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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 paper, the kinetics of the binding reaction A+B⇄C are solved exactly via the stochastic master equation, in which molecular populations are considered as time-dependent, integer-valued random variables.
Abstract: The kinetics of the binding reaction A+B⇄C are solved exactly via the stochastic master equation, in which molecular populations are considered as time-dependent, integer-valued random variables. This transient solution extends previous work on the irreversible bimolecular reaction and the equilibrium state of the reversible bimolecular reaction. For small ensembles of reactants, comparisons are made between the results of the deterministic and stochastic approaches to the problem, and methods are presented to numerically evaluate the solution.

83 citations

Journal ArticleDOI
TL;DR: In this article, the difference between Liouville-Riemann fractional derivatives and non-standard analysis of fractional Poisson processes is discussed. But the present paper only considers Poisson process models with long-range dependence.
Abstract: Fractional master equations may be defined either by means of Liouville–Riemann (L–R) fractional derivative or via non-standard analysis. The first approach describes processes with long-range dependence whilst the second approach deals with processes involving independent increments. The present papers put in evidence some of the differences between these two modellings, and to this end it especially considers more fractional Poisson processes.

82 citations

Journal ArticleDOI
TL;DR: In this paper, the quantum correlation properties of a dissipative Bose-Hubbard dimer in the presence of a coherent drive were theoretically explored and the critical behavior in a well-defined thermodynamical limit of large excitation numbers was considered and analyzed within a Gaussian approach.
Abstract: We theoretically explore the quantum correlation properties of a dissipative Bose-Hubbard dimer in the presence of a coherent drive. In particular, we focus on the regime where the semiclassical theory predicts a bifurcation with a spontaneous spatial symmetry breaking. The critical behavior in a well-defined thermodynamical limit of large excitation numbers is considered and analyzed within a Gaussian approach. The case of a finite boson density is also examined by numerically integrating the Lindblad master equation for the density matrix. We predict the critical behavior around the bifurcation points accompanied by large quantum correlations of the mixed steady state, in particular, exhibiting a peak in the logarithmic entanglement negativity.

82 citations

Journal ArticleDOI
TL;DR: In this paper, the authors present results of simulations of a quantum Boltzmann master equation (QBME) describing the kinetics of a dilute Bose gas confined in a trapping potential in the regime of Bose condensation.
Abstract: We present results of simulations of a quantum Boltzmann master equation (QBME) describing the kinetics of a dilute Bose gas confined in a trapping potential in the regime of Bose condensation. The QBME is the simplest version of a quantum kinetic master equation derived in previous work. We consider two cases of trapping potentials: a three-dimensional square-well potential with periodic boundary conditions and an isotropic harmonic oscillator. We discuss the stationary solutions and relaxation to equilibrium. In particular, we calculate particle distribution functions, fluctuations in the occupation numbers, the time between collisions, and the mean occupation numbers of the one-particle states in the regime of onset of Bose condensation.

82 citations

Journal ArticleDOI
TL;DR: In this paper, a generalization of the quantum adiabatic theorem for open systems described by a Markovian master equation with time-dependent Liouvillian was presented.
Abstract: We provide a rigorous generalization of the quantum adiabatic theorem for open systems described by a Markovian master equation with time-dependent Liouvillian $\mathcal{L}(t)$. We focus on the finite system case relevant for adiabatic quantum computing and quantum annealing. Adiabaticity is defined in terms of closeness to the instantaneous steady state. While the general result is conceptually similar to the closed-system case, there are important differences. Namely, a system initialized in the zero-eigenvalue eigenspace of $\mathcal{L}(t)$ will remain in this eigenspace with a deviation that is inversely proportional to the total evolution time $T$. In the case of a finite number of level crossings, the scaling becomes ${T}^{\ensuremath{-}\ensuremath{\eta}}$ with an exponent $\ensuremath{\eta}$ that we relate to the rate of the gap closing. For master equations that describe relaxation to thermal equilibrium, we show that the evolution time $T$ should be long compared to the corresponding minimum inverse gap squared of $\mathcal{L}(t)$. Our results are illustrated with several examples.

82 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
2023140
2022344
2021431
2020460
2019420
2018427