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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 generalized master equation is applied to analyze time-dependent transport through a finite quantum wire with an embedded subsystem, and the parabolic quantum wire and the leads with several subbands are described by a continuous model.
Abstract: In this paper, we apply the generalized master equation to analyze time-dependent transport through a finite quantum wire with an embedded subsystem. The parabolic quantum wire and the leads with several subbands are described by a continuous model. We use an approach originally developed for a tight-binding description selecting the relevant states for transport around the bias-window defined around the values of the chemical potential in the left and right leads in order to capture the effects of the nontrivial geometry of the system in the transport. We observe a partial current reflection as a manifestation of a quasi-bound state in an embedded well and the formation of a resonance state between an off-set potential hill and the boundary of the system.
60 citations
TL;DR: In this paper, the authors derived formulae for the eigenvalues and spectral gap of the master equation for general collision kernels and proved the existence of a spectral gap independent of the number of particles.
Abstract: In this paper we derive formulae for the eigenvalues and spectral gap of the master equation for general collision kernels. We prove a conjecture of Mark Kac's on the existence of a spectral gap independent of the number of particles. We relate the eigenvalues to the “nonlinear” eigenvalues that occur in the exact solutions of model Boltzmann equations due to M. Ernst.
60 citations
TL;DR: In this paper, a hierarchy of hydrodynamic equations which are equivalent to the exact quantum Liouville equation for coupled electronic states is derived to describe nonadiabatic nuclear dynamics.
Abstract: A hydrodynamic approach is developed to describe nonadiabatic nuclear dynamics. We derive a hierarchy of hydrodynamic equations which are equivalent to the exact quantum Liouville equation for coupled electronic states. It is shown how the interplay between electronic populations and coherences translates into the coupled dynamics of the corresponding hydrodynamic fields. For the particular case of pure quantum states, the hydrodynamic hierarchy terminates such that the dynamics may be described in terms of the local densities and momentum fields associated with each of the electronic states.
60 citations
TL;DR: It is shown that, contrary to intuition, full-time solutions of order-2n accuracy require an order-(2n+2) master equation, which has a wide-ranging impact on the validity of coupling (or friction) sensitive results derived from second-order convolutionless, Nakajima-Zwanzig, Redfield, and Born-Markov master equations.
Abstract: We consider open quantum systems with dynamics described by master equations that have perturbative expansions in the system-environment interaction. We show that, contrary to intuition, full-time solutions of order-2n accuracy require an order-(2n+2) master equation. We give two examples of such inaccuracies in the solutions to an order-2n master equation: order-2n inaccuracies in the steady state of the system and order-2n positivity violations. We show how these arise in a specific example for which exact solutions are available. This result has a wide-ranging impact on the validity of coupling (or friction) sensitive results derived from second-order convolutionless, Nakajima-Zwanzig, Redfield, and Born-Markov master equations.
60 citations
TL;DR: In this article, a cloud of cold N two-level atoms driven by a resonant laser beam shows cooperative effects both in the scattered radiation field and in the radiation pressure force acting on the cloud center of mass.
Abstract: A cloud of cold N two-level atoms driven by a resonant laser beam shows cooperative effects both in the scattered radiation field and in the radiation pressure force acting on the cloud center-of-mass. The induced dipoles synchronize and the scattered light presents superradiant and/or subradiant features. We present a quantum description of the process in terms of a master equation for the atomic density matrix in the scalar, Born-Markov approximations, reduced to the single-excitation limit. From a perturbative approach for weak incident field, we derive from the master equation the effective Hamiltonian, valid in the linear regime. We discuss the validity of the driven timed Dicke ansatz and of a partial wave expansion for different optical thicknesses and we give analytical expressions for the scattered intensity and the radiation pressure force on the center of mass. We also derive an expression for collective suppression of the atomic excitation and the scattered light by these correlated dipoles.
60 citations