共查询到20条相似文献,搜索用时 15 毫秒
1.
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. 相似文献
2.
We deal in this paper with systems driven by white or colored Poisson noise. For a free Brownian particle under the influence of white Poisson noise an exact generalized master equation in position space is obtained. In the Gaussian and Smoluchowski limits, known results are recovered. For a general process defined by a stochastic differential equation, with colored Poisson noise, we find an approximate generalized master equation, including first order terms in the correlation time and the first correction to the gaussianity. Under a more restrictive approximation, the stationary distribution function is given. This is used to study the phase transition in the steady state for a Verhulst model. Corrections to the gaussianity are discussed in this case. 相似文献
3.
H. Grabert 《Zeitschrift für Physik B Condensed Matter》1982,49(2):161-172
The paper reexamines the treatment of irreversible quantum systems by master equations. Shortcomings of the conventional theory of quantum Markov processes pointed out by Talkner are analyzed. It is shown that a frequently used quantum regression hypothesis is not correct, in general. A new generalized master equation determining the relaxation to equilibrium is derived by means of time-dependent projection operator techniques. It is shown that this master equation also determines the time evolution of equilibrium correlations and response functions. The Markovian approximation is discussed, and a new type of Markovian limit, the Brownian motion limit, is introduced besides the weak coupling limit. The shortcomings of the conventional approach are resolved by deriving new formulae for the time evolution of the correlation and response functions of a quantum Markov process. The symmetries of the process are emphasized, and it is shown how the fluctuation-dissipation theorem and the detailed balance symmetry emerge from the master equation approach. 相似文献
4.
《Physica A》1988,149(3):507-534
A theory of light scattering under random perturbations is formulated. The stochastic process considered in this paper is general enough in the sense that the process reduces to a single two-state jump process on the one limit and to the Gaussian process on the other limit. The light scattering rate, which is essentially a four-time correlation function, can be evaluated exactly for this model with the aid of the “partial cumulant expansion method”. Based on this a new method of a generalized master equation approach with memory effect is proposed. It is shown that the imhomogeneous term in a time-convolution expansion formula plays an essential role in the second order optical process, although the term is usually neglected in most problems of the master equation approach. The scattering rate is finally expressed as a superposition of continued fractions. Numerical calculations are performed and detailed discussions on coherence properties of the process are given. 相似文献
5.
L.A. Lugiato 《Physica A》1975,81(4):565-596
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. 相似文献
6.
7.
Using published results on continuous time random walk theories, we show that the random walk theory of Gissler and Rother is equivalent to a master equation with jumps to further neighbor sites. We extend the theory to include time correlations over two jumps. No special assumptions are made in the analysis, so that the theory may be applied to any lattice type with a general time probability distribution for jumps; a generalized second-order differential equation is given for the results. In the special case of an exponential time probability density, a simple homogeneous second order differential equation is obtained which is shown to be equivalent to a certain two-state master equation model. 相似文献
8.
Anomalous transport in fluid fleld with random waiting time depending on the preceding jump length
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《中国物理 B》2016,(11)
Anomalous(or non-Fickian) transport behaviors of particles have been widely observed in complex porous media.To capture the energy-dependent characteristics of non-Fickian transport of a particle in flow fields,in the present paper a generalized continuous time random walk model whose waiting time probability distribution depends on the preceding jump length is introduced,and the corresponding master equation in Fourier-Laplace space for the distribution of particles is derived.As examples,two generalized advection-dispersion equations for Gaussian distribution and levy flight with the probability density function of waiting time being quadratic dependent on the preceding jump length are obtained by applying the derived master equation. 相似文献
9.
We derive a fractional Fokker-Planck equation for subdiffusion in a general space- and time-dependent force field from power law waiting time continuous time random walks biased by Boltzmann weights. The governing equation is derived from a generalized master equation and is shown to be equivalent to a subordinated stochastic Langevin equation. 相似文献
10.
Michio Tokuyama 《Physica A》1980,102(3):399-430
A new method of finding nonlinear Langevin type equations of motion for relevant macrovariables and the corresponding master equation for systems far from thermal equilibrium is presented by generalizing the time-convolutionless formalism proposed previously for equilibrium hamiltoian systems by Tokuyama and Mori. The Langevin type equation consists of a fluctuating force, and the nonlinear drift coefficients which are always identical to those of the master equation. A simple formula which relates the drift coefficients to the time correlation of the fluctuating forces is derived. This is a generalization of the fluctuation-dissipation theorem of the second kind in equilibrium systems and is valid not only for transport phenomena due to internal fluctuations but also for transport phenomena due to externally-driven fluctuations. A new cumulant expansion of the master equation is also obtained. The conditions under which a Langevin and a Fokker-Planck equation of a generalized type for non-equilibrium open systems can be derived are clarified.The theory is illustrated by studying hydrodynamic fluctuations near the Rayleigh-Bénard instability. The effects of two kinds of fluctuations, internal fluctuations of irrelevant macrovariables and external (thermal) noises, on the convective instability are investigated. A stochastic Ginzburg-Landau type equation for the order parameter and the corresponding nonlinear Fokker-Planck equation are derived. 相似文献
11.
