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Master equation
About: Master equation is a research topic. Over the lifetime, 10541 publications have been published within this topic receiving 276095 citations.
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TL;DR: In this paper, a two macro-variable dynamical model based on Kubo's treatement of the master equation was developed to investigate the role of nearest neighbors correlations in the relaxation of the High Spin fraction in spin crossover compounds.
Abstract: In order to investigate the role of nearest neighbors correlations in the relaxation of the High Spin fraction in spin crossover compounds, we have developed a two macro-variable dynamical model based on Kubo's treatement of the master equation. This is compared to the local equilibrium approach, where short-range correlations are assumed to follow adiabatically the long range-order parameter. The sigmoidal shape of the relaxation, previously associated with the effects of interactions, and the so-called “tail effect”, i.e. the extra-slowing down at long times due to the correlations are obtained. The accurate comparison to experimental relaxation data confirms the coexistence of short-range and long-range interactions in spin-crossover solids.
62 citations
TL;DR: The asymptotic dependence of trapping time on N, the number of sites per trap, found to be proportional to N ln N by Pearlstein (1966) and by Robinson (1967) in square networks, has been verified and extended to the triangular case.
62 citations
TL;DR: In this paper, Green's functions are derived for Laplace transformed master equations (here described in the language of hopping excitons) on finite chains with either periodic or free-end boundary conditions, and with either a disruptive (substitutional impurity) or a nondisruptive quencher.
Abstract: Four separate but related contributions to the theory of quenched stochastic processes in one dimension are presented. First, Green's functions are derived for Laplace transformed master equations (here described in the language of, but not restricted to, hopping excitons) on finite chains with either periodic or free‐end boundary conditions, and with either a disruptive (substitutional impurity) or a nondisruptive quencher. We solve these problems in spectral form for short‐range quenching with arbitrary quencher location and quenching rate parameter Qo. Second, the analogous random walk situations are treated. The solution of the generating function (finite‐difference analog of the Laplace transform) equation is identical to that of the Laplace‐transformed master equation with a disruptive quencher, but not with a nondisruptive quencher. Unlike the master equation case, slowly damped oscillations of the random walk chain excitation function can exist. Other differences also exist and are discussed; thes...
62 citations
TL;DR: In this article, it was shown that the quantum evolution of the pumped couplers can be closed in a two-qubit Hilbert space spanned by vacuum and single-photon states only.
Abstract: Schemes for optical-state truncation of two cavity modes are analysed. The systems, referred to as the nonlinear quantum scissors devices, comprise two coupled nonlinear oscillators (Kerr nonlinear coupler) with one or two of them pumped by external classical fields. It is shown that the quantum evolution of the pumped couplers can be closed in a two-qubit Hilbert space spanned by vacuum and single-photon states only. Thus, the pumped couplers can behave as a two-qubit system. Analysis of time evolution of the quantum entanglement shows that Bell states can be generated. A possible implementation of the couplers is suggested in a pumped double-ring cavity with resonantly enhanced Kerr nonlinearities in an electromagnetically induced transparency scheme. The fragility of the generated states and their entanglement due to the standard dissipation and phase damping are discussed by numerically solving two types of master equations.
62 citations
TL;DR: In this article, the authors used the methods developed by Prigogine and coworkers to establish a rigorous statistical mechanical theory for non-uniform classical systems and derived the general equations of evolution for the singlet distribution and for the s -body correlation functions.
62 citations