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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 article, an exact gauge covariant equation of motion for the SU(N) quantum chromodynamic Wigner operator was derived, which naturally splits up into an on-shell constraint equation and a transport equation.
187 citations
TL;DR: In this paper, a comprehensive study of correlations in linear and nonlinear chemical reactions is presented using coupled chemical and diffusion master equations, and the approach to the steady-state Poisson distribution from an initial non-Poissonian distribution is given by a power law rather than the exponential predicted by neglecting correlations.
Abstract: A comprehensive study of correlations in linear and nonlinear chemical reactions is presented using coupled chemical and diffusion master equations. As a consequence of including correlations in linear reactions the approach to the steady-state Poisson distribution from an initial non-Poissonian distribution is given by a power law rather than the exponential predicted by neglecting correlations. In nonlinear reactions we show that a steadystate Poisson distribution is achieved in small volumes, whereas in large volumes a non-Poissonian distribution is built up via the correlation. The spatial correlation function is calculated for two examples, one which exhibits an instability, the other which exhibits a second-order phase transition, and correlation length and correlation time are calculated and shown to become infinite as the critical point is approached. The critical exponents are found to be classical.
186 citations
TL;DR: A stochastic model for a general system of first-order reactions in which each reaction may be either a conversion reaction or a catalytic reaction is derived and it is shown that the distribution of all the system components is a Poisson distribution at steady state.
186 citations
TL;DR: In this paper, the authors present a qualitative analysis of how the transmission coefficient for nonadiabatic barrier crossing can be affected by resonances and highlight the connections and differences between classical friction and quantum mechanical dephasing effects in barrier crossing.
Abstract: A remarkably rich picture of the dynamics of chemical reactions in condensed-phase systems has emerged in recent years. The interplay of friction, electronic nonadiabaticity, and intramolecular energy flow have been elucidated by use of pictures based on classical trajectories. The authors review the qualitative ideas of that picture. There are some significant limitations of that approach to reaction dynamics that arise from quantum interference effects. Using a trajectory picture along with the quantum superposition principle, they give qualitative arguments describing how the transmission coefficient for nonadiabatic barrier crossing can be affected by resonances. They highlight the connections and differences between classical friction and quantum mechanical dephasing effects in barrier crossing. They also discuss the relation of this trajectory-based picture and the traditional language of radiationless processes based on the Golden Rule and master equations.
185 citations
TL;DR: The correct master equation has five exponential decay terms, with preexponential factors that depend upon the diffusion constants and, in a completely symmetrical fashion, upon the orientations of absorbing and emitting dipoles.
Abstract: Reexamination of the theory of fluorescence time dependence owing to rotational diffusion of rigid macromolecules reveals deficiencies or hidden restrictions in each of the previous treatments. The correct master equation has five exponential decay terms, with preexponential factors that depend upon the diffusion constants and, in a completely symmetrical fashion, upon the orientations of absorbing and emitting dipoles.
185 citations