Kinetic equations for the quantized motion of a particle in a randomly perturbed potential field

Journal Article · Sat Dec 01 04:00:00 EST 1973 · J. Math. Phys. (N.Y.), v. 14, no. 12, pp. 1829-1836

DOI:https://doi.org/10.1063/1.1666255· OSTI ID:4331674

Besieris, I M; Tappert, F D

Within the framework of the first-order smoothing approximation and the long-time, Markovian approximation, kinetic equations are derived for the stochastic Wigner equation (the exact equation of evolution of the phase-space Wigner distribution function) and the stochastic Liouville equation (correspondence limit approximation) associated with the quantized motion of a particle described by a stochastic Schrodinger equation. In the limit of weak fluctuations - and long times, the transport equation for the average probability density of the particle in momentum space which was reported recently by Papanicolaou is recovered. Also, on the basis of the Novikov functional formalism, it is established that several of the approximate kinetic equations derived are identical to the exact statistical equations in the special case that the potential field is a delta -correlated (in time), homogeneous, wide-sense stationary, Gaussian process. (auth)

• Research Organization: Virginia Polytechnic Inst. and State Univ., Blacksburg
• Sponsoring Organization: USDOE
• NSA Number: NSA-29-028535
• OSTI ID: 4331674
• Journal Information: J. Math. Phys. (N.Y.), v. 14, no. 12, pp. 1829-1836, Journal Name: J. Math. Phys. (N.Y.), v. 14, no. 12, pp. 1829-1836; ISSN JMAPA
• Country of Publication: Country unknown/Code not available
• Language: English

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PHASE SPACE
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