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The quantum Langevin equation from the independent-oscillator model. (English) Zbl 0656.60074
Quantum probability and applications III, Proc. Conf., Oberwolfach/FRG 1987, Lect. Notes Math. 1303, 103-106 (1988).
[For the entire collection see Zbl 0627.00022.] Consider the quantum Langevin equation for the position operator x(t) of a Brownian particle in an extended potential V(x) $$ m\ddot x+\int\sp{t}\sb{-\infty}\mu (t-t')\dot x(t')dt'+V'(x)=F(t), $$ where the coupling to the heat bath is characterized by a friction or radiation- reaction force (with memory function $\mu$ (t)) and by a random Gaussian operator force F(t) with (symmetric) correlation $$ 2\sp{- 1}<F(t)F(t')+F(t')F(t)>=\pi\sp{-1}\int\sp{\infty}\sb{0}[Re({\bar \mu}(\omega +i0\sp+))]\hslash \omega \coth (\hslash \omega /2kT)\cos \omega (t-t')d\omega. $$ The term in square brackets completely characterizes the Langevin equation. The paper shows that this model can be derived on the basis of the independent-oscillator model of the heat bath, where the Brownian particle is coupled with springs to a large number of surrounding bath particles.
Reviewer: C.A.Braumann

60H99Stochastic analysis