Quantum Stochastic Generators

Details Quantum Stochastic Generators Quantum Stochastic Generators

2003-09-12

arxiv.org/abs/quant-ph/0309102v3

Physics

Quantum Physics

18 pages, no figures, updated with discussion on various notions of time-ordered exponentials (Ito/Stratonovich/exponentiated)

Scientific paper

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.

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