Master equation

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

Fully quantum fluctuation theorems

Abstract: Systems that are driven out of thermal equilibrium typically dissipate random quantities of energy on microscopic scales. Crooks fluctuation theorem relates the distribution of these random work costs to the corresponding distribution for the reverse process. By an analysis that explicitly incorporates the energy reservoir that donates the energy and the control system that implements the dynamic, we obtain a quantum generalization of Crooks theorem that not only includes the energy changes in the reservoir but also the full description of its evolution, including coherences. Moreover, this approach opens up the possibility for generalizations of the concept of fluctuation relations. Here, we introduce conditional fluctuation relations that are applicable to nonequilibrium systems, as well as approximate fluctuation relations that allow for the analysis of autonomous evolution generated by global time-independent Hamiltonians. We furthermore extend these notions to Markovian master equations, implicitly modeling the influence of the heat bath.

Out-of-equilibrium open quantum systems: A comparison of approximate quantum master equation approaches with exact results

Abstract: We present the Born-Markov approximated Redfield quantum master equation (RQME) description for an open system of noninteracting particles (bosons or fermions) on an arbitrary lattice of $N$ sites in any dimension and weakly connected to multiple reservoirs at different temperatures and chemical potentials. The RQME can be reduced to the Lindblad equation, of various forms, by making further approximations. By studying the $N=2$ case, we show that RQME gives results which agree with exact analytical results for steady-state properties and with exact numerics for time-dependent properties over a wide range of parameters. In comparison, the Lindblad equations have a limited domain of validity in nonequilibrium. We conclude that it is indeed justified to use microscopically derived full RQME to go beyond the limitations of Lindblad equations in out-of-equilibrium systems. We also derive closed-form analytical results for out-of-equilibrium time dynamics of two-point correlation functions. These results explicitly show the approach to steady state and thermalization. These results are experimentally relevant for cold atoms, cavity QED, and far-from-equilibrium quantum dot experiments.

Automatic estimation of pressure-dependent rate coefficients

Abstract: A general framework is presented for accurately and efficiently estimating the phenomenological pressure-dependent rate coefficients for reaction networks of arbitrary size and complexity using only high-pressure-limit information. Two aspects of this framework are discussed in detail. First, two methods of estimating the density of states of the species in the network are presented, including a new method based on characteristic functional group frequencies. Second, three methods of simplifying the full master equation model of the network to a single set of phenomenological rates are discussed, including a new method based on the reservoir state and pseudo-steady state approximations. Both sets of methods are evaluated in the context of the chemically-activated reaction of acetyl with oxygen. All three simplifications of the master equation are usually accurate, but each fails in certain situations, which are discussed. The new methods usually provide good accuracy at a computational cost appropriate for automated reaction mechanism generation.

From a Generalized Chapman−Kolmogorov Equation to the Fractional Klein−Kramers Equation†

Abstract: A non-Markovian generalization of the Chapman−Kolmogorov transition equation for continuous time random processes governed by a waiting time distribution is investigated. It is shown under which conditions a long-tailed waiting time distribution with a diverging characteristic waiting time leads to a fractional generalization of the Klein−Kramers equation. From the latter equation a fractional Rayleigh equation and a fractional Fokker−Planck equation are deduced. These equations are characterized by a slow, nonexponential relaxation of the modes toward the Gibbs−Boltzmann and the Maxwell thermal equilibrium distributions. The derivation sheds some light on the physical origin of the generalized diffusion and friction constants appearing in the fractional Fokker−Planck equation.