The strong system-bath correlation is a typical initial condition in many condensed matter and some quantum optical systems. Here, the dynamics of a spin interacting with a spin bath through an intermediate spin are studied. Initial correlations between the spin and the intermediate spin are taken into account. The exact analytical expression for the evolution operator of the spin is found. Furthermore, correlated projection superoperator techniques are applied to the model and a time-convolutionless master equation to second order is derived. It is shown that the time-convolutionless master equation to second order reproduces the exact dynamics for timescales of the order 1/γ, where γ is the coupling of the central spin to the intermediate spin. It is found that there is a strong dependence on the initial system-bath correlations in the dynamics of the reduced system, which cannot be neglected.
Abstract. Firstly, the Markovian stochastic Schrödinger equations are presented, together with their connections with the theory of measurements in continuous time. Moreover, the stochastic evolution equations are translated into a simulation algorithm, which is illustrated by two concrete examples -the damped harmonic oscillator and a two-level atom with homodyne photodetection. Then, we consider how to introduce memory effects in the stochastic Schrödinger equation via coloured noise. Specifically, the approach by using the Ornstein-Uhlenbeck process is illustrated and a simulation for the non-Markovian process proposed. Finally, an analytical approximation technique is tested with the help of the stochastic simulation in a model of a dissipative qubit.
The strong system-bath correlation is a typical initial condition in many condensed matter and some quantum optical systems. Here, the dynamics of a spin interacting with a spin bath through an intermediate spin are studied. Initial correlations between the spin and the intermediate spin are taken into account. The exact analytical expression for the evolution operator of the spin is found. Furthermore, correlated projection superoperator techniques are applied to the model and a timeconvolutionless master equation to second order is derived. It is shown that the time-convolutionless master equation to second order reproduces the exact dynamics for time-scales of the order 1/γ, where γ is the coupling of the central spin to the intermediate spin. It is found that there is a strong dependence on the initial system-bath correlations in the dynamics of the reduced system, which cannot be neglected.
Open quantum systems are studied from the thermodynamical point of view unifying the principle of maximum informational entropy and the hypothesis of relaxation times hierarchy. The result of the unification is a non-Markovian and local-in-time master equation that provides a direct connection for dynamical and thermodynamical properties of open quantum systems. The power of the approach is illustrated by the application to the damped harmonic oscillator and the damped driven two-level system, resulting in analytical expressions for the non-Markovian and nonequilibrium entropy and inverse temperature.
-The dynamics of finite dimension open quantum systems is studied with the help of the simplest possible form of projection operators, namely the ones which project only onto one dimensional subspaces. The simplicity of the action of the projection operators always leads to an analytical solution of the dynamical master equation, even in the non-Markovian case, in any perturbative order. The analytical solution correctly reproduces the short-time dynamics, and can be used to recursively recover the dynamics for an arbitrary time interval with arbitrary precision. The necessary number of relevant degrees of freedom to completely characterise an open quantum system is (n − 1)(n + 2)/2, where n is the dimension of the Hilbert space of the open system. The method is illustrated by two examples, the relaxation of a qubit in a thermal bath and the dynamics of two interacting qubits in a common environment.Introduction. -The understanding of the dynamics of open quantum systems is necessary to describe many interesting phenomena such as photosynthesis [1], the transport in living cells [2] and the dynamics of quantum systems in strong laser fields [3]. Recently, several different approaches to study open systems have been suggested [4-8, 10, 13]. These approaches significantly differ from each other and describe certain properties of open systems from different points of view. By choosing the most appropriate method to describe an open system one may successfully study the relevant characteristics of the system with a reasonable accuracy. Despite the significant success of the theoretical investigation it is still difficult to derive analytical or, even, numerical results for a general open system, especially, in the non-Markovian case. Typically, non-Markovian master equations have very complicated dependence on time and even a numerical study of such equations is a non-trivial task.In this letter we suggest an approach, based on a special class of projection operators, which allows to study the dynamics of a broad class of open systems. Application of the suggested technique to finite dimension open quantum systems always leads to an integrable set of differential equations. The number of the equations, which are necessary to characterise an open system, is lesser than the dimension of the reduced density operator of the open
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