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Quantum stochastic Dirac boundary value problem, and the ultrarelativistic limit

V. P. Belavkin

Reports on Mathematical PhysicsDec 1, 200010 citations

On Quantum Stochastic Differential Equations as Dirac Boundary-Value Problems

V. P. Belavkin

Mathematical NotesMay 1, 20010 citations

Non-relativistic Limit of a Dirac particle Interacting with the Quantum Radiation Field (Trends in Infinite Dimensional Analysis and Quantum Probability)

Asao Arai

数理解析研究所講究録Aug 1, 20020 citations

Non-relativistic Limit of a Dirac particle Interacting with the Quantum Radiation Field (Trends in Infinite Dimensional Analysis and Quantum Probability)

Asao Arai

数理解析研究所講究録Aug 1, 20020 citations

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

V. P. Belavkin

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.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.

arXiv:math-ph/0512075Dec 22, 20050 citations

INFINITE-DIMENSIONAL STOCHASTIC ANALYSIS AND FOUNDATIONS OF QUANTUM MECHANICS

Andrei Yu. Khrennikov

WORLD SCIENTIFIC eBooksApr 1, 20070 citations

On the Equivalence of Quantum Stochastics and A Dirac Boundary Value Problem, and an Inductive Stochastic Limit (New Development of Infinite-Dimensional Analysis and Quantum Probability)

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