Master equation

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

Stochastic Neural Field Theory and the System-Size Expansion

Abstract: We analyze a master equation formulation of stochastic neurodynamics for a network of synaptically coupled homogeneous neuronal populations each consisting of N identical neurons. The state of the network is specified by the fraction of active or spiking neurons in each population, and transition rates are chosen so that in the thermodynamic or deterministic limit ($N\rightarrow\infty$) we recover standard activity-based or voltage-based rate models. We derive the lowest order corrections to these rate equations for large but finite N using two different approximation schemes, one based on the Van Kampen system-size expansion and the other based on path integral methods. Both methods yield the same series expansion of the moment equations, which at $\mathcal{O}(1/N)$ can be truncated to form a closed system of equations for the first- and second-order moments. Taking a continuum limit of the moment equations while keeping the system size N fixed generates a system of integrodifferential equations for the ...

Markovian master equations: a critical study

Abstract: We derive Markovian master equations for single and interacting harmonic systems in different scenarios, including strong internal coupling. By comparing the dynamics resulting from the corresponding master equations with numerical simulations of the global system's evolution, we delimit their validity regimes and assess the robustness of the assumptions usually made in the process of deriving the reduced Markovian dynamics. The results of these illustrative examples serve to clarify the general properties of other open quantum system scenarios subject to treatment within a Markovian approximation.

From the time-dependent, multiple-well master equation to phenomenological rate coefficients

Abstract: We discuss at some length the relationship between solutions to the time-dependent, multiple-well master equation and a macroscopic description of the chemistry in terms of phenomenological rate coefficients In so doing, we derive two different methods of obtaining the rate coefficients from the eigenvalues and eigenvectors of G, the transition matrix of the master equation We apply the first of the two methods to the C2H3 + C2H2 and C3H3 + C3H3 reactions, problems we have treated previously using the “experimental” (or exponential-decay) approach, and obtain considerably more and somewhat different results than we obtained in our earlier work

Near-Unity Cooper Pair Splitting Efficiency

Abstract: The two electrons of a Cooper pair in a conventional superconductor form a spin singlet and therefore a maximally entangled state. Recently, it was demonstrated that the two particles can be extracted from the superconductor into two spatially separated contacts via two quantum dots in a process called Cooper pair splitting (CPS). Competing transport processes, however, limit the efficiency of this process. Here we demonstrate efficiencies up to 90%, significantly larger than required to demonstrate interaction-dominated CPS, and on the right order to test Bell's inequality with electrons. We compare the CPS currents through both quantum dots, for which large apparent discrepancies are possible. The latter we explain intuitively and in a semiclassical master equation model. Large efficiencies are required to detect electron entanglement and for prospective electronics-based quantum information technologies.

One-atom lasers.

Abstract: One-atom lasers are important because their governing equations can be solved exactly, even with a quantized field. We present a fully quantum-mechanical treatment of one-atom lasers modeled by quantum-optical master equations. These are solved numerically without any significant approximations. We show that laser action is possible with one atom, and that it might be achievable experimentally. Laser action is characterized by the dominance of stimulated emission over spontaneous emission. We use the one-atom laser model to investigate, without approximation, some interesting generic laser phenomena. Under certain conditions lasers produce intensity squeezed light, and then the laser linewidth increases with the pumping rate, in contrast with standard lasers. We also report ``self-quenching'' behavior: lasers with incoherent pumping out of the lower laser level turn off when the pumping is sufficiently fast because the coherence between the laser levels is destroyed.