量子Stratonovich随机演算与量子Wong-Zakai定理
Quantum Stratonovich Stochastic Calculus and the Quantum Wong-Zakai Theorem
摘要：
我们扩展伊藤- Stratonovich分析或量子随机微分方程，介绍了加德纳和Collett的发射（创建），吸收（湮灭）过程，包括散射（守恒）过程。工作的量子随机演算的框架内，我们定义Stratonovich演算的代数修改的伊藤一个，并给出Stratonovich时间有序指数的存在条件。我们表明，转换公式的系数有一个惊人的相似格林函数公式从标准微扰理论。我们表明，微积分方便地描述马尔可夫极限的规则开放的量子动力学系统中的Wong-Zakai近似定理的经典随机分析的方式大致相同。我们以前的极限结果扩展到多维证明，利用图解公约。
英文摘要：
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.
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