两能级原子主方程和激光通道主方程的解之间的超对称性

提出了研究原子演化的Ket-Bra纠缠态方法,并用此方法给出了原子主方程的Kraus算符形式的解.在得到此新解后,发现它和激光通道主方程的解形式相似,表现了光场算符a,a~(+)与原子算符σ_-,σ_+之间具有某种超对称性.通过进一步的探讨,寻找到了Pauli算符的多种Bose表示.     

Master equations with memory for systems driven by classical noise

A non-Markovian master equation is obtained for a two level atom driven by a phase noisy laser. The derivation is based on obtaining an equation for the density operator of the system averaged over the previous histories of the external noise. Averaging over the current value of the noise variable by means of the Zwanzig-Nakajima projection operator technique leads to a master equation with memory and a local-in-time master equation. The solutions to the resultant non-Markovian master equation, the structural properties of the equation, and the amenability of the equation to unravelling by the quantum trajectory method are all investigated.     

A Theoretical Solution for a Nonlinear Master Equation

Based on the master equation describing the interaction of a single-mode bosonic state with a heat bath at finite temperature in the Born-Markov approximation, we constructed a new nonlinear master equation and derived the infinite operator sum representation of quasi-Kraus operators for the density operator     

Correspondence Between the Operational Element of an Amplitude Damping Harmonic Oscillator to the Kraus Operator of the Master Equation for Dissipation

We find the correspondence between the operational element of an amplitude damping harmonic oscillator and the Kraus operator solution to the master equation for dissipation. This reveals the equivalence between the two approaches to tackling the dissipation of oscillator-reservoir: one is solving the Kraus operator of the master equation, and the other is deriving the operational element of time evolution operator in the reservoir mode.     

Ket-Bra纠缠态方法研究含时外场中与热库耦合Qubit的演化

采用Ket-Bra纠缠态方法求解主方程, 研究了具有含时外场情况下单qubit和无相互作用的两qubit与热库耦合时的量子退相干、退纠缠现象. 对两qubit情形, 我们以共生纠缠度(concurrence)作为纠缠度量, 研究了其纠缠动力学演化过程. 研究表明即使系统内部不存在直接、间接的相互作用, 施加含时外场也能引起纠缠的震荡和复活, 这为通过施加控制外场抑制开放系统的退相干、退纠缠过程提供了理论支持.     

Optimally chosen Nakajima–Zwanzig master equation for mean field approximation

We define an ensemble of projection operators, each of which has an exact associated Nakajima–Zwanzig master equation for quantum open system evolution. A mean field approximation for the memory kernels is introduced that yields a completely determined inhomogeneous master equation for every projection operator. A specific projection operator is then chosen so that the master equation optimally matches an abstract mathematical form which preserves positivity, complete positivity, and correctly equilibrates. We study a nitrogen vacancy center in diamond interacting with ¹³C impurities to illustrate the method.     

Solving nonlinear master equation describing quantum damping by virtue of the entangled state representation

This paper solves the newly constructed nonlinear master equation dρ/dt=κ[2f (N) aρ (1/f (N-1))a+-a+aρ-ρa+a],where f(N) is an operator-valued function of N=a+a,for describing amplitude damping channel,and derives the infinite operator sum representation of quasi-Kraus operators for the density operator.It also shows that in this nonlinear process the initial pure number state density operator will evolve into the binomial field (a mixed state) when f (N)=1/(N+1)～(1/2).     

Higher order effects in the master equation for coupled systems

The usual derivations of the master equation for coupled systems such as the laser make an assumption of weak coupling both for the coupling of the components to their heat baths and for the internal coupling between the components. It is this second condition that we wish to relax. In the usual derivation of the irreversible part of the master equation the approximation is made that the density operator for the coupled system factorizes into a product of the density operators for the two components. However when strong coupling is present, such as in high intensity lasers this approximation is no longer valid. To illustrate how the irreversible part of the master equation may be derived without making the factorization ansatz we consider the case of two coupled boson fields. Our derivation leads to additional terms in the usual master equation arising from correlations between the heat baths introduced by the coupling. This modified master equation yields the correct stationary solution for the density operator of the coupled system, whereas the usual master equation leads to a stationary solution for the density operator correct for the free components only.     

Exact Solution for Non-Markovian Master Equation Using Hyper-operator Approach

Non-Markovian master equation of Harmonic oscillator and two-level systems are investigated using the hyper-operator approach. Exact solution of time evolution operator of Harmonic oscillator is obtained exactly. For two-level system the time evolution operator is exactly found and coefficients satisfy ordinary differential equation.     

A generalized Redfield equation with initial spin-lattice correlation

Using projection operator techniques, the Liouville equation for the spin density matrix, equipped with a time-dependent, anisotropic source, can be recast in the form of a Redfield-like master equation. The master equation is applied to the calculation of the E.S.R. intensity of a spin system exhibiting the triplet mechanism of CIDEP.     

Master equations for coupled systems

A formalism to cope with the problem of dynamically coupled systems is developed. A time-dependent projection operator of the type given by Willis-Picard and Grabert-Weidlich is used to derive a time-convolutionless master equation from the Liouville equation for the total composite system. A systematic perturbational expansion formula with respect to the interaction between systems is also given. Finally, the comparison with the usual non-Markoffian master equation is discussed.     

