Master equation

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

Wave kinetics of relativistic quantum plasmas

Abstract: A quantum kinetic equation, valid for relativistic unmagnetized plasmas, is derived here. This equation describes the evolution of a quantum quasi-distribution, which is the Wigner function for relativistic spinless charged particles in a plasma, and it is exactly equivalent to a Klein-Gordon equation. Our quantum kinetic equation reduces to the Vlasov equation in the classical limit, where the Wigner function is replaced by a classical distribution function. An approximate form of the quantum kinetic equation is also derived, which includes first order quantum corrections. This is applied to electron plasma waves, for which a new dispersion relation is obtained. It is shown that quantum recoil effects contribute to the electron Landau damping with a third order derivative term. The case of high frequency electromagnetic waves is also considered. Its dispersion relation is shown to be insensitive to quantum recoil effects for equilibrium plasma distributions.

Continuous measurements, quantum trajectories, and decoherent histories

Abstract: Quantum open systems are described in the Markovian limit by master equations in Lindblad form. I argue that common ``quantum trajectory'' techniques representing continuous measurement schemes, which solve the master equation by unravelling its evolution into stochastic trajectories in Hilbert space, correspond closely to particular sets of decoherent (or consistent) histories. This is illustrated by a simple model of photon counting. An equivalence is shown for these models between standard quantum jumps and the orthogonal jumps of Di\'osi, which have already been shown to correspond to decoherent histories. This correspondence is compared to simple treatments of trajectories based on repeated or continuous measurements.

Frozen discord in non-markovian dephasing channels

Abstract: We investigate the dynamics of quantum and classical correlations in a system of two qubits under local colored-noise dephasing channels. The time evolution of a single qubit interacting with its own environment is described by a memory kernel non-Markovian master equation. The memory effects of the non-Markovian reservoirs introduce new features in the dynamics of quantum and classical correlations compared to the white noise Markovian case. Depending on the geometry of the initial state, the system can exhibit frozen discord and multiple sudden transitions between classical and quantum decoherence [L. Mazzola, J. Piilo and S. Maniscalco, Phys. Rev. Lett. 104 (2010) 200401]. We provide a geometric interpretation of those phenomena in terms of the distance of the state under investigation to its closest classical state in the Hilbert space of the system.

Exact conditions for the preservation of a canonical distribution in markovian relaxation processes

Abstract: Necessary and sufficient conditions have been determined for the exact preservation of a canonical distribution characterized by a time‐dependent temperature (canonical invariance) in Markovian relaxation processes governed by a master equation. These conditions, while physically realizable, are quite restrictive so that canonical invariance is the exception rather than the rule. For processes with a continuous energy variable, canonical invariance requires that the integral master equation is exactly equivalent to a Fokker‐Planck equation with linear transition moments of a special form. For processes with a discrete energy variable, canonical invariance requires, in addition to a special form of the level degeneracy, equal spacing of the energy levels and transitions between nearest‐neighbor levels only. Physically, these conditions imply that canonical invariance is maintained only for weak interactions of a special type between the relaxing subsystem and the reservoir. It is also shown that canonical ...

Maximum Caliber: a variational approach applied to two-state dynamics.

Abstract: We show how to apply a general theoretical approach to nonequilibrium statistical mechanics, called Maximum Caliber, originally suggested by E. T. Jaynes Annu. Rev. Phys. Chem. 31, 579 1980, to a problem of two-state dynamics. Maximum Caliber is a variational principle for dynamics in the same spirit that Maximum Entropy is a variational principle for equilibrium statistical mechanics. The central idea is to compute a dynamical partition function, a sum of weights over all microscopic paths, rather than over microstates. We illustrate the method on the simple problem of two-state dynamics, A ↔B, first for a single particle, then for M particles. Maximum Caliber gives a unified framework for deriving all the relevant dynamical properties, including the microtrajectories and all the moments of the time-dependent probability density. While it can readily be used to derive the traditional master equation and the Langevin results, it goes beyond them in also giving trajectory information. For example, we derive the Langevin noise distribution rather than assuming it. As a general approach to solving nonequilibrium statistical mechanics dynamical problems, Maximum Caliber has some advantages: 1 It is partition-function-based, so we can draw insights from similarities to equilibrium statistical mechanics. 2 It is trajectory-based, so it gives more dynamical information than population-based approaches like master equations; this is particularly important for few-particle and single-molecule systems. 3 It gives an unambiguous way to relate flows to forces, which has traditionally posed challenges. 4 Like Maximum Entropy, it may be useful for data analysis, specifically for time-dependent phenomena. © 2008 American Institute of Physics. DOI: 10.1063/1.2918345