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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 studied the excitonic dynamics of a driven quantum dot under the influence of a phonon environment and developed a master equation that can be valid over a much larger range of excitonphonon coupling strengths and temperatures than in the case of the standard weak-coupling approach.
Abstract: We study the excitonic dynamics of a driven quantum dot under the influence of a phonon environment, going beyond the weak exciton-phonon coupling approximation. By combining the polaron transform and time-local projection operator techniques, we develop a master equation that can be valid over a much larger range of exciton-phonon coupling strengths and temperatures than in the case of the standard weak-coupling approach. For the experimentally relevant parameters considered here, we find that the weak-coupling and polaron theories give very similar predictions for low temperatures (below 30 K), while at higher temperatures we begin to see discrepancies between the two. This is because, unlike the polaron approach, the weak-coupling theory is incapable of capturing multiphonon effects, while it also does not properly account for phonon-induced renormalization of the driving frequency. In particular, we find that the weak-coupling theory often overestimates the damping rate when compared to the polaron theory. Finally, we extend our theory to include non-Markovian effects and find that, for the parameters considered here, they have little bearing on the excitonic Rabi rotations when plotted as a function of pulse area.
157 citations
TL;DR: This work model stochastic chemical systems with diffusion by a reaction-diffusion master equation and is a flexible hybrid algorithm in that the diffusion can be handled either on the meso- or on the macroscale level.
Abstract: We model stochastic chemical systems with diffusion by a reaction-diffusion master equation. On a macroscopic level, the governing equation is a reaction-diffusion equation for the averages of the chemical species. On a mesoscopic level, the master equation for a well stirred chemical system is combined with a discretized Brownian motion in space to obtain the reaction-diffusion master equation. The space is covered in our method by an unstructured mesh, and the diffusion coefficients on the mesoscale are obtained from a finite element discretization of the Laplace operator on the macroscale. The resulting method is a flexible hybrid algorithm in that the diffusion can be handled either on the meso- or on the macroscale level. The accuracy and the efficiency of the method are illustrated in three numerical examples inspired by molecular biology.
156 citations
TL;DR: In this paper, the continuity equation relating the change in time of the position probability density to the gradient of the probability current density is generalized to PT-symmetric quantum mechanics and the normalization condition of eigenfunctions is modified in accordance with this new conservation law.
Abstract: The continuity, equation relating the change in time of the position probability density to the gradient of the probability current density is generalized to PT-symmetric quantum mechanics. The normalization condition of eigenfunctions is modified in accordance with this new conservation law and illustrated with some detailed examples.
155 citations
TL;DR: In this paper, the Fano diagonalization method is applied to a system in which the atomic transitions are coupled to a discrete set of (cavity) quasimodes, which in turn are coupled with a continuum set of external quasims with slowly varying coupling constants and mode density.
Abstract: This paper deals with non-Markovian behavior in atomic systems coupled to a structured reservoir of quantum electromagnetic field modes, with particular relevance to atoms interacting with the field in high-Q cavities or photonic band-gap materials. In cases such as the former, we show that the pseudomode theory for single-quantum reservoir excitations can be obtained by applying the Fano diagonalization method to a system in which the atomic transitions are coupled to a discrete set of (cavity) quasimodes, which in turn are coupled to a continuum set of (external) quasimodes with slowly varying coupling constants and continuum mode density. Each pseudomode can be identified with a discrete quasimode, which gives structure to the actual reservoir of true modes via the expressions for the equivalent atom-true mode coupling constants. The quasimode theory enables cases of multiple excitation of the reservoir to now be treated via Markovian master equations for the atom-discrete quasimode system. Applications of the theory to one, two, and many discrete quasimodes are made. For a simple photonic band-gap model, where the reservoir structure is associated with the true mode density rather than the coupling constants, the single quantum excitation case appears to be equivalent to a case with two discrete quasimodes.
155 citations
TL;DR: In this article, a path-integral formalism is proposed to explore the quantum statistics of photons interacting with complex structures in the multiphoton regime, and a framework based on a pathintegral framework provides a route to explore such dynamics.
Abstract: The analysis of photon scattering is a major challenge in the multiphoton regime. A framework based on a path-integral formalism provides a route to explore such dynamics, helping to investigate the quantum statistics of photons interacting with complex structures.
154 citations