This article is cited in 4 papers

On the Strong Resolvent Convergence of the Schrödinger Evolution to Quantum Stochastics

A. M. Chebotarev^a, G. V. Ryzhakov<sup>b

a</sup> M. V. Lomonosov Moscow State University, Faculty of Physics
^b M. V. Lomonosov Moscow State University

Abstract: For a class of Hamiltonians including a model of the quantum detector of gravitational waves, we prove the strong convergence of the Schrödinger evolution to quantum stochastics. We show that the strong resolvent limit of a sequence of self-adjoint Hamiltonians is a symmetric boundary-value problem in Fock space, and the limit evolution of the partial trace with respect to the mixed state cannot be described by a unique equation of Lindblad type. On the contrary, each component of the mixed state generates a proper evolution law.

UDC: 517.958

Received: 13.12.2002
Revised: 06.07.2003

DOI: 10.4213/mzm297

 English version: Mathematical Notes, 2003, 74:5, 717–733

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