Prog. Theor. Phys. Vol. 91 No. 2 (1994) pp. 219-236
Derivation of Master Equation for Totally Quadratic System in Quantum Brownian Motion
Department of Physics, Kyoto University, Kyoto 606-01
(Received October 13, 1993)
We consider Quantum Brownian motion of a toy model, which is a harmonic oscillator that interacts with environment consisting of harmonic oscillators through both qQ and pP types of coupling. At first, we formally derive exact master equation following Unruh and Zurek's method. Subsequently we estimate the behavior of the coefficients in the master equation at initial stage and at late time stage under weak coupling approximation. We find that, as the model with qQ coupling only, the system in supraohmic environment is less dissipative and less diffusive beyond the cutoff time scale than the system in ohmic environment. The cause is due to the weakness of spectral densities of environment in infrared sector. We also find that the remarkable feature of the coexistence of qQ and pP coupling is steep dependence of dissipative coefficients on time at initial stage compared with the case of qQ coupling only or pP coupling only. Further we find that the sign of the dissipation coefficient at initial stage can be negative, that is, the system can be anti-dissipative.
DOI : 10.1143/PTP.91.219
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Citing Article(s) :
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