Jump to ContentJump to Main Navigation
The Theory of Open Quantum Systems$
Users without a subscription are not able to see the full content.

Heinz-Peter Breuer and Francesco Petruccione

Print publication date: 2007

Print ISBN-13: 9780199213900

Published to Oxford Scholarship Online: January 2010

DOI: 10.1093/acprof:oso/9780199213900.001.0001

Show Summary Details
Page of

PRINTED FROM OXFORD SCHOLARSHIP ONLINE (www.oxfordscholarship.com). (c) Copyright Oxford University Press, 2018. All Rights Reserved. Under the terms of the licence agreement, an individual user may print out a PDF of a single chapter of a monograph in OSO for personal use (for details see www.oxfordscholarship.com/page/privacy-policy).date: 19 September 2018

The Stochastic Simulation Method

The Stochastic Simulation Method

Chapter:
(p.361) 7 THE STOCHASTIC SIMULATION METHOD
Source:
The Theory of Open Quantum Systems
Author(s):

Heinz-Peter Breuer

Francesco Petruccione

Publisher:
Oxford University Press
DOI:10.1093/acprof:oso/9780199213900.003.07

The formulation of the dynamics of open quantum systems by means of stochastic processes in Hilbert space leads to efficient Monte–Carlo simulation techniques which are introduced and examined in this chapter. Depending on whether the stochastic process is a piecewise deterministic process or a diffusion process, the corresponding individual realizations consist of intervals of deterministic evolution periods interrupted by instantaneous quantum jumps, or of continuous, nowhere differentiable paths. Various Monte Carlo algorithms for both types of processes are described in detail, and their convergence behaviour and their numerical performance is investigated for a number of applications, such as the damped harmonic oscillator, the driven two-level system, and the damped driven Morse oscillator.

Keywords:   piecewise deterministic processes, stochastic Schrödinger equations, stochastic differential equations, Monte-Carlo simulations, Euler algorithm, Heun algorithm, Runge–Kutta algorithm, Platen–Kloeden algorithm, harmonic oscillator, driven Morse oscillator

Oxford Scholarship Online requires a subscription or purchase to access the full text of books within the service. Public users can however freely search the site and view the abstracts and keywords for each book and chapter.

Please, subscribe or login to access full text content.

If you think you should have access to this title, please contact your librarian.

To troubleshoot, please check our FAQs , and if you can't find the answer there, please contact us .