The Brownian motion stochastic Schrödinger equation

Strunz, Walter T.

doi:10.1016/s0301-0104(01)00299-3

Cited by 48 publications

(48 citation statements)

References 34 publications

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“…It has also been shown [11,12] that the Markovian Redfield equation can preserve positivity if one applies a slippage of initial conditions that takes into account the non-Markovian effects on the early dynamics. Similar considerations have been proposed for different master equations [13,14,15]. As far as one considers the weak-coupling regime, all the master equations derived till now in the literature at second order of perturbation theory can be deduced from the non-Markovian Redfield equation.…”

Section: Introductionmentioning

confidence: 65%

Quantum master equation for a system influencing its environment

Esposito

Gaspard

2003

Phys. Rev. E

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A perturbative quantum master equation is derived for a system interacting with its environment, which is more general than the ones derived before. Our master equation takes into account the effect of the energy exchanges between the system and the environment and the conservation of energy in the finite total system. This master equation describes relaxation mechanisms in isolated nanoscopic quantum systems. In its most general form, this equation is non-Markovian and a Markovian version of it rules the long-time relaxation. We show that our equation reduces to the Redfield equation in the limit where the energy of the system does not affect the density of state of its environment. This master equation and the Redfield one are applied to a spin-environment model defined in terms of random matrices and compared with the solutions of the exact von Neumann equation. The comparison proves the necessity to allow energy exchange between the subsystem and the environment in order to correctly describe the relaxation in an isolated nanoscopic total system.

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Section: Introductionmentioning

confidence: 65%

Quantum master equation for a system influencing its environment

Esposito

Gaspard

2003

Phys. Rev. E

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“…A suitable basis to treat the environment B is a coherent state basis, |z 1 , z 2 , · · · , z n , · · · = |z in the Bargmann representation [1,30]. In such basis the resolution of the identity is given by 1 = dµ(z)|z z| with…”

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confidence: 99%

Multiple-Time Correlation Functions for Non-Markovian Interaction: Beyond the Quantum Regression Theorem

2005

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Multiple time correlation functions are found in the dynamical description of different phenomena. They encode and describe the fluctuations of the dynamical variables of a system. In this paper we formulate a theory of non-Markovian multiple-time correlation functions (MTCF) for a wide class of systems. We derive the dynamical equation of the reduced propagator, an object that evolve state vectors of the system conditioned to the dynamics of its environment, which is not necessarily at the vacuum state at the initial time. Such reduced propagator is the essential piece to obtain multiple-time correlation functions. An average over the different environmental histories of the reduced propagator permits us to obtain the evolution equations of the multiple-time correlation functions. We also study the evolution of MTCF within the weak coupling limit and it is shown that the multiple-time correlation function of some observables satisfy the Quantum Regression Theorem (QRT), whereas other correlations do not. We set the conditions under which the correlations satisfy the QRT. We illustrate the theory in two different cases; first, solving an exact model for which the MTCF are explicitly given, and second, presenting the results of a numerical integration for a system coupled with a dissipative environment through a non-diagonal interaction.PACS numbers: 3.65 Yz, 42.50 Lc Introduction and motivation. Many research contexts are focused on the dynamics of a system (S) that is affected by an environment (B) from which it cannot be considered isolated. Examples of such situations are encountered in statistical physics, condensed matter and quantum optics. We found a concrete example in the description of the dynamics of an atom (S) immersed in an electromagnetic field (B) [1,2].In some circumstances, the analysis of the dynamics of the system is done using the expectation values of its observables over state vectors of the whole system, and then averaging over the environmental degrees of freedom. However, in some other situations, like when studying the response of a system to an external EM field, some additional information is needed. In particular, for the analysis of the spectroscopic properties of a system some multiple-time correlation function (MTCF) has to be computed, usually a two-time correlation function.The dynamics of the system S is usually described through its reduced density operator. Such operator verifies some master equation that in the Markovian case is of Lindblad type [1,3,4,5,6,7]. Complementary to the master equation approach, a series of Monte-Carlo type of approaches based on the so called stochastic Schrödinger equations [1,4,8,9,10] have been developed in the last decade. In such schemes, the dynamics of system state vectors is integrated, and after an average is made over many realizations of environment histories that eventually are understood as a noise and takes into account the environment influence on S. In the non-Markovian case, within the context of nuclear magnetic resonance, the ...

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“…The crucial difference to the current result is that the propagator in [18] corresponds in fact to a zerotemperature expression of an artificial environment containing negative frequency oscillators. The new stochastic propagator G QBM (t) has a clear physical interpretation as visible in (22) and (23). Furthermore, it allows us to make the direct connection to the Langevin equation (6) as accomplished in this section.…”

Section: Quantum Brownian Motion Propagatormentioning

confidence: 91%

Stochastic pure states for quantum Brownian motion

Strunz¹

2005

New J. Phys.

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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.

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The Brownian motion stochastic Schrödinger equation

Cited by 48 publications

References 34 publications

Quantum master equation for a system influencing its environment

Quantum master equation for a system influencing its environment

Multiple-Time Correlation Functions for Non-Markovian Interaction: Beyond the Quantum Regression Theorem

Stochastic pure states for quantum Brownian motion

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