Master equation

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

The Poisson Representation. I. A New Technique for Chemical Master Equations

Abstract: We introduce a new technique for handling chemical master equations, based on an expansion of the probability distribution in Poisson distributions. This enables chemical master equations to be transformed into Fokker-Planck and stochastic differential equations and yields very simple descriptions of chemical equilibrium states. Certain nonequilibrium systems are investigated and the results are compared with those obtained previously. The Gaussian approximation is investigated and is found to be valid almost always, except near critical points. The stochastic differential equations derived have a few novel features, such as the possibility of pure imaginary noise terms and the possibility of higher order noise, which do not seem to have been previously studied by physicists. These features are allowable because the transform of the probability distribution is a quasiprobability, which may be negative or even complex.

Deterministic Dicke-state preparation with continuous measurement and control

Abstract: We characterize the long-time projective behavior of the stochastic master equation describing a continuous, collective spin measurement of an atomic ensemble both analytically and numerically. By adding state-based feedback, we show that it is possible to prepare highly entangled Dicke states deterministically.

Environment-Induced Decoherence and the Transition from Quantum to Classical

Abstract: We study dynamics of quantum open systems, paying special attention to those aspects of their evolution which are relevant to the transition from quantum to classical. We begin with a discussion of the conditional dynamics of simple systems. The resulting models are straightforward but suffice to illustrate basic physical ideas behind quantum measurements and decoherence. To discuss decoherence and environment-induced superselection einselection in a more general setting, we sketch perturbative as well as exact derivations of several master equations valid for various systems. Using these equations we study einselection employing the general strategy of the predictability sieve. Assumptions that are usually made in the discussion of decoherence are critically reexamined along with the ``standard lore'' to which they lead. Restoration of quantum-classical correspondence in systems that are classically chaotic is discussed. The dynamical second law -it is shown- can be traced to the same phenomena that allow for the restoration of the correspondence principle in decohering chaotic systems (where it is otherwise lost on a very short time-scale). Quantum error correction is discussed as an example of an anti-decoherence strategy. Implications of decoherence and einselection for the interpretation of quantum theory are briefly pointed out.

Non-Markovian entanglement dynamics of noisy continuous-variable quantum channels

Abstract: We investigate the entanglement dynamics of continuous-variable quantum channels in terms of an entangled squeezed state of two cavity fields in a general non-Markovian environment. Using the Feynman-Vernon influence functional theory in the coherent-state representation, we derive an exact master equation with time-dependent coefficients reflecting the non-Markovian influence of the environment. The influence of environments with different spectral densities, e.g., Ohmic, sub-Ohmic, and super-Ohmic, is numerically studied. The non-Markovian process shows its remarkable influence on the entanglement dynamics due to the sensitive time dependence of the dissipation and noise functions within the typical time scale of the environment. The Ohmic environment shows a weak dissipation-noise effect on the entanglement dynamics, while the sub-Ohmic and super-Ohmic environments induce much more severe noise. In particular, the memory of the system interacting with the environment contributes a strong decoherence effect to the entanglement dynamics in the super-Ohmic case.

Master equation models for chemical reactions of importance in combustion

Abstract: ▪ Abstract The master equation provides a quantitative description of the interaction between collisional energy transfer and chemical reaction for dissociation, isomerization, and association processes. The approach is outlined for both irreversible and reversible dissociation, isomerization, and association reactions. There is increasing interest, especially in combustion, in association reactions that involve several linked potential wells, with the possibility of isomerization, collisional stabilization, and dissociation along several product channels. A major aim of the application of the master equation to such systems is the linking of the eigenvalues obtained by its solution to the rate coefficients for the phenomenological chemical reactions that describe the system and that are used in combustion models. The approach is illustrated by reference to the reactions C2H5 + O2, H + SO2, and the dissociation and isomerization of alkyl radicals.