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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 a general expression for the emission probability and a master equation for the mazer, and showed that the probability for emission by an excited thermal atom (stimulated maser emission) is very different from the expectation as given by the de Broglie resonances (induced mazer emission).
Abstract: The photon emission probability in a micromaser changes drastically when the kinetic energy of the pumping atoms is comparable to the atom-field interaction energy. In this situation, the atomic center-of-mass motion has to be treated quantum mechanically and the de Broglie wavelength of the atom inside the cavity is an important physical parameter. The interplay between reflection and transmission of the atoms leads to a new mechanism for induced emission. A photon is emitted by an excited atom when the de Broglie wavelength fits resonantly into the cavity. These resonances lead to the process of microwave amplification via $z$-motion-induced emission of radiation (mazer). We derive and illustrate a general expression for the emission probability and a master equation for the mazer. We note that the probability for emission by an excited thermal atom (stimulated maser emission) is very different from the emission probability as given by the de Broglie resonances (induced mazer emission).
76 citations
TL;DR: The paper presents an alternative, which focuses on the discrete partial differential equation (PDE) structure of the CME, and recommends use of the Rothe method (first time, then space) for clear theoretical and algorithmic reasons.
Abstract: In systems biology, the stochastic description of biochemical reaction kinetics is increasingly being employed to model gene regulatory networks and signaling pathways. Mathematically speaking, such models require the numerical solution of the underlying evolution equation, known as the chemical master equation (CME). Until now, the CME has primarily been treated by Monte Carlo techniques, the most prominent of which is the stochastic simulation algorithm [D. T. Gillespie, J. Comput. Phys., 22 (1976), pp. 403-434]. The paper presents an alternative, which focuses on the discrete partial differential equation (PDE) structure of the CME. This allows us to adopt ideas from adaptive discrete Galerkin methods as first suggested by Deuflhard and Wulkow [IMPACT Comput. Sci. Engrg., 1 (1989), pp. 269-301] for polyreaction kinetics and independently developed by Engblom. From the two different options for discretizing the CME as a discrete PDE, Engblom chose the method of lines approach (first space, then time), whereas we strongly advocate use of the Rothe method (first time, then space) for clear theoretical and algorithmic reasons. Numerical findings at two rather challenging problems illustrate the promising features of the proposed method and, at the same time, indicate lines of necessary further improvement of the method worked out here.
76 citations
TL;DR: The complete solution of the master equation for a system of interacting particles of finite density is presented and by using a new form of the Bethe ansatz, the totally asymmetric exclusion process on a ring is solved for arbitrary initial conditions and time intervals.
Abstract: The complete solution of the master equation for a system of interacting particles of finite density is presented. By using a new form of the Bethe ansatz, the totally asymmetric exclusion process on a ring is solved for arbitrary initial conditions and time intervals.
76 citations
01 Feb 1997
TL;DR: The Batalin-Vilkovisky master equations are pre-cisely the integrability equations for deformations of algebras and differential algesbras as discussed by the authors.
Abstract: The Batalin-Vilkovisky master equations, both classical and quantum, are pre- cisely the integrability equations for deformations of algebras and differential algebras re- spectively. This is not a coincidence; the Batalin-Vilkovisky approach is here translated into the language of deformation theory.
76 citations
01 Jan 2002
TL;DR: The damped harmonic oscillator is arguably the simplest open quantum system worth studying and is also of great practical importance because it is an essential ingredient in the theoretical description of many quantum-optical experiments as mentioned in this paper.
Abstract: The damped harmonic oscillator is arguably the simplest open quantum system worth studying. It is also of great practical importance because it is an essential ingredient in the theoretical description of many quantum-optical experiments. One can assume rather safely that the quantum master equation of the simple harmonic oscillator would not be studied so extensively if it did not play such a central role in the quantum theory of lasers and the masers. Not surprisingly, then, all major textbook accounts of theoretical quantum optics [1],[2],[3],[4],[5],[6],[7],[8],[9],[10],[11],[12],[13],[14],[15] contain a fair amount of detail about damped harmonic oscillators. Fock state representations or phase space functions of some sort are invariably employed in these treatments.
76 citations