Generalized Repeated Interaction Model and Transfer Functions
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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.
KeywordsRepeated 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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- J.A. Ball, G. Groenewald, T. Malakorn, Conservative structured noncommutative multidimensional linear systems. The state space method generalizations and applications, 179–223, Oper. Theory Adv. Appl., 161, Birkhäuser, Basel (2006).Google Scholar
- J.A. Ball, V. Vinnikov, Lax–Phillips scattering and conservative linear systems: a Cuntz-algebra multidimensional setting, Mem. Amer. Math. Soc., 178 (2005).Google Scholar
- J. Gough, R. Gohm, Yanagisawa: Linear Quantum feedback Networks, Phys. Rev. A, 78 (2008).Google Scholar
- R. Gohm, Noncommutative stationary processes, Lecture Notes in Mathematics, 1839, Springer-Verlag, Berlin (2004).Google Scholar
- R. Gohm, Transfer function for pairs of wandering subspaces, Spectral theory,mathematical system theory, evolution equations, differential and difference equations, 385– 398, Oper. Theory Adv. Appl., 221, Birkhäuser/Springer Basel AG, Basel, (2012).Google Scholar
- P.D. Lax, R.S. Phillips, Scattering theory, Pure and Applied Mathematics 26 Academic press, New York-London, (1967).Google Scholar
- M. Reed, B. Simon, Methods of modern mathematical physics. III. Scattering theory. Academic PressGoogle Scholar
- [Harcourt Brace Jovanovich, Publishers], New York-London, (1979).Google Scholar
- B. Sz.-Nagy, C. Foias, Harmonic analysis of operators on Hilbert space, North– Holland Publ., Amsterdam-Budapest (1970).Google Scholar