Quantum Stochastic Generators
Quantum Physics
2007-05-23 v3
Abstract
We discuss stochastic derivations, stochastic Hamiltonians and the flows that they generate, algebraic fluctuaion-dissipation theorems, etc., in a language common to both classical and quantum algebras. It is convenient to define distinct notions of time-ordered exponentials to take account of the breakdown of the Leibniz rule in the Ito calculus. We introduce a notion of quantum Stratonovich calculus and show how it relates to Stratonovich-Dyson time ordered exponentials. We then use it to demonstrate a natural way to add stochastic derivations.
Cite
@article{arxiv.quant-ph/0309102,
title = {Quantum Stochastic Generators},
author = {John Gough},
journal= {arXiv preprint arXiv:quant-ph/0309102},
year = {2007}
}
Comments
18 pages, no figures, updated with discussion on various notions of time-ordered exponentials (Ito/Stratonovich/exponentiated)and their distinct role in quantum stochastic limits