H. Grabert P. Talkner P. Hänggi H. Thomas 《Zeitschrift für Physik B Condensed Matter》1978,29(3):273-280
We study the time-evolution of the joint and the conditional probability of macroscopic variables of a closed system from a microscopic point of view. We derive an exact generalized master equation for their time rate of change which consists of two parts, one instantaneous and local in state space, the other retarded and nonlocal in state space. It is represented by stochastic operators depending both on the initial preparation and on the initial macrodistribution, which reflects the non-Markovian character of the process. The connection with the time-evolution of the single-event probability is discussed.Work Supported by the Swiss National Science Foundation 相似文献
12.
13.
An exact non-equilibrium Ornstein-Zernike (OZ) equation is derived for lattice fluid systems whose time development is given by a generalized master equation. The derivation is based on a generalization of the Montroll-Weiss continuous-time random walk on a lattice, and on their relationship with master equation solutions. Time dependent direct and total correlation functions are defined in terms of the generating functions for the probability densities of the random walker, such that, in the infinite time limit the equilibrium OZ equation is recovered. A perturbative analysis of the time dependent OZ equation is shown to be formally analogous to the perturbation of the Bloch equation in quantum field theory. Analytic results are obtained, under the mean spherical approximation, for the time dependent total correlation function for a one-dimensional lattice fluid with exponential attraction. 相似文献
14.
The theory of the mean first passage time is developed for a general discrete non-Markov process whose time evolution is governed by a generalized master equation. The mean first passage time is determined by an adjoint matrix
+ in a form analogous to the Fokker Planck case. The theory is illustrated by two examples: A one-dimensional unit step non-Markov process and a non-Markov process with two-step transitions. Explicit expressions for the mean first passage time are derived. 相似文献
15.
Nobuhiko Mishima Tomio Yamakoshi Petrosky Miwae Yamazaki 《Journal of statistical physics》1976,14(4):359-380
An extension is given for the Fourier expansion method with the contraction technique, which was introduced by Balescu for quantum statistical systems. This is attained by introducing a diagrammatic method with a concept of moving contraction. Then the hierarchy equation for the Contracted Fourier coefficient of the Wigner distribution function is obtained. As an application, a generalized master equation involvingn-body collision effects and quantum statistical effects is also derived. 相似文献
16.
If the generalized momentum in the hamiltonian equations is considered as a rapidly varying stochastic function of time then a solution of the master equation is most easily obtained by applying the central limit theorem in much the same way as one does with the Langevin equation. 相似文献
17.
Robert Zwanzig 《Journal of statistical physics》1983,30(2):255-262
The migration of a classical dynamical system between regions of configuration space can be treated as a continuous time random walk between these regions. Derivation of a classical analog of the quantum mechanical generalized master equation provides expressions for the waiting time distribution in terms of transition memory functions. A short memory approximation to these memory functions is equivalent to the well-known transition state method. An example is discussed for which this approximation seems reasonable but is entirely wrong. 相似文献
18.
T. Mančal 《Czechoslovak Journal of Physics》1998,48(4):463-468
A general non-perturbative method is used for the solution of the generalized master equation (GME) for a simple two-level
model of the exciton-phonon system coupled to the termodynamic bath. The Argyres-Kelley projection superoperator is used to
exclude superfluous information contained in the density matrix. A new partly analytic method of the solution of the generalized
master equation is suggested and new analytical expressions for the memory functions are derived.
Presented at the Czech-Israeli-German Symposium “Dynamical Processes in Condensed Molecular Systems”, Prague, Czech Republic,
26–30 May 1997. 相似文献
19.
Victor F. Los 《Journal of statistical physics》2005,119(1-2):241-271
It is shown that the method proposed in V. F. Los [J. Phys. A: Math. Gen. 34: 638–6403 (2001)], which allows for turning the inhomogeneous time-convolution generalized master equation (TC-GME) into homogeneous (while retaining initial correlations) time-convolution generalized master equation (TC-HGME) for the relevant part of a distribution function, is fully applicable to the quantum case and to the time-convolutionless GME (TCL-GME). It is demonstrated by rederiving the TC-HGME and showing that it works in both the classical and quantum physics cases. The time-convolutionless HGME (TCL-HGME) retaining initial correlations, which is formally the same for both the classical and quantum physics, has also been derived. Both the TC-HGME and TCL-HGME are exact equations applicable on any timescale and allow for consecutive treating the initial correlations and collisions on the equal footing. A new equation for a momentum distribution function retaining initial correlations has been obtained in the linear in the density of quantum particles approximation. Connection of this equation to the quantum Boltzmann equation is discussed. 相似文献
20.
Anomalous transport in fluid field with random waiting time depending on the preceding jump length
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Anomalous (or non-Fickian) transport behaviors of particles have been widely observed in complex porous media. To capture the energy-dependent characteristics of non-Fickian transport of a particle in flow fields, in the present paper a generalized continuous time random walk model whose waiting time probability distribution depends on the preceding jump length is introduced, and the corresponding master equation in Fourier-Laplace space for the distribution of particles is derived. As examples, two generalized advection-dispersion equations for Gaussian distribution and lévy flight with the probability density function of waiting time being quadratic dependent on the preceding jump length are obtained by applying the derived master equation. 相似文献