Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The law of large numbers for quantum stochastic filtering and control of
  many particle systems   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 Scr\"odinger 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.

33
The categories of this paper are: plasm-ph
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
9
The categories of this paper are: nlin
11
The categories of this paper are: hep-lat
0
The categories of this paper are: hep-ph
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
16
The categories of this paper are: stat
12
The categories of this paper are: nucl-th
27
The categories of this paper are: comp-gas
24
The categories of this paper are: dg-ga
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
25
The categories of this paper are: patt-sol