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Open Physics
tom 9
nr 1
The dynamical properties of an overdamped Brownian particle moving in an asymmetric bistable system with quantum fluctuations are investigated. Within the strong-friction limit (the quantum Smoluchowski regime), the analytic expression for the relaxation time of the system is derived by means of the projection-operator method, in which the effects of the memory kernels are taken into account. Based on the relaxation time, we consider both the overdamped quantum case and its classical counterpart.In these contexts, the effects of the quantum fluctuations and the asymmetry of the potential are discussed. It is found that: (i) The quantum effects in an asymmetric bistable system on time scales of the relaxation process are more prominent for lower temperatures and smaller asymmetries of the potential. (ii) The quantum effects speed up the rate of fluctuation decay of the state-space variable for lower temperatures. (iii) The asymmetry of the potential first slows down the rate of fluctuation decay of the state-space variable and then increases it.
Bistable systems present two degenerate metastable configurations separated by an energy barrier. Thermal or quantum fluctuations can promote the transition between the configurations at a rate which depends on the dynamical properties of the local environment (i.e., a thermal bath). In the case of classical systems, strong system-bath interaction has been successfully modelled by the Generalised Langevin Equation (GLE) formalism. Here we show that the efficient GLE algorithm introduced in Phys. Rev. B 89, 134303 (2014) can be extended to include some crucial aspect of the quantum fluctuations. In particular, the expected isotopic effect is observed along with the convergence of the quantum and classical transition rates in the strong coupling limit. Saturation of the transition rates at low temperature is also retrieved, in qualitative, yet not quantitative, agreement with the analytic predictions. The discrepancies in the tunnelling regime are due to an incorrect sampling close to the barrier top. The domain of applicability of the quasiclassical GLE is also discussed.
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