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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: A formalism that accounts for the interaction of a local quantum system, such as an atom or a cavity, with traveling pulses of quantized radiation with Markovian coupling of the stationary system to the input and output fields and nondispersive asymptotic propagation of the pulses before and after the interaction.
Abstract: We present a formalism that accounts for the interaction of a local quantum system, such as an atom or a cavity, with traveling pulses of quantized radiation. We assume Markovian coupling of the stationary system to the input and output fields and nondispersive asymptotic propagation of the pulses before and after the interaction. This permits derivation of a master equation where the input and output pulses are treated as single oscillator modes that both couple to the local system in a cascaded manner. As examples of our theory, we analyze reflection by an empty cavity with phase noise, stimulated atomic emission by a quantum light pulse, and formation of a Schr\"odinger-cat state by the dispersive interaction of a coherent pulse and a single atom in a cavity.
62 citations
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TL;DR: In this article, a self-contained review of master equation approaches to modeling phonon effects in optically driven self-assembled quantum dots is provided, including weak-coupling master equations that are perturbative in the exciton-phonon coupling.
Abstract: We provide a self-contained review of master equation approaches to modelling phonon effects in optically driven self-assembled quantum dots. Coupling of the (quasi) two-level excitonic system to phonons leads to dissipation and dephasing, the rates of which depend on the excitation conditions, intrinsic properties of the QD sample, and its temperature. We describe several techniques, which include weak-coupling master equations that are perturbative in the exciton-phonon coupling, as well as those based on the polaron transformation that can remain valid for strong phonon interactions. We additionally consider the role of phonons in altering the optical emission characteristics of quantum dot devices, outlining how we must modify standard quantum optics treatments to account for the presence of the solid-state environment.
62 citations
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TL;DR: The master equation simulations are in excellent agreement with the experimental OH yields measured in N2 or He buffer gas near 300 K, but they do not explain a recent report that the OH yields are independent of pressure in nearly pure O2 buffer gas.
Abstract: Master equation calculations were carried out to simulate the production of hydroxyl free radicals initiated by the reaction of acetyl free radicals (CH3(CO)˙) with molecular oxygen. In particular, the competition between the unimolecular reactions and bimolecular reactions of vibrationally excited intermediates was modeled by using a single master equation. The vibrationally excited intermediates (isomers of acetylperoxyl radicals) result from the initial reaction of acetyl free radical with O2. The bimolecular reactions were modeled using a novel pseudo-first-order microcanonical rate constant approach. Stationary points on the multi-well, multi-channel potential energy surface (PES) were calculated at the DFT(B3LYP)/6-311G(2df,p) level of theory. Some additional calculations were carried out at the CASPT2(7,5)/6-31G(d) level of theory to investigate barrierless reactions and other features of the PES. The master equation simulations are in excellent agreement with the experimental OH yields measured in N2 or He buffer gas near 300 K, but they do not explain a recent report that the OH yields are independent of pressure in nearly pure O2 buffer gas.
62 citations
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TL;DR: In this paper, the reaction coordinate master equation is extended to incorporate system-environment correlations and the resultant non-Markovian dynamical effects, and energy transfer dynamics for both underdamped and overdamped oscillator environments that are in perfect agreement with the numerical hierarchical equations of motion over a wide range of parameters.
Abstract: We explore excitonic energy transfer dynamics in a molecular dimer system coupled to both structured and unstructured oscillator environments. By extending the reaction coordinate master equation technique developed in [J. Iles-Smith, N. Lambert, and A. Nazir, Phys. Rev. A 90, 032114 (2014)], we go beyond the commonly used Born-Markov approximations to incorporate system-environment correlations and the resultant non-Markovian dynamical effects. We obtain energy transfer dynamics for both underdamped and overdamped oscillator environments that are in perfect agreement with the numerical hierarchical equations of motion over a wide range of parameters. Furthermore, we show that the Zusman equations, which may be obtained in a semiclassical limit of the reaction coordinate model, are often incapable of describing the correct dynamical behaviour. This demonstrates the necessity of properly accounting for quantum correlations generated between the system and its environment when the Born-Markov approximations no longer hold. Finally, we apply the reaction coordinate formalism to the case of a structured environment comprising of both underdamped (i.e. sharply peaked) and overdamped (broad) components simultaneously. We find that though an enhancement of the dimer energy transfer rate can be obtained when compared to an unstructured environment, its magnitude is rather sensitive to both the dimer-peak resonance conditions and the relative strengths of the underdamped and overdamped contributions.
62 citations
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TL;DR: This work considers electron spin qubits in quantum dots and defines a measurement efficiency e to characterize reliable measurements via n-shot readouts and proposes various implementations based on a double dot and a quantum point contact and shows that they allow spin readout under realistic conditions.
Abstract: We consider electron spin qubits in quantum dots and define a measurement efficiency e to characterize reliable measurements via n-shot readouts. We propose various implementations based on a double dot and a quantum point contact (QPC) and show that the associated efficiencies e vary between 50% and 100%, allowing single-shot readout in the latter case. We model the readout microscopically and derive its time dynamics in terms of a generalized master equation, calculate the QPC current, and show that it allows spin readout under realistic conditions.
61 citations