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 Mat. Zametki, 2001, Volume 69, Issue 6, Pages 803–819 (Mi mz695)

On Quantum Stochastic Differential Equations as Dirac Boundary-Value Problems

V. P. Belavkin

Nottingham Trent University

Abstract: We prove that a single-jump unitary quantum stochastic evolution is unitarily equivalent to the Dirac boundary-value problem on the half-line in an extended space. It is shown that this solvable model can be derived from the Schrödinger boundary-value problem for a positive relativistic Hamiltonian on the half-line as the inductive ultrarelativistic limit corresponding to the input flow of Dirac particles with asymptotically infinite momenta. Thus the problem of stochastic approximation can be reduced to a quantum mechanical boundary-value problem in the extended space. The problem of microscopic time reversibility is also discussed in the paper.

DOI: https://doi.org/10.4213/mzm695

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English version:
Mathematical Notes, 2001, 69:6, 735–748

Bibliographic databases:

UDC: 517

Citation: V. P. Belavkin, “On Quantum Stochastic Differential Equations as Dirac Boundary-Value Problems”, Mat. Zametki, 69:6 (2001), 803–819; Math. Notes, 69:6 (2001), 735–748

Citation in format AMSBIB
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