On the diffusion operator of the multivariate master equation

The eigenfunctions of the diffusion operator of the multivariate master equation, describing reaction diffusion systems, are calculated for various boundary conditions. This serves as a starting point for a systematic study of the general solution of the master equation. As a first application a perturbation expansion in the inverse of the diffusion constant is carried out.     

Solution of the master equation for quantum systems weakly coupled to reservoirs and far from thermal equilibrium

The Liouville operator of the master equation is decomposed into a part describing the proper system and another operator describing the interaction of the proper system with a set of reservoirs. If the motion of the proper system is described by a Hamiltonian, the corresponding solutions of the density matrix equation are spanned by all conserved quantities and are thus highly degenerate. We demonstrate how this degeneracy may be lifted by applying some sort of perturbation theory for degenerate systems. If there is only one relevant conserved quantity and if the heatbaths connect the quantum numbers of this conserved quantity by nearest-neighbour steps, the solution of the problem can be found explicitly. Otherwise the solution of the original master equation is reduced to a much simpler master equation of orderN, whereN is the number of conserved quantities. An application to a new type of parametric processes in nonlinear optics is given.     

非广延反应扩散系统的广义主方程

依据非平衡统计及密度算子方程，通过计算概率分布函数的时间变化，得到了非广延反应扩散系统在压力作用时其特征函数满足的广义主方程，其中非广延反应扩散系统的压力在Tsallis统计的框架下给出.与唯象理论中的主方程比较，新得到的方程不仅依赖于非广延参量q而且有更多的非线性项，因此更具有普遍性.当新的方程应用到单分子反应模型时, 非广延性对系统的稳定性将产生重要的作用, 特别是当系统接近临界状态时. 关键词： 主方程 非广延反应扩散系统 涨落     

Nakajima-Zwanzig's generalized master equation: Evaluation of the kernel of the integro-differential equation

A method is presented, which allows the exact elimination of the projection operator from the kernel of the Nakajima-Zwanzig generalized master equation without using perturbational expansions. Expressions for kernels of generalized master equations using several frequently occuring types of projection operators are derived explicitly. The application of this method for the exact derivation of generalized master equations describing the coherent and the coupled coherent and incoherent exciton motion is proposed. As another application, the derivation of the Smoluchowski equation is suggested.     

Theory of open systems I

A new method of treating open systems is presented. The normal treatment using the generalized master equation with the projection of Argyres and Kelley is meaningful only if the state of the reservoir never deviates appreciably from the reference state which appears in the projection. Otherwise, one must make at least a partial resummation of the perturbative expansion of the kernel of the generalized master equation. The present method avoids the introduction of a projection operator and allows us to overcome such resummation difficulties. It is based on an integrodifferential equation for the statistical operator of the composite system, which naturally provides a hierarchy of equations involving the statistical operator ?(t) of the open system and suitable quantities describing higher and higher order bath-system correlations. Treating the deviations of the bath from its initial equilibrium or stationary state as expansion parameters, one gets an approximation scheme, each step of which gives a closed system of equations for ?(t) and a suitable set of correlation quantities.Eliminating such quantities one obtains a closed linear integrodifferential equation for ?(t). The zeroth approximation in the deviations coincides with the Born approximation of the generalized master equation which uses the projection of Argyres and Kelley.On the other hand, even the first approximation is equivalent to the resummation of infinite contribution of the Born series of such a generalised master equation. When it is suitable, the concentration of the bath can also be used as an expansion parameter to handle the hierarchy.     

General-dyne unravelling of a thermal master equation

We analyze the unravelling of the quantum optical master equation at finite temperature due to direct, continuous, general-dyne detection of the environment. We first express the general-dyne Positive Operator Valued Measure (POVM) in terms of the eigenstates of a non-Hermitian operator associated to the general-dyne measurement. Then we derive the stochastic master equation obtained by considering the interaction between the system and a reservoir at thermal equilibrium, which is measured according to the POVM previously determined. Finally, we present a feasible measurement scheme, which reproduces general-dyne detection for any value of the parameter characterizing the stochastic master equation.     

Study of decoherence with a generalized master equation

The behavior of macroscopic system is investigated with a generalized master equation. Making use of a coarse-grained position operator based on the SO(3,1), we can derive that the macroscopic nature of this operator induces decoherence leading to classical behavior.     

Stationary momentum space solution of the Fokker-Planck equation for a simple model of a laser oscillator exhibiting spatial dispersion

Starting from a multimode hamiltonian for a system of radiating oscillators coupled with atomic reservoirs, the secular master equation for the radiation-density operator is calculated in the interaction picture after elimination of the atomic variables. Using the differential operator representation for coherent states this equation is transcribed into a multimode Fokker-Planck equation. The stationary solution in momentum space is given for the threshold region. Fourier transformation to configuration space results in a quasi-free energy formula for a laser oscillator exhibiting spatial dispersion.     

Open quantum Markovian systems and the microreversibility

The concept of microreversibility (detailed balance) as applied to open quantum Markovian systems is introduced. The properties of such systems obeying detailed balance are studied in detail. It is shown how microreversibility may be used to obtain the steady state solution for the density operator. Some properties of the eigenfunctions of the Liouville operator are discussed. The general formalism is applied to Pauli master equation and some other master equations describing the relaxation of oscillators, two-level atoms in contact with heat bath; parametric frequency conversion and a single mode laser.