Master equation

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

The H + C2H2(+M) ⇄ C2H3(+M) and H + C2H2(+M) ⇄ C2H5(+M) reactions: Electronic structure, variational transition-state theory, and solutions to a two-dimensional master equation

Abstract: In this article we investigate the kinetics of the H + C2H2 and H + C2H4 reactions, as well as their reverse dissociations, in some detail. High level electronic structure calculations are used to characterize the potential energy surfaces, and these results are not adjusted to obtain good agreement with experiment in the subsequent kinetic analysis. An approximate two-dimensional master equation is used to determine phenomenological rate coefficients, k(T,p). The effects of angular momentum conservation, tunneling, and the use of variational transition-state theory (as opposed to conventional transition-state theory) to compute microcanonical rate coefficients are investigated in detail. For both reactions, the low-pressure limit is approached very slowly, because reaction just above threshold must occur strictly by tunneling. Assuming a single-exponential-down model for P(E,E′), we deduce from experiment values of 〈ΔEd〉, the average energy transferred in a deactivating collision, as a function of temperature for both C2H3 and C2H5 in baths of He, Ar, and N2. Our results support the idea that 〈ΔEd〉 increases roughly linearly with temperature, at least for weak colliders. The agreement between theory and experiment is remarkably good for both reactions. Values of k(T,p) for the two reactions are given in the Troe format for use in modeling.

Entanglement oscillations in non-Markovian quantum channels

Abstract: We study the non-Markovian dynamics of a two-mode bosonic system interacting with two uncorrelated thermal bosonic reservoirs. We present the solution to the exact microscopic Master equation in terms of the quantum characteristic function and study in detail the dynamics of entanglement for bipartite Gaussian states. In particular, we analyze the effects of short-time system-reservoir correlations on the separability thresholds and show that the relevant parameter is the reservoir spectral density. If the frequencies of the involved modes are within the reservoir spectral density, entanglement persists for a longer time than in a Markovian channel. On the other hand, when the reservoir spectrum is out of resonance, short-time correlations lead to a faster decoherence and to the appearance of entanglement oscillations.

Derivation of a master equation for charge-transfer processes in atom-surface collisions

Abstract: The time-dependent Anderson model for multiple levels interacting with a continuum is studied using the slave-boson Green's-function technique, with an eye to understanding charge-transfer phenomena for an atomic species moving outside a metallic surface. It is shown that in the finite-temperature and low-velocity limit, the equations for the occupation numbers satisfy a master equation. Application to charge-exchange processes in atom-surface-scattering experiments shows that the presence of strong intra-atomic correlation effects can drastically change the charge-transfer dynamics.

Quantum kinetic theory: A quantum kinetic master equation for condensation of a weakly interacting Bose gas without a trapping potential

Abstract: A quantum kinetic master equation (QKME) for bosonic atoms is formulated. It is a quantum stochastic equation for the kinetics of a dilute quantum Bose gas, and describes the behavior and formation of Bose condensation. The key assumption in deriving the QKME is a Markov approximation for the atomic collision terms. In the present paper the basic structure of the theory is developed, and approximations are stated and justified to delineate the region of validity of the theory. Limiting cases of the QKME include the quantum Boltzmann master equation and the Uehling-Uhlenbeck equation, as well as an equation analogous to the Gross-Pitaevskii equation.

From completely positive maps to the quantum Markovian semigroup master equation

Abstract: A central problem in the theory of the dynamics of open quantum systems is the derivation of a rigorous and computationally tractable master equation for the reduced system density matrix. Most generally, the evolution of an open quantum system is described by a completely positive linear map. We show how to derive a completely positive Markovian master equation (the Lindblad equation) from such a map by a coarse-graining procedure. We provide a novel and explicit recipe for calculating the coefficients of the master equation, using perturbation theory in the weak-coupling limit. The only parameter external to our theory is the coarse-graining time-scale. We illustrate the method by explicitly deriving the master equation for the spin-boson model. The results are evaluated for the exactly solvable case of pure dephasing, and an excellent agreement is found within the time-scale where the Markovian approximation is expected to be valid. The method can be extended in principle to include non-Markovian effects.