论文标题
量子随机过滤和控制许多粒子系统的大量定律
The law of large numbers for quantum stochastic filtering and control of many particle systems
论文作者
论文摘要
关于量子颗粒系统的大量动态定律有广泛的文献，即在描述大型相同相互作用粒子集合中粒子的限制单个行为的方程式。所得方程通常称为非线性scoudinger方程或hartree方程，或毛taevski方程。在本文中，我们将其中一些收敛结果扩展到了随机框架。具体来说，我们与许多粒子量子系统的Belavkin随机滤波进行合作。所得的限制方程是一种新型的方程，可以看作是McKean-Vlasov类型的复杂值无限尺寸非线性扩散。该结果是作者在上一篇论文中开发的量子均值游戏理论的关键要素。
There is an extensive literature on the dynamic law of large numbers for systems of quantum particles, that is, on the derivation of an equation describing the limiting individual behavior of particles inside a large ensemble of identical interacting particles. The resulting equations are generally referred to as nonlinear Scrödinger equations or Hartree equations, or Gross-Pitaevski equations. In this paper we extend some of these convergence results to a stochastic framework. Concretely we work with the Belavkin stochastic filtering of many particle quantum systems. The resulting limiting equation is an equation of a new type, which can be seen as a complex-valued infinite dimensional nonlinear diffusion of McKean-Vlasov type. This result is the key ingredient for the theory of quantum mean-field games developed by the author in a previous paper.
