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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, the authors derived exact equations of motion for a system interacting with a reservoir by means of projection-operator techniques, and the kernel of the master equation obtained in case a) is investigated in the thermodynamic limit of the reservoir.
78 citations
TL;DR: The role of the potential energy landscape in determining the relaxation dynamics of model clusters is studied using a master equation, and connections are made to relaxation processes in proteins and structural glasses.
Abstract: The role of the potential energy landscape in determining the relaxation dynamics of model clusters is studied using a master equation. Two types of energy landscape are examined: a single funnel, as exemplified by 13-atom Morse clusters, and the double funnel landscape of the 38-atom Lennard-Jones cluster. Interwell rate constants are calculated using Rice-Ramsperger-Kassel-Marcus theory within the harmonic approximation, but anharmonic model partition functions are also considered. Decreasing the range of the potential in the Morse clusters is shown to hinder relaxation toward the global minimum, and this effect is related to the concomitant changes in the energy landscape. The relaxation modes that emerge from the master equation are interpreted and analyzed to extract interfunnel rate constants for the Lennard-Jones cluster. Since this system is too large for a complete characterization of the energy landscape, the conditions under which the master equation can be applied to a limited database are explored. Connections are made to relaxation processes in proteins and structural glasses.
78 citations
TL;DR: The perturbative master equation (Bloch-Redfield) is used extensively to study dissipative quantum mechanics, particularly for qubits, despite the 25-year-old criticism that it violates positivity (generating negative probabilities) as discussed by the authors.
Abstract: The perturbative master equation (Bloch–Redfield) is used extensively to study dissipative quantum mechanics—particularly for qubits—despite the 25-year-old criticism that it violates positivity (generating negative probabilities). We take an arbitrary system coupled to an environment containing many degrees-of-freedom and cast its perturbative master equation (derived from a perturbative treatment of Nakajima–Zwanzig or Schoeller–Schon equations) in the form of a Lindblad master equation. We find that the equation's parameters are time dependent. This time dependence is rarely accounted for and invalidates Lindblad's dynamical semigroup analysis. We analyse one such Bloch–Redfield master equation (for a two-level system coupled to an environment with a short but non-vanishing memory time), which apparently violates positivity. We analytically show that, once the time dependence of the parameters is accounted for, positivity is preserved.
77 citations
TL;DR: In this paper, the migration of a classical dynamical system between regions of configuration space can be treated as a continuous time random walk between these regions, and a short memory approximation to these memory functions is equivalent to the well-known transition state method.
Abstract: The migration of a classical dynamical system between regions of configuration space can be treated as a continuous time random walk between these regions. Derivation of a classical analog of the quantum mechanical generalized master equation provides expressions for the waiting time distribution in terms of transition memory functions. A short memory approximation to these memory functions is equivalent to the well-known transition state method. An example is discussed for which this approximation seems reasonable but is entirely wrong.
77 citations