On the strong resolvent convergence of the Schrödinger evolution to quantum stochastics

A. M. Chebotarev, G. V. Ryzhakov

Research output: Contribution to journalArticlepeer-review

2 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)717-733
Number of pages17
JournalMathematical Notes
Volume74
Issue number5-6
DOIs
Publication statusPublished - 2003
Externally publishedYes

Keywords

  • Lindblad equation
  • Open quantum system
  • Quantum stochastic differential equation
  • Schrödinger equation
  • Strong resolvent limit

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