Generalized Repeated Interaction Model and Transfer Functions

  • Santanu DeyEmail author
  • Kalpesh J. Haria
Conference paper
Part of the Operator Theory: Advances and Applications book series (OT, volume 240)


Using a scheme involving a lifting of a row contraction we introduce a toy model of repeated interactions between quantum systems. In this model there is an outgoing Cuntz scattering system involving two wandering subspaces. We associate to this model an input/output linear system which leads to a transfer function. This transfer function is a multi-analytic operator, and we show that it is inner if we assume that the system is observable. Finally it is established that transfer functions coincide with characteristic functions of associated liftings.


Repeated interaction quantum system multivariate operator theory row contraction contractive lifting outgoing Cuntz scattering system transfer function multi-analytic operator input-output formalism linear system observability scattering theory characteristic function 


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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of MathematicsIndian Institute of Technology BombayMumbaiIndia

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