共查询到20条相似文献,搜索用时 15 毫秒
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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
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D. Bedeaux 《Physics letters. A》1977,62(1):10-12
It is shown that the random force in the Langevin equation for a nonlinear system may be chosen in such a way that the resulting equation is mathematically equivalent to the master equation. 相似文献
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Dr. Daniel F. Walls 《Zeitschrift für Physik A Hadrons and Nuclei》1970,234(3):231-241
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 However when strong coupling is present, such as in high intensity lasers this approximation is no longer valid.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. 相似文献
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Glenn T. Evans 《Molecular physics》2013,111(5):1337-1343
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. 相似文献
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In this work we derive a master equation to describe the interaction of emitters with structured reservoirs. The equation is applicable when the ‘freezing’ of atomic population decay and the existence of an atom-photon bound state are possible. Furthermore, the equation may be used for arbitrarily strong excitations of the reservoir. We show that for a wide range of reservoir spectral densities, this master equation can be reduced to the Markovian form. Applications to spontaneous emission and resonance fluorescence near the band edge are considered. We demonstrate that the stationary state is strongly dependent on the initial state of the decaying atom-field system. For resonance fluorescence, we confirm the prediction of positive stationary atomic inversion. 相似文献
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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. 相似文献
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Recently, a nonlinear master equation has been suggested to account for the effect of diffusion in the fluctuations of nonlinear systems away from equilibrium. An asymptotic expansion of the solutions of this master equation in the inverse of the diffusion constant is presented. The applicability of the method is illustrated with several examples of model chemical reactions. 相似文献
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H. Grabert 《Zeitschrift für Physik B Condensed Matter》1977,26(1):79-83
It is shown that the generalized Langevin equation derived by Mori is equivalent to the generalized master equation of Nakajima and Zwanzig. Both equations of motion are related, just in the same way as Heisenberg and Schrödinger picture are related. 相似文献
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Akira Onuki 《Journal of statistical physics》1978,19(4):325-332
A general master equation is shown to be equivalent to a Langevin equation whose noise is expressed as a linear superposition of Poissonian random variables (multi-Poissonian noise). As typical examples, a birth and death process and a Boltzmann-Langevin equation are given. 相似文献
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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. 相似文献
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Moshe Gitterman
George H. Weiss
《Physica A》1991,170(3):503-510A common strategy for approximating a master equation is to replace it by a diffusion-like equation. Many methods for deriving the form of such an equation have been suggested in the literature. We compare two of these in the light of an example in which the master equation can be solved exactly. One of these is the van KampenΩ-expansion, which generally does not give a useful approximation to the equilibrium solution, and the second is a technique which preserves the noise-free dynamics and gives the correct equilibrium solution. It is shown that the second moment calculated in the latter approximation is not an accurate one at short times. The difficulty is the restriction of the approximating equation to the diffusion form. 相似文献
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In order to describe quantum fluctuations a general method is developed, which also may be applied to nonstationary systems as well as to states far from thermodynamic equilibrium. After a concise derivation of the master equation quantum mechanically determined dissipation and fluctuation coefficients are introduced, for which several theorems and relations are given. By using these coefficients there is set up a general Fokker-Planck equation for the diffusion of the statistical operator due to quantum fluctuations. 相似文献
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F. J. Luider 《Zeitschrift für Physik A Hadrons and Nuclei》1978,284(2):187-188
In a number of publications the master equation of the exciton model of pre-equilibrium theory for nuclear reactions is solved by iterative means. It is shown in this note that an exact and analytical solution of this particular type of master equation exists and can be calculated. The time integral over the solution of this master equation can be obtained by a simple method, from which the summed pre-equilibrium and equilibrium emission spectra can be calculated very easily. 相似文献
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M. Razavy 《Physica A》1976,84(3):591-602
The present work consist of two parts: In the first part we apply the method of quasilinearization to the differential equation describing the time development of the quantum-mechanical probability density. In this way we derive the master equation without resorting to perturbation theory. In the second part of the paper, for a general form of the master equation which is an integro-differential equation, we test the accuracy of the Fokker-Planck approximation with the help of a solvable model. Then we study an alternative way of reducing the integro-differential equation to a partial differential equation. By expanding the transition probability W(q, q′), and the distribution function in terms of a complete set of functions, we show that for certain forms of W(q, q′), the master equation can be transformed exactly to partial differential equations of finite order. 相似文献
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Non-equilibrium properties of a model system comprised of a subsystem of magnetic moments strongly coupled to a selected Bose field mode and weakly coupled to a heat bath made of a plurality of Bose field modes was studied on the basis of non-equilibrium master equation approach combined with the approximating Hamiltonian method. A variational master equation derived within this approach is tractable numerically and can be readily used to derive a set of ordinary differential equations for various relevant physical variables belonging to the subsystem of magnetic moments. Upon further analysis of the thus obtained variational master equation, an influence of the macroscopic filling of the selected Bose field mode at low enough temperatures on the relaxation dynamics of magnetic moments was revealed. 相似文献
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Natsuki Hashitsumae Fumiaki Shibata Mayumi Shing¯u 《Journal of statistical physics》1977,17(4):155-169
A new memoryless expression for the equation of motion for the reduced density matrix is derived. It is equivalent to that proposed by Tokuyama and Mori, but has a more convenient form for the application of the perturbational expansion method. The master equation derived from this form of equation in the first Born approximation is applied to two examples, the Brownian motion of a quantal oscillator and that of a spin. In both examples the master equation is rewritten into the coherent-state representation. A comparison is made with the stochastic theory of the spectral line shape given by Kubo, and it is shown that this theory of the line shape can be incorporated into the framework of the present theory. 相似文献