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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 obtained general integral formulas for probabilities in the asymmetric simple exclusion process (ASEP) on the integer lattice with nearest neighbor hopping rates p to the right and q = 1-p to the left.
Abstract: In this paper we obtain general integral formulas for probabilities in the asymmetric simple exclusion process (ASEP) on the integer lattice with nearest neighbor hopping rates p to the right and q=1-p to the left. For the most part we consider an N-particle system but for certain of these formulas we can take the limit as N goes to infinity. First we obtain, for the N-particle system, a formula for the probability of a configuration at time t, given the initial configuration. For this we use Bethe Ansatz ideas to solve the master equation, extending a result of Schuetz for the case N=2. The main results of the paper, derived from this, are integral formulas for the probability, for given initial configuration, that the m'th left-most particle is at x at time t. In one of these formulas we can take the limit as N goes to infinity, and it gives the probability for an infinite system where the initial configuration is bounded on one side. For the special case of the totally asymmetric simple exclusion process (TASEP) our formulas reduce to the known ones.
147 citations
13 Aug 2019
146 citations
TL;DR: In this article, a theoretical framework for describing a wave packet of light prepared in a state of definite photon number interacting with an arbitrary quantum system (e.g., a quantum harmonic oscillator or a multilevel atom) is presented.
Abstract: We present a theoretical framework that describes a wave packet of light prepared in a state of definite photon number interacting with an arbitrary quantum system (e.g., a quantum harmonic oscillator or a multilevel atom). Within this framework we derive master equations for the system as well as for output field quantities such as quadratures and photon flux. These results are then generalized to wave packets with arbitrary spectral distribution functions. Finally, we obtain master equations and output field quantities for systems interacting with wave packets in multiple spatial and/or polarization modes.
145 citations
TL;DR: In this article, it was shown that the laser model process converges weakly in the sense of the matrix elements to a quantum diffusion whose equation is explicitly obtained, in the same sense as the Heisenberg evolution of an observable of the system to the solution of a quantum Langevin equation.
Abstract: We show that, in the weak coupling limit, the laser model process converges weakly in the sense of the matrix elements to a quantum diffusion whose equation is explicitly obtained. We prove convergence, in the same sense, of the Heisenberg evolution of an observable of the system to the solution of a quantum Langevin equation. As a corollary of this result, via the quantum Feynman-Kac technique, one can recover previous results on the quantum master equation for reduced evolutions of open systems. When applied to some particular model (e.g. the free Boson gas) our results allow to interpret the Lamb shift as an Ito correction term and to express the pumping rates in terms of quantities related to the original Hamiltonian model.
144 citations
TL;DR: In this article, the response of continuous-time random walks to an oscillating external field within the generalized master equation approach was studied, focusing on the time dependence of the two first moments of the walker's displacement.
Abstract: We discuss the response of continuous-time random walks to an oscillating external field within the generalized master equation approach. We concentrate on the time dependence of the two first moments of the walker's displacement. We show that for power-law waiting-time distributions with $0l\ensuremath{\alpha}l1$ corresponding to a semi-Markovian situation showing nonstationarity, the mean particle position tends to a constant; namely, the response to the external perturbation dies out. On the other hand, the oscillating field leads to a new additional contribution to the dispersion of the particle position, proportional to the square of its amplitude and growing with time. These new effects, amenable to experimental observation, result directly from the nonstationary property of the system.
144 citations