On Stochastic Schroedinger Equation as a Dirac Boundary-value Problem, and an Inductive Stochastic Limit
Abstract
We prove that a single-jump quantum stochastic unitary evolution is equivalent to a Dirac boundary value problem on the half line in one extra dimension. It is shown that this exactly solvable model can be obtained from a Schroedinger boundary value problem for a positive relativistic Hamiltonian in the half-line as the inductive ultrarelativistic limit, correspondent to the input flow of Dirac particles with asymptotically infinite momenta. Thus the problem of stochastic approximation is reduced to the to the quantum-mechanical boundary value problem in the extra dimension. The question of microscopic time reversibility is also studied for this paper.
Cite
@article{arxiv.math-ph/0512075,
title = {On Stochastic Schroedinger Equation as a Dirac Boundary-value Problem, and an Inductive Stochastic Limit},
author = {V. P. Belavkin},
journal= {arXiv preprint arXiv:math-ph/0512075},
year = {2007}
}
Comments
15 pages. Paper read at the International Conference `Evolution Equations and Their Appications', Baden-Baden 1999, Germany