Quantum filtering for interacting quantum particles

I plan to give an introduction to the new theory of the law of large numbers for continuously observed interacting quantum-particle systems developed during the last 3 - 4 years. The topic can be conditionally divided into 3 parts: 1) mathematical theory of quantum filtering (Belavkin's) equations for mixed states (in infinite-dimensional spaces, derived heuristically about 40 years ago), including their derivation from the processes of discrete measurements (with the rates of convergence), 2) new quantum filtering equations describing the law of large numbers for interacting quantum systems, 3) quantum dynamic games and quantum mean field games.

Main publications on the theme are as follows:

Vassili N. Kolokoltsov. On quantum stochastic master equations. https://arxiv.org/abs/2406.08962 Electron. J. Probab. 30 (2025), PNO = 57, pp 1-21,

Vassili N. Kolokoltsov. On the Mathematical Theory of Quantum Stochastic Filtering Equations for Mixed States. (RJMP) Russian Journal of Mathematical Physics 32:3 (2025), 510-529.

Vassili N. Kolokoltsov. Continuous time random walks modeling of quantum measurement and fractional equations of quantum stochastic filtering and control. https://arXiv:2008.07355 Fractional Calculus and Applied Analysis 25 (2022), 128 - 165

Vassili N. Kolokoltsov. Quantum mean field games. https://arxiv.org/pdf/2005.02350.pdf Annals Applied Probability 32:3 (2022), 2254 - 2288.

Vassili N. Kolokoltsov. Dynamic Quantum Games. Dynamic Games and Applications. Open Access, v. 12 (2022), 552-573.

Vassili N. Kolokoltsov. The law of large numbers for quantum stochastic filtering and control of many particle systems. Theoretical and Mathematical Physics 208:1 (2021), 97-121. English translation 208(1), 937-957. https://arXiv:2008.07375

Vassili N. Kolokoltsov. Quantum Mean-Field Games with the Observations of Counting Type. Games MDPI (2021), 12, 7.

Язык доклада: английский