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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.


Papers
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Journal ArticleDOI
TL;DR: In this paper, quantum jump, Monte Carlo wave function, and quantum-trajectory methods are discussed and applied to a number of current problems in quantum optics, and relate them to ensemble descriptions.
Abstract: Dissipation, the irreversible loss of energy and coherence, from a microsystem is the result of coupling to a much larger macrosystem (or reservoir) that is so large that one has no chance of keeping track of all of its degrees of freedom. The microsystem evolution is then described by tracing over the reservoir states, which results in an irreversible decay as excitation leaks out of the initially excited microsystems into the outer reservoir environment. Earlier treatments of this dissipation used density matrices to describe an ensemble of microsystems, either in the Schr\"odinger picture with master equations, or in the Heisenberg picture with Langevin equations. The development of experimental techniques to study single quantum systems (for example, single trapped ions, or cavity-radiation-field modes) has stimulated the construction of theoretical methods to describe individual realizations conditioned on a particular observation record of the decay channel. These methods, variously described as quantum-jump, Monte Carlo wave function, and quantum-trajectory methods, are the subject of this review article. We discuss their derivation, apply them to a number of current problems in quantum optics, and relate them to ensemble descriptions.

1,232 citations

Journal ArticleDOI
TL;DR: Fluctuation theorems (FTs) as discussed by the authors describe some universal properties of nonequilibrium fluctuations and are derived from a quantum perspective by introducing a two-point measurement on the system.
Abstract: Fluctuation theorems (FTs), which describe some universal properties of nonequilibrium fluctuations, are examined from a quantum perspective and derived by introducing a two-point measurement on the system. FTs for closed and open systems driven out of equilibrium by an external time-dependent force, and for open systems maintained in a nonequilibrium steady state by nonequilibrium boundary conditions, are derived from a unified approach. Applications to fermion and boson transport in quantum junctions are discussed. Quantum master equations and Green's functions techniques for computing the energy and particle statistics are presented.

1,203 citations

Journal ArticleDOI
TL;DR: In this article, it has been shown that the Helmholtz free energy difference between two equilibrium configurations of a system may be obtained from an ensemble of finite-time (nonequilibrium) measurements of the work performed in switching an external parameter of the system.
Abstract: In has recently been shown that the Helmholtz free-energy difference between two equilibrium configurations of a system may be obtained from an ensemble of finite-time (nonequilibrium) measurements of the work performed in switching an external parameter of the system. Here this result is established, as an identity, within the master equation formalism. Examples are discussed and numerical illustrations provided.

1,192 citations

Book
16 Jan 2009
TL;DR: The Fokker-Planck Equation in several dimensions and the white noise limit for diffusion processes was defined in this paper. But this was not the case in the case of stochastic differential equations.
Abstract: A Historical Introduction.- Probability Concepts.- Markov Processes.- The Ito Calculus and Stochastic Differential Equations.- The Fokker-Planck Equation.- The Fokker-Planck Equation in Several Dimensions.- Small Noise Approximations for Diffusion Processes.- The White Noise Limit.- Beyond the White Noise Limit.- Levy Processes and Financial Applications.- Master Equations and Jump Processes.- The Poisson Representation.- Spatially Distributed Systems.- Bistability, Metastability, and Escape Problems.- Simulation of Stochastic Differential Equations.

1,153 citations

Book
01 Sep 1990
TL;DR: In this article, elementary transition state theory Microscopic Rate Coefficients Practical Implementation of RRKM Theory Collisional Energy Transfer The Master Equation Conclusions and Conclusion.
Abstract: Introduction Elementary Transition State Theory Microscopic Rate Coefficients Practical Implementation of RRKM Theory Collisional Energy Transfer The Master Equation Conclusions.

1,141 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023140
2022344
2021431
2020460
2019420
2018427