Quantum Stratonovich Stochastic Calculus and the Quantum Wong-Zakai Theorem

Details Quantum Stratonovich Stochastic Calculus and the Quantum Wong-Zakai Theorem Quantum Stratonovich Stochastic Calculus and the Quantum Wong-Zakai Theorem

2005-11-13

arxiv.org/abs/math-ph/0511046v2

J. Math. Phys. 47, 113509, 2006

Physics

Mathematical Physics

24 pages

Scientific paper

10.1063/1.2354331

We extend the Ito -to- Stratonovich analysis or quantum stochastic differential equations, introduced by Gardiner and Collett for emission (creation), absorption (annihilation) processes, to include scattering (conservation) processes. Working within the framework of quantum stochastic calculus, we define Stratonovich calculus as an algebraic modification of the Ito one and give conditions for the existence of Stratonovich time-ordered exponentials. We show that conversion formula for the coefficients has a striking resemblance to Green's function formulae from standard perturbation theory. We show that the calculus conveniently describes the Markov limit of regular open quantum dynamical systemsin much the same way as in the Wong-Zakai approximation theorems of classical stochastic analysis. We extend previous limit results to multiple-dimensions with a proof that makes use of diagrammatic conventions.

Affiliated with

Also associated with

No associations

Rating

Quantum Stratonovich Stochastic Calculus and the Quantum Wong-Zakai Theorem does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Quantum Stratonovich Stochastic Calculus and the Quantum Wong-Zakai Theorem, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Quantum Stratonovich Stochastic Calculus and the Quantum Wong-Zakai Theorem will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-423484