A representation of the Belavkin equation via Feynman path integrals. (English) Zbl 1028.81035
In 1989 Belavkin proposed a stochastic partial differential equation obtained from the Schrödinger equation by adding a Brownian motion (white noise) term to account for the interaction with the measuring device. The subject is known as continuous measument theory in the literature. A representation of the solution of Belavkin’s equation in terms of an oscillatory (i.e., Fresnel type) Feynman path integral is given using the Cameron-Martin formula, and it is shown that the integral corresponds to a stochastic Mehler kernel.
Reviewer: G.Roepstorff (Aachen)
MSC:
81S40 | Path integrals in quantum mechanics |
60H15 | Stochastic partial differential equations (aspects of stochastic analysis) |
60H05 | Stochastic integrals |
81P15 | Quantum measurement theory, state operations, state preparations |