In the first part of this talk I shall describe the structure of discrete-time and continuous-time quantum stochastic cocycles and the appropriate scaling for the convergence of the former to the latter, in the form of a Donsker-type invariance principle (functional central limit theorem). This will be illustrated by the repeated interactions model of Attal and Pautrat.
In the second part I plan to show how quasifree-driven QS cocycles arise naturally as limits of QRW’s in the above model. In particular we shall see how the covariance of a quasifree Brownian motion emerges from the data of a faithful normal state on an underlying particle algebra.
Based on joint work with Alex Belton and Michal Gnacik, with Ollie Margetts, and with Ping Zhong.
This video was produced by the International Centre for Mathematical Sciences, as part of the workshop Mathematical Physics in Quantum Technology: From Finite to Infinite Dimensions.
