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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 paper, a mean-field coupling between a system of noninteracting subsystems and the bath is investigated, and the existence and uniqueness of solutions of the corresponding nonlinear evolution equations are studied in a more abstract framework.
Abstract: The notion of a nonlinear quantum dynamical semigroup is introduced, and the existence and uniqueness of solutions of the corresponding nonlinear evolution equations are studied in a more abstract framework. The construction of nonlinear quantum dynamical semigroups is carried out for two different mean-field models. First a mean-field coupling between a system of noninteracting subsystems and the bath is investigated. As examples, a nonlinear frictional Schrodinger equation and a model for a quantum Boltzmann equation are discussed. Second, a many-body system with mean-field interaction coupled to a bath is considered. Here, again, the form of the generator is derived; however, it cannot be obtained rigorously, except for some particular examples. Finally, the quantum Ising-Weiss model is briefly studied.

73 citations

Journal ArticleDOI
TL;DR: It is found that the one-atom laser exhibits most of the typical features of a normal laser, but in the region far below threshold some aspects, among them the linewidth, are changed due to eigenvalues of the master equation with imaginary parts.
Abstract: We present a detailed numerical study of the one-atom laser, that is, a single two-level atom interacting with one lasing mode, whereby both the atom and the photon field are coupled to reservoirs. The stationary as well as the dynamical properties of the model are calculated directly from the quantum master equation with the help of two numerical methods. These numerical methods do not need any quasi-probability representation and they do not require approximations. We find that the one-atom laser exhibits most of the typical features of a normal laser. In the region far below threshold some aspects, among them the linewidth, are changed due to eigenvalues of the master equation with imaginary parts

73 citations

Journal ArticleDOI
TL;DR: An exact canonical master equation of the Lindblad form is derived for a central spin interacting uniformly with a sea of completely unpolarized spins in this article, and the Kraus operators for the dynamical map are also derived.
Abstract: An exact canonical master equation of the Lindblad form is derived for a central spin interacting uniformly with a sea of completely unpolarized spins. The Kraus operators for the dynamical map are also derived. The non-Markovianity of the dynamics in terms of the divisibility breaking of the dynamical map and the increase of the trace distance fidelity between quantum states is shown. Moreover, it is observed that the irreversible entropy production rate is always negative (for a fixed initial state) whenever the dynamics exhibits non-Markovian behavior. In continuation with the study of witnessing non-Markovianity, it is shown that the positive rate of change of the purity of the central qubit is a faithful indicator of the non-Markovian information backflow. Given the experimental feasibility of measuring the purity of a quantum state, a possibility of experimental demonstration of non-Markovianity and the negative irreversible entropy production rate is addressed. This gives the present work considerable practical importance for detecting the non-Markovianity and the negative irreversible entropy production rate.

73 citations

Journal ArticleDOI
TL;DR: The methodology is illustrated with four examples and the emphasis is placed on how to handle the situation when a CSE merges with the quasi-continuum of IEREs, indicating that one or more chemical reactions begin to take place on vibrational-rotational relaxation time scales.
Abstract: In this article we discuss at length the determination of phenomenological rate coefficients from the solution to a time-dependent, multiple-well master equation. Both conservative and non-conservative formulations are considered. The emphasis is placed on how to handle the situation when a CSE (chemically significant eigenvalue of the transition matrix) merges with the quasi-continuum of IEREs (internal energy relaxation eigenvalues), indicating that one or more chemical reactions begin to take place on vibrational-rotational relaxation time scales. The methodology is illustrated with four examples.

73 citations

Journal ArticleDOI
TL;DR: In this article, the exact equation of motion for the reduced density matrix of a system weakly coupled to a bath is obtained using projection operator techniques, which reduces to a generalized master equation when the bath relaxation is faster than the relaxation of the system induced by the weak interaction with the bath.
Abstract: The equation of motion for the reduced density matrix of a system weakly coupled to a bath is obtained using projection operator techniques. The exact equation of motion reduces to a generalized master equation when the bath relaxation is faster than the relaxation of the system induced by the weak interaction with the bath. The equation separates into streaming or systematic terms and dissipative terms which are separately equal to zero at equilibrium. We find both statistical and dynamical system frequency shifts; the statistical shifts are present in equilibrium but the dynamical shifts affect the time-dependence, only. The general results are applied to the two-level system model for tunneling in condensed phases.

73 citations


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