Hasegawa, H. ; Klauder, J. R. ; Lakshmanan, M.
(1985)
*Towards a satisfactory formulation of the quantum Langevin equation*
Journal of Physics A: Mathematical and General, 18
(3).
L123.
ISSN 0305-4470

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Official URL: http://iopscience.iop.org/0305-4470/18/3/005

Related URL: http://dx.doi.org/10.1088/0305-4470/18/3/005

## Abstract

The quantum mechanical Langevin equation for a damped harmonic oscillator with operator-valued-noise, da_{t}/dt=(-i omega - gamma )A_{t}+ lambda w(t), is reinvestigated. By assuming the canonical commutation relation at initial time, (A_{0}, A_{0}∗)=1, and a Hermitian operator for the Gaussian quantum noise w(t), it is shown that Streater's procedure to satisfy (A_{t},A_{t} ∗)=1 for all later time yields an improved result: the noise operator w(t) can be determined universally and normalised such that, by choosing lambda ^{2}=2 gamma ( beta h(cross) omega )^{-1}, the (symmetrised) power spectrum of w(t) is equal to the physically significant form 1/2 beta h(cross) omega coth(1/2 beta h(cross) omega ), where beta is the inverse temperature of the heat bath, thus ensuring the beta -KMS correlation functions for any pair of operators.

Item Type: | Article |
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Source: | Copyright of this article belongs to Institute of Physics. |

ID Code: | 84988 |

Deposited On: | 28 Feb 2012 12:45 |

Last Modified: | 28 Feb 2012 12:45 |

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