1997/02/27 by Alexander M. Chebotarev, А. М. Чеботарев, Chebotarev, Alexander M.
Computer Science · Mathematics · Physics and Astronomy · #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Mechanics and Applications #Quantum Physics (quant-ph) #Random Matrices and Applications #quant-ph
paper · pdf · doi:10.48550/arxiv.quant-ph/9702061
28 pages, LaTeX, 86Kb (AMS classification 81S25, 47N50, 46L60)
arxiv created 1997/02/27 · openalex publication_date 1997/02/27 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We show a new remarkable connection between the symmetric form of a quantum stochastic differential equation (QSDE) and the strong resolvent limit of Schrödinger equations in Fock space: the strong resolvent limit is unitary equivalent to QSDE in the adapted (or Ito) form, and the weak limit is unitary equivalent to the symmetric (or Stratonovich) form of QSDE. We prove that QSDE is unitary equivalent to a symmetric boundary value problem for the Schrödinger equation in Fock space. The boundary condition describes standard jumps of the phase and amplitude of components of Fock vectors belonging to the range of the resolvent. The corresponding Markov evolution equation (the Lindblad or Markov master equation) is derived from the boundary value problem for the Schrödinger equation.