Dissipation in media with memory: A master equation in the statistical resonance approximation

Abstract

Articles you may be interested inStatistically testing the validity of analytical and computational approximations to the chemical master equation J. Chem. Phys. 138, 204108 (2013); 10.1063/1.4807390 Biexponential theory of Drude dissipation via hierarchical quantum master equation Translation-covariant Markovian master equation for a test particle in a quantum fluidA non-Markovian master equation is derived for the reduced probability density matrix of a subsystem interacting with a general reservoir of coupled anharmonic modes. Relaxation of the subsystem is mediated through resonant interactions with the reservoir. These interactions correspond to local vibrational motions with finite lifetimes due to diffusion/dephasing. The derivation assumes that the density of these interaction modes is very large so that they can be treated using statistical methods. The resulting master equation is shown to preserve probability, Hermiticity, and translational invariance, and conditions are stated which guarantee the positivity of the reduced density. At long time the master equation reduces to a Markovian equation of dynamical semigroup type. In the high temperature limit the theory is parameter free, and shows good agreement with the exact master equation of a spin-boson system.

Numerical method for integrodifferential generalized Langevin and master equations

“…If the spin Hamiltonian is H = then the equation for the density matrix ρ(t) is of the form [3,4] dρ(t) dt…”

“…Generalized Langevin equations (GLE) [1] and nonMarkovian master equations [2,3,4], which arise in the treatment of systems interacting with environmental degrees of freedom, often have an integro-differential form. Unlike ordinary differential equations which can be readily solved using Runge-Kutta, Predictor-Corrector and other well known numerical schemes [5] there are no general methods for solving equations of integro-differential type.…”

Open Quantum Dynamics: Complete Positivity and Entanglement

“…see Refs. [39,[60][61][62][63][64][65][66]). Indeed, as already stressed, it arises because of the possibility of an uncontrollable statistical coupling of the experimentally accessible system with an inert entity, the ancilla.…”

“…[63][64][65][66]). The argument is that any Markov approximation neglects a certain initial span of time, namely a transient, during which no semigroup timeevolution is possible due to unavoidable memory effects.…”

On Completely Positive Non-Markovian Evolution of a d-Level System

“…[2,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30]). However, the complete positivity of the resulting time evolution is still an important problem to be investigated.…”