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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: The Strong Disorder RG approach for random systems has been extended in many new directions since our previous review of 2005 [Phys. Rep. 412, 277] as mentioned in this paper, and the aim of the present colloquium paper is to give an overview of these various recent developments.
Abstract: The Strong Disorder RG approach for random systems has been extended in many new directions since our previous review of 2005 [Phys. Rep. 412, 277]. The aim of the present colloquium paper is thus to give an overview of these various recent developments. In the field of quantum disordered models, recent progress concern Infinite Disorder Fixed Points for short-ranged models in higher dimensions $d>1$, Strong Disorder Fixed Points for long-ranged models, scaling of the entanglement entropy in critical ground-states and after quantum quenches, the RSRG-X procedure to construct the whole set excited stated and the RSRG-t procedure for the unitary dynamics in Many-Body-Localized Phases, the Floquet dynamics of periodically driven chains, the dissipative effects induced by the coupling to external baths, and Anderson Localization models. In the field of classical disordered models, new applications include the contact process for epidemic spreading, the strong disorder renormalization procedure for general master equations, the localization properties of random elastic networks and the synchronization of interacting non-linear dissipative oscillators.
61 citations
TL;DR: The time-convolutionless master equation for the electronic populations is derived for a generic electron-phonon Hamiltonian and shows the appearance of the recurrence phenomena on a time scale determined by the slowest mode of the system.
Abstract: The time-convolutionless master equation for the electronic populations is derived for a generic electron-phonon Hamiltonian. The equation can be used in the regimes where the golden rule approach is not applicable. The equation is applied to study the electronic relaxation in several models with the finite number of normal modes. For such mesoscopic systems the relaxation behavior differs substantially from the simple exponential relaxation. In particular, the equation shows the appearance of the recurrence phenomena on a time scale determined by the slowest mode of the system. The formal results are quite general and can be used for a wide range of physical systems. Numerical results are presented for a two level system coupled to Ohmic and super-Ohmic baths, as well as for a model of charge-transfer dynamics between semiconducting organic polymers.
61 citations
TL;DR: A systematic approach to the linear-noise approximation for stochastic reaction systems with distributed delays is developed based upon a dynamical generating functional describing the probability measure over all possible paths of the dynamics.
Abstract: We develop a systematic approach to the linear-noise approximation for stochastic reaction systems with distributed delays. Unlike most existing work our formalism does not rely on a master equation; instead it is based upon a dynamical generating functional describing the probability measure over all possible paths of the dynamics. We derive general expressions for the chemical Langevin equation for a broad class of non-Markovian systems with distributed delay. Exemplars of a model of gene regulation with delayed autoinhibition and a model of epidemic spread with delayed recovery provide evidence of the applicability of our results.
61 citations
TL;DR: In this article, a closed-form solution to the eigenvalue problem of a class of master equations that describe open quantum systems with loss and dephasing but without gain is presented.
Abstract: We present a closed-form solution to the eigenvalue problem of a class of master equations that describe open quantum systems with loss and dephasing but without gain. The method relies on the existence of a conserved number of excitations in the Hamiltonian part and the fact that none of the Lindblad operators describe an excitation of the system. In the absence of dephasing Lindblad operators, the eigensystem of the Liouville operator can be constructed from the eigenvalues and eigenvectors of the effective non-Hermitian Hamiltonian used in the quantum jump approach. Open versions of spin chains, the Tavis-Cummings model, and coupled Harmonic oscillators without gain can be solved using this technique.
61 citations
TL;DR: In this paper, the authors used a multi-well, multichannel master equation approach to model the HOONO reaction between He and NO2 in both 220 and 430 K in both He and N2.
Abstract: Data for the reactions between OH and NO2 have been modeled using a multiwell, multichannel master equation approach. In this work, new ab initio quantum chemical results for cis−cis- and trans−perp-HOONO at the QCISD(T)/cc-pVDZ level are used with the multiple-well, multiple-channel master equation approach in order to model the data between 220 and 430 K in both He and N2. The results are in good agreement with the experimental data over the entire ranges of temperature and pressure. The contribution from HOONO is evaluated for the experimental conditions. It is also evaluated for the conditions described by the U.S. Standard Atmosphere (1976). Although the HONO2 pathway dominates over all atmospheric conditions, up to ∼20% of the reaction is predicted to yield HOONO near the tropopause. If the atmospheric fate of HOONO is different than that of HONO2, this can affect atmospheric chemistry models.
60 citations