Master equation

About: Master equation is a research topic. Over the lifetime, 10541 publications have been published within this topic receiving 276095 citations.

From the Multiple-Well Master Equation to Phenomenological Rate Coefficients: Reactions on a C3H4 Potential Energy Surface

Abstract: Using various forms of electronic-structure theory to characterize the important features of the potential energy surface, RRKM theory to calculate microcanonical rate coeffients, and several formulations of the master equation to predict phenomenological rate coefficients, we have studied a number of reactions that occur on the C3H4 potential We discuss the results in some detail and compare them with experiment when possible Generally, the agreement with experiment is excellent “Multiple-well effects” are emphasized throughout the discussion We cast our results in the form of modified Arrhenius functions for use in chemical kinetics modeling

Uncoupled continuous-time random walks: Solution and limiting behavior of the master equation.

Abstract: A detailed study is presented for a large class of uncoupled continuous-time random walks (CTRWs). The master equation is solved for the Mittag-Leffler survival probability. The properly scaled diffusive limit of the master equation is taken and its relation with the fractional diffusion equation is discussed. Finally, some common objections found in the literature are thoroughly reviewed.

Tunneling through molecules and quantum dots: Master-equation approaches

Abstract: An important class of approaches to the description of electronic transport through molecules and quantum dots is based on the master equation. We discuss various formalisms for deriving a master equation and their interrelations. It is shown that the master equation derived by K\"onig et al. [Phys. Rev. Lett. 76, 1715 (1996); Phys. Rev. B 54, 16820 (1996)] is equivalent to the Wangsness-Bloch-Redfield master equation. The roles of the large-reservoir and Markov approximations are clarified. At low temperatures, when the quasiparticle lifetime becomes large, the Markov approximation can be derived from the assumption of weak tunneling under certain conditions. Interactions in the leads are shown to be irrelevant for the transport in the case of momentum-independent tunneling. It is explained why the $T$-matrix formalism gives incomplete results except for diagonal density operators to second order in the tunneling amplitudes. The time-convolutionless master equation is adapted to tunneling problems and a diagrammatic scheme for generating arbitrary orders in the tunneling amplitudes is developed.