation of reactive flux theory
arXiv:cond-mat/0303319 · doi:10.1063/1.1579473
Abstract
On the basis of a coherent state representation of quantum noise operator and an ensemble averaging procedure a scheme for quantum Brownian motion has been proposed recently [Banerjee {\it et al}, Phys. Rev. E {\bf65}, 021109 (2002); {\bf66}, 051105 (2002)]. We extend this approach to formulate reactive flux theory in terms of quantum phase space distribution functions and to derive a time dependent quantum transmission coefficient - a quantum analogue of classical Kramers'-Grote-Hynes coefficient in the spirit of Kohen and Tannor's classical formulation. The theory is valid for arbitrary noise correlation and temperature. The specific forms of this coefficient in the Markovian as well as in the non-Markovian limits have been worked out in detail for intermediate to strong damping regime with an analysis of quantum effects. While the classical transmission coefficient is independent of temperature, its quantum counterpart has significant temperature dependence particularly in the low temperature regime.
20 pages, 10 figures, RevTex4
References in corpus (13)
- Brownian motors: noisy transport far from equilibrium
- Gaussian Wavepacket Dynamics: semiquantal and semiclassical phase space formalism
- Approach to Quantum Kramers' Equation and Barrier Crossing Dynamics
- The generalized Kramers' theory for nonequilibrium open one-dimensional systems
- Generalized quantum Fokker-Planck, diffusion and Smoluchowski equations with true probability distribution functions
- Analytical and numerical investigation of escape rate for a noise driven bath
- Theory of non-stationary activated rate processes : nonexponential relaxation kinetics
- Quantum Kramers' equation for energy diffusion and barrier crossing dynamics in the low friction regime
- The Kramers Problem in the Energy-Diffusion Limited Regime
- A simple semiclassical approach to Kramers' problem
- Irreversibble Bimolecular Reactions of Langevin Particles
- On the Generalized Kramers Problem with Exponential Memory Friction
- Quantum Smoluchowski equation: Escape from a metastable state
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