Solution of the master equation for Wigner's quasiprobability distribution in phase space for the Brownian motion of a particle in a double well potential
- Department of Electronic and Electrical Engineering, Trinity College, Dublin 2 (Ireland)
Quantum effects in the Brownian motion of a particle in the symmetric double well potential V(x)=ax{sup 2}/2+bx{sup 4}/4 are treated using the semiclassical master equation for the time evolution of the Wigner distribution function W(x,p,t) in phase space (x,p). The equilibrium position autocorrelation function, dynamic susceptibility, and escape rate are evaluated via matrix continued fractions in the manner customarily used for the classical Fokker-Planck equation. The escape rate so yielded has a quantum correction depending strongly on the barrier height and is compared with that given analytically by the quantum mechanical reaction rate solution of the Kramers turnover problem. The matrix continued fraction solution substantially agrees with the analytic solution. Moreover, the low-frequency part of the spectrum associated with noise assisted Kramers transitions across the potential barrier may be accurately described by a single Lorentzian with characteristic frequency given by the quantum mechanical reaction rate.
- OSTI ID:
- 21024120
- Journal Information:
- Journal of Chemical Physics, Vol. 127, Issue 7; Other Information: DOI: 10.1063/1.2759486; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9606
- Country of Publication:
- United States
- Language:
- English
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