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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 temperature effect on vibrational relaxation and the vibrational energy transfer from the vibrationally excited donor to the acceptor was studied and the validity of the rate constants obtained from the use of the weak coupling approximation and the strong coupling approximation was discussed.
Abstract: In this paper, we are concerned with the temperature effect on vibrational relaxation and the vibrational energy transfer from the vibrationally excited donor to the acceptor. For the temperature effect, we present numerical results to show the temperature dependence of the rate constant of vibrational relaxation and to discuss the validity of the rate constants obtained from the use of the weak coupling approximation and the strong coupling approximation. It is shown that although the temperature effect is extremely large over the temperature range T=0 to T=ϑE, the Einstein temperature of the medium, for the temperature range T=0 to T=0.3 ϑE, the rate constant varies slowly with temperature. For the vibrational energy transfer, we derive the master equation to describe the time dependent behavior of the excited donor, and the expression for the rate constant of vibrational energy transfer. The master equation is solved to study the temporal behavior of the excited donor as a function of the acceptor conc...

79 citations

Journal ArticleDOI
TL;DR: In this article, weakly nonlinear passive materials for prospective applications in integrated quantum photonics were proposed, where strong enhancement of native optical nonlinearities by electromagnetic field confinement in photonic crystal resonators can lead to single-photon generation only exploiting the quantum interference of two coupled modes and the effect of photon blockade under resonant coherent driving.
Abstract: We propose the use of weakly nonlinear passive materials for prospective applications in integrated quantum photonics. It is shown that strong enhancement of native optical nonlinearities by electromagnetic field confinement in photonic crystal resonators can lead to single-photon generation only exploiting the quantum interference of two coupled modes and the effect of photon blockade under resonant coherent driving. For realistic system parameters in state of the art microcavities, the efficiency of such single-photon source is theoretically characterized by means of the second-order correlation function at zero time delay as the main figure of merit, where major sources of loss and decoherence are taken into account within a standard master equation treatment. These results could stimulate the realization of integrated quantum photonic devices based on non-resonant material media, fully integrable with current semiconductor technology and matching the relevant telecom band operational wavelengths, as an alternative to single-photon nonlinear devices based on cavity-QED with artificial atoms or single atomic-like emitters.

79 citations

Journal ArticleDOI
TL;DR: In this paper, the authors provide necessary and sufficient conditions for a general Markovian Gaussian master equation to have a unique pure steady state, described by simple matrix equations, and demonstrate some examples including Gaussian cluster states.
Abstract: This paper provides some necessary and sufficient conditions for a general Markovian Gaussian master equation to have a unique pure steady state. The conditions are described by simple matrix equations; thus the so-called environment engineering problem for pure-Gaussian-state preparation can be straightforwardly dealt with in the linear algebraic framework. In fact, based on one of those conditions, for an arbitrary given pure Gaussian state, we obtain a complete parametrization of the Gaussian master equation having that state as a unique steady state; this leads to a systematic procedure for engineering a desired dissipative system. We demonstrate some examples including Gaussian cluster states.

79 citations

Journal ArticleDOI
TL;DR: A comprehensive approach to modeling open quantum systems consistent with thermodynamics is presented, and the use of the stochastic surrogate Hamiltonian for modeling ultrafast spectroscopy and quantum control is reviewed.
Abstract: A comprehensive approach to modeling open quantum systems consistent with thermodynamics is presented. The theory of open quantum systems is employed to define system bath partitions. The Markovian master equation defines an isothermal partition between the system and bath. Two methods to derive the quantum master equation are described: the weak coupling limit and the repeated collision model. The role of the eigenoperators of the free system dynamics is highlighted, in particular, for driven systems. The thermodynamical relations are pointed out. Models that lead to loss of coherence, i.e., dephasing are described. The implication of the laws of thermodynamics to simulating transport and spectroscopy is described. The indications for self-averaging in large quantum systems and thus its importance in modeling are described. Basic modeling by the surrogate Hamiltonian is described, as well as thermal boundary conditions using the repeated collision model and their use in the stochastic surrogate Hamiltonian. The problem of modeling with explicitly time dependent driving is analyzed. Finally, the use of the stochastic surrogate Hamiltonian for modeling ultrafast spectroscopy and quantum control is reviewed.

79 citations

Journal ArticleDOI
TL;DR: A unified description of all classes of exact solutions to these equations in terms of the confluent Heun functions is presented in this paper, where a proper linear combination of such solutions can present bounded one-way-running waves.
Abstract: The Teukolsky Master Equation is the basic tool for study of perturbations of the Kerr metric in linear approximation. It admits separation of variables, thus yielding the Teukolsky Radial Equation and the Teukolsky Angular Equation. We present here a unified description of all classes of exact solutions to these equations in terms of the confluent Heun functions. Large classes of new exact solutions are found and classified with respect to their characteristic properties. Special attention is paid to the polynomial solutions which are singular ones and introduce collimated one-way-running waves. It is shown that a proper linear combination of such solutions can present bounded one-way-running waves. This type of waves may be suitable as models of the observed astrophysical jets.

78 citations


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