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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: Fractal time random walks with generalized Mittag-Leffler functions as waiting time densities are studied in this article, where exact Greens functions corresponding to fractional diffusion are obtained using Mellin transform techniques.
Abstract: Fractal time random walks with generalized Mittag-Leffler functions as waiting time densities are studied. This class of fractal time processes is characterized by a dynamical critical exponent 0<ω≤1, and is equivalently described by a fractional master equation with time derivative of noninteger order ω. Exact Greens functions corresponding to fractional diffusion are obtained using Mellin transform techniques. The Greens functions are expressible in terms of general H-functions. For ω<1 they are singular at the origin and exhibit a stretched Gaussian form at infinity. Changing the order ω interpolates smoothly between ordinary diffusion ω=1 and completely localized behavior in the ω→0 limit.
97 citations
TL;DR: In this paper, a quantum generalization of the Crooks fluctuation theorem is presented, which not only includes the energy changes in the reservoir, but also the full description of its evolution, including coherences.
Abstract: Systems that are driven out of thermal equilibrium typically dissipate random quantities of energy on microscopic scales. Crooks fluctuation theorem relates the distribution of these random work costs with the corresponding distribution for the reverse process. By an analysis that explicitly incorporates the energy reservoir that donates the energy, and the control system that implements the dynamic, we here obtain a quantum generalization of Crooks theorem that not only includes the energy changes in the reservoir, but the full description of its evolution, including coherences. This approach moreover opens up for generalizations of the concept of fluctuation relations. Here we introduce `conditional' fluctuation relations that are applicable to non-equilibrium systems, as well as approximate fluctuation relations that allow for the analysis of autonomous evolution generated by global time-independent Hamiltonians. We furthermore extend these notions to Markovian master equations, implicitly modeling the influence of the heat bath.
97 citations
TL;DR: This work analyzes a synthetic biochemical circuit, the toggle switch, and compares the results to those obtained from a numerical solution of the master equation.
Abstract: We use large deviation methods to calculate rates of noise-induced transitions between states in multistable genetic networks. We analyze a synthetic biochemical circuit, the toggle switch, and compare the results to those obtained from a numerical solution of the master equation.
97 citations
TL;DR: In this paper, the influence of dissipation on one and two-qubit rotations in coupled semiconductor quantum dots was investigated using a pseudo-spin-boson model with adiabatically varying parameters.
Abstract: We investigate the influence of dissipation on one- and two-qubit rotations in coupled semiconductor quantum dots, using a (pseudo-)spin-boson model with adiabatically varying parameters. For weak dissipation, we solve a master equation, compare with direct perturbation theory, and derive an expression for the ``fidelity loss'' during a simple operation that adiabatically moves an electron between two coupled dots. We discuss the possibility of visualizing coherent quantum oscillations in electron ``pump'' currents, combining quantum adiabaticity and Coulomb blockade. In two-qubit spin-swap operations where the role of intermediate charge states has been discussed recently, we apply our formalism to calculate the fidelity loss due to charge tunneling between two dots.
97 citations
TL;DR: In this article, a coarse-grain collisional model was developed to describe the internal energy relaxation and dissociation processes based on a smaller number of equations, as opposed to existing reduced models assuming thermal equilibrium between the rotational and translational energy modes.
96 citations