On Stochastic Schroedinger Equation as a Dirac Boundary-value Problem, and an Inductive Stochastic Limit

Details On Stochastic Schroedinger Equation as a Dirac Boundary-value Problem, and an Inductive Stochastic Limit On Stochastic Schroedinger Equation as a Dirac Boundary-value Problem, and an Inductive Stochastic Limit

2005-12-22

arxiv.org/abs/math-ph/0512075v1

Published in: Evolution Equations and Their Appications, Marcel Dekker, Inc: New York 2000, pp. 311--327

Physics

Mathematical Physics

15 pages. Paper read at the International Conference `Evolution Equations and Their Appications', Baden-Baden 1999, Germany

Scientific paper

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.

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