Master equation

About: Master equation is a research topic. Over the lifetime, 10541 publications have been published within this topic receiving 276095 citations.

Nonequilibrium quantum dynamics in the condensed phase via the generalized quantum master equation.

Abstract: The Nakajima-Zwanzig generalized quantum master equation provides a general, and formally exact, prescription for simulating the reduced dynamics of a quantum system coupled to a quantum bath. In this equation, the memory kernel accounts for the influence of the bath on the system’s dynamics, and the inhomogeneous term accounts for initial system-bath correlations. In this paper, we propose a new approach for calculating the memory kernel and inhomogeneous term for arbitrary initial state and system-bath coupling. The memory kernel and inhomogeneous term are obtained by numerically solving a single inhomogeneous Volterra equation of the second kind for each. The new approach can accommodate a very wide range of projection operators, and requires projection-free two-time correlation functions as input. An application to the case of a two-state system with diagonal coupling to an arbitrary bath is described in detail. Finally, the utility and self-consistency of the formalism are demonstrated by an explicit calculation on a spin-boson model.

Vibrational Nonequilibrium Effects in the Conductance of Single Molecules with Multiple Electronic States

Abstract: Vibrational nonequilibrium effects in charge transport through single-molecule junctions are investigated. Focusing on molecular bridges with multiple electronic states, it is shown that electronic-vibrational coupling triggers a variety of vibronic emission and absorption processes, which influence the conductance properties and mechanical stability of single-molecule junctions profoundly. Employing a master equation and a nonequilibrium Green's function approach, these processes are analyzed in detail for a generic model of a molecular junction and for benzenedibutanethiolate bound to gold electrodes.

Regularity Theory and Extension Problem for Fractional Nonlocal Parabolic Equations and the Master Equation

Abstract: We develop the regularity theory for solutions to space-time nonlocal equations driven by fractional powers of the heat operator $(\partial_t-\Delta)^su(t,x)=f(t,x)~{for}~0

General Theory and Applications to Unstable Particles

Abstract: The aim of the first part of these lecture notes is to give a concise and self-contained introduction into a mathematically sound theory of quantum Markovian master equations The text is intended for those who are interested in practical applications and are not experts in mathematical physics Therefore the original proofs are highly simplified or replaced by heuristic ones However, the final results are always consistent with the rigorous mathematical theory Subsection 12 is devoted to the general properties of an irreversible evolution for a quantum open system In contrast to the classical theory the problem of the most general admissible dynamical transformation of quantum mixed states is not a trivial one and leads to the notion of complete positivity The main result of this discussion is the general form of the Markovian master equation satisfying the complete positivity condition Three methods of derivation of Markovian master equations from the underlying Hamiltonian dynamics of the open system coupled to the reservoir are presented in Subsect 13 In contrast to many of the derivations which can be found in the literature the attention is paid to a mathematically proper form of the obtained equations of motion The next subsection contains few examples of possible extensions of the presented formalism The open systems influenced by varying external conditions, systems with different “channels of evolution” and the simplified description of many-body open systems in terms of nonlinear single-particle evolution equations are briefly discussed In Subsect 15 a model of N 2-level atoms interacting with the electromagnetic field in thermal equilibrium is worked out in some details and serves as an illustration of the general result

Yang-Baxter Equation and Quantum Enveloping Algebras

Abstract: Mathematical preliminaries origin of the Yang-Baxter equation classical Yang-Baxter equation quantum enveloping algebras quantum Clebsch-Gordan co-efficients simple Yang-Baxter equation trigonometric and rational solutions non-generic q values.