Towards a satisfactory formulation of the quantum Langevin equation

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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The quantum mechanical Langevin equation for a damped harmonic oscillator with operator-valued-noise, dat/dt=(-i omega - gamma )At+ lambda w(t), is reinvestigated. By assuming the canonical commutation relation at initial time, (A0, A0∗)=1, and a Hermitian operator for the Gaussian quantum noise w(t), it is shown that Streater's procedure to satisfy (At,At ∗)=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.

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ID Code:84988
Deposited On:28 Feb 2012 12:45
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