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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 correlated projection superoperator technique is applied to the model of a central spin coupled to a spin bath via full Heisenberg interaction, and analytical solutions to both the Nakajima-Zwanzig and the time-convolutionless master equation are determined and compared with the results of the exact solution.
Abstract: The dynamics of an open quantum system is usually studied by performing a weak-coupling and weak-correlation expansion in the system-bath interaction. For systems exhibiting strong couplings and highly non-Markovian behavior this approach is not justified. We apply a recently proposed correlated projection superoperator technique to the model of a central spin coupled to a spin bath via full Heisenberg interaction. Analytical solutions to both the Nakajima-Zwanzig and the time-convolutionless master equation are determined and compared with the results of the exact solution. The correlated projection operator technique significantly improves the standard methods and can be applied to many physical problems such as the hyperfine interaction in a quantum dot.
60 citations
TL;DR: In this paper, the dissociation and recombination of H2 over the temperature range 1000-5000 K are calculated in a non-empirical manner, which involves the calculation of the state-to-state energy transfer rate coefficients, the solution of the 349 coupled equations which form the master equation, and the determination of the phenomenological rate coefficients.
Abstract: The dissociation and recombination of H2 over the temperature range 1000-5000 K are calculated in a nonempirical manner. The computation procedure involves the calculation of the state-to-state energy transfer rate coefficients, the solution of the 349 coupled equations which form the master equation, and the determination of the phenomenological rate coefficients. The nonempirical results presented here are in good agreement with experimental data at 1000 and 3000 K.
60 citations
TL;DR: The model recovers experimental observations on hetropolymers when using their properties inside the pore, such as stiffness and polymer-pore interaction, and shows that the most probable translocation time is proportional to the polymer length, and inversely proportional toThe first or second power of the voltage, depending on the initial conditions.
Abstract: We study voltage driven translocation of a single stranded DNA through a membrane channel. Our model, based on a master equation approach, investigates the probability density function of the translocation times, and shows that it can be either double peaked or mono peaked, depending on the system parameters. We show that the most probable translocation time is proportional to the polymer length, and inversely proportional to the first or second power of the voltage, depending on the initial conditions. The model recovers experimental observations on hetropolymers when using their properties inside the pore, such as stiffness and polymer-pore interaction.
60 citations
TL;DR: This work has calculated the critical density at which phase separation takes place in the zero-range process of traffic jam formation and shown that within a certain range of densities above the critical value a metastable homogeneous state exists before coarsening sets in.
Abstract: A multicluster model of traffic flow is studied, in which the motion of cars is described by a stochastic master equation. Assuming that the escape rate from a cluster depends only on the cluster size, the dynamics of the model is directly mapped to the mathematically well-studied zero-range process. Knowledge of the asymptotic behavior of the transition rates for large clusters allows us to apply an established criterion for phase separation in one-dimensional driven systems. The distribution over cluster sizes in our zero-range model is given by a one-step master equation in one dimension. It provides an approximate mean-field dynamics, which, however, leads to the exact stationary state. Based on this equation, we have calculated the critical density at which phase separation takes place. We have shown that within a certain range of densities above the critical value a metastable homogeneous state exists before coarsening sets in. Within this approach we have estimated the critical cluster size and the mean nucleation time for a condensate in a large system. The metastablity in the zero-range process is reflected in a metastable branch of the fundamental flux-density diagram of traffic flow. Our work thus provides a possible analytical description of traffic jam formation as well as important insight into condensation in the zero-range process.
60 citations
TL;DR: This work presents examples of how the master equation for gene products such as mRNA and proteins can be reduced to a simpler problem using asymptotic methods, and analyses the relationship between the reduced models and the original.
Abstract: Stochastic phenomena in gene regulatory networks can be modelled by the chemical master equation for gene products such as mRNA and proteins. If some of these elements are present in significantly higher amounts than the rest, or if some of the reactions between these elements are substantially faster than others, it is often possible to reduce the master equation to a simpler problem using asymptotic methods. We present examples of such a procedure and analyse the relationship between the reduced models and the original.
60 citations