Heisenberg equation-of-motion methods applied to non-Markovian open systems

Carole Addis

James D. Cresser

A method is presented by which the stochastic Schrodinger equation can be derived for systems coupled to a reservoir in cases in which the system-reservoir interaction is non-Markovian, and under the condition that the initial system reservoir state is decorrelated. The method is based on a Heisenberg equation of motion approach applied in conjunction with a technique of dealing with system-reservoir interactions introduced by Mollow in his treatment of the AC Stark effect. The general Diosi-Strunz stochastic Schrodinger equation is regained, but the method developed here offers a different perspective on obtaining the final form of this equation for specific applications. The method is illustrated for a damped two level atom, a driven damped harmonic oscillator, and quantum Brownian motion.

Yusui Chen

G. K. Paramonov, Peter Saalfrank

An efficient method for the numerical solution of a non-Markovian, open-system density matrix equation of motion in coordinate representation is developed. We apply the scheme to model simulations of the laser-assisted $\mathrm{O}+\mathrm{H}\ensuremath{\rightarrow}\mathrm{O}\mathrm{H}$ association reaction in an environment. The suggested approach is based on the application of the time-evolution operator to the ``closed-system'' part of the overall Hamiltonian and transformation of the open-system equation of motion to the Heisenberg picture suitable for numerical propagation. A dual role of the system-environment coupling with respect to the infrared (ir) laser-driven association of OH is demonstrated: the association probability is increased due to the coupling at relatively weak laser fields, but decreased at strong laser fields. Moreover, at a certain strength of the ir laser field, the association probability does not depend on the strength of the system-bath coupling at all.

Inés de Vega, Daniel Alonso

This review gives a summary of the many techniques that are used in the analysis of open quantum systems. Emphasis is on those cases where it is unsuitable to use a memoryless or Markovian point of view, generally because there is no large separation of time scales between system and environment dynamics. The approaches reviewed include master equations, Heisenberg equations of motion, chain mapping representations, and various stochastic methods such as path integral Monte Carlo and stochastic equations. Guidance is given on how to evaluate the suitability of each of these methods for application in different physical problems.

Lajos Diósi, Walter T. Strunz