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The Hamiltonian Generating Quantum Stochastic Evolutions in the Limit from Repeated to Continuous Interactions

    https://doi.org/10.1142/S1230161215500225Cited by:1 (Source: Crossref)

    We consider a quantum stochastic evolution in continuous time defined by the quantum stochastic differential equation of Hudson and Parthasarathy. On one side, such an evolution can also be defined by a standard Schrödinger equation with a singular and unbounded Hamiltonian operator K. On the other side, such an evolution can also be obtained as a limit from Hamiltonian repeated interactions in discrete time. We study how the structure of the Hamiltonian K emerges in the limit from repeated to continuous interactions. We present results in the case of 1-dimensional multiplicity and system spaces, where calculations can be explicitly performed, and the proper formulation of the problem can be discussed.