ИСТИНА

The derivation of an equation describing the limiting individual behavior of particles inside a large ensemble of identical interacting particles is a well developed topic in quantum mechanics literature. The resulting equations are generally referred to as nonlinear Scr\'odinger equations or Hartree equations, or Gross-Pitaevski equations. We extend these theories to a stochastic framework. Concretely we work with the Belavkin stochastic filtering of continuously observed multi-particle quantum systems. In this way we derive limiting nonlinear quantum equations of a new type, which can be looked at as complex-valued infinite dimensional nonlinear diffusion of McKean-Vlasov type. These equations play the key role for the theory of quantum mean-field games developed recently by the author. The results of the talk can be considered as a development of the ideas from the well known works of Belavkin and Maslov on the scaling limit of quantum and classical systems of interacting particles. The talk aims to further develop the ideas from author's papers (1) The law of large numbers for quantum stochastic filtering and control of many particle systems. Theoretical and Mathematical Physics 208:1 (2021), 97-121, and (2) Quantum mean field games. Annals Applied Probability 32:3 (2022), 2254 - 2288.