Stochastic pure states for quantum Brownian motion

Abstract

A semiclassical approach to explore the bistable kinetics of a Brownian particle in anonequilibrium environment Pradipta Ghosh, Anindita Shit, Sudip Chattopadhyay et al. Abstract. We give a new description of quantum Brownian motion in terms of stochastic pure states. The corresponding path integral propagator allows us to establish a direct connection to the classical Langevin equation, in the Schrödinger picture. We show that in the quantum domain, one is naturally led to consider two stochastic processes driving the Brownian dynamics, one of them representing thermal fluctuations, as in the classical case. The second process reflects growing entanglement between the Brownian particle and its environment, and is therefore a truly quantum noise process. Technically, our result rests on the representation of the full propagator of the Brownian particle and its environment in a coherent state basis. For open system dynamics that may be described by a master equation, such stochastic schemes have already been proven to be efficient Monte Carlo methods. Here, we give a new stochastic scheme that covers low temperatures and strong friction, the latter limit being the case Einstein originally investigated.

Description of non-Markovian effect in open quantum system with the discretized environment method

“…Independently on the γ value, a second physical cutoff can be used that is figured out from Eq. (12). We see indeed that a state in the environment has an effect on the system only if its initial population n 0 ν is non negligible.…”

Stochastic simulation of dissipation and non-Markovian effects in open quantum systems

“…The two coupled equations, Eqs. (17)(18) provide an exact reformulation of the system evolution if du S/E and dv S/E verify…”

“…The difference in computing time comes from the fact that smaller numerical time step should be used as the coupling strength increases to achieve good numerical accuracy, the main difficulty being to properly evaluate time integrals in Eq. (18). Denoting the time step by ∆t, ∆tω 0 = 1.2 × 10 −3 and ∆tω 0 = 2.2 × 10 −4 have been used for weak and strong coupling respectively.…”

“…The difference in numerical accuracy can be assigned to the second term in Eq. (18) which turns out to be crucial for numerical implementation. Stochastic simulations for strong coupling parameters (open circles) slightly differ from the results obtained with the hierarchical approach in ref.…”

Quantum Monte Carlo method applied to non-Markovian barrier transmission

“…In the Markovian limit, several methods have been proposed to treat fluctuation and dissipation starting from a quantum master equation of the system density [19,20,[22][23][24][25][26][27][28]. These methods have been extended also to treat non-Markovian effects, such as in quantum state diffusion (QSD) [29][30][31][32] or quantum Monte Carlo (QMC) methods [33]. Several groups have shown that these effects could eventually be simulated using a Feynman-Vernon influence functional [21,34] or directly stochastic master equations [35,36].…”