Agarwal, G. S.
(1971)
*Brownian motion of a quantum oscillator*
Physical Review A, 4
(2).
pp. 739-747.
ISSN 1050-2947

Full text not available from this repository.

Official URL: http://pra.aps.org/abstract/PRA/v4/i2/p739_1

Related URL: http://dx.doi.org/10.1103/PhysRevA.4.739

## Abstract

The theory of Brownian motion of a quantum oscillator is developed. The Brownian motion is described by a model Hamiltonian which is taken to be the one describing the interaction between this oscillator and a reservoir. Use is made of the master equation recently derived by the author, to obtain the equation of motion for the various reduced phase-space distribution functions that are obtained by mapping the density operator onto c-number functions. The equations of motion for the reduced phase-space distribution functions are found to be of the Fokker-Planck type. On transforming the Fokker-Planck equation to real variables, it is found to have the same form as the Fokker-Planck equation obtained by Wang and Uhlenbeck to describe the Brownian motion of a classical oscillator. The Fokker-Planck equation is solved for the conditional probability (Green's function) which is found to be in the form of a two-dimensional Gaussian distribution. This solution is then used to obtain various time-dependent quantum statistical properties of the oscillator. Next, the entropy for a quantum oscillator undergoing Brownian motion is calculated and we show that this system approaches equilibrium as t→∞. Finally we show that in the weak-coupling limit the Fokker-Planck equation reduces to the one obtained by making the usual rotating-wave approximation.

Item Type: | Article |
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Source: | Copyright of this article belongs to The American Physical Society. |

ID Code: | 78886 |

Deposited On: | 23 Jan 2012 11:21 |

Last Modified: | 23 Jan 2012 11:21 |

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