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arXiv:1804.09501 · Annales Henri Poincaré

Stochastic Spikes and Poisson Approximation of One-Dimensional Stochastic Differential Equations with Applications to Continuously Measured Quantum Systems

Martin Kolb, Matthias Liesenfeld

Published Feb 11, 2019• 3 citations
arXivHTMLPDF
DOI
10.1007/s00023-019-00772-9

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This paper studies a class of quantum stochastic differential equations, modeling an interaction of a system with its environment in the quantum noise approximation. The space representing quantum noise is the symmetric Fock space over L2R+. Using the isomorphism of this space with the space of square-integrable functionals of the Poisson process, the equations can be represented as classical stochastic differential equations, driven by Poisson processes. This leads to a discontinuous dynamical state reduction which we compare to the Ghirardi-–Rimini–Weber model. A purely quantum object, the norm process, is found, which plays the role of an observer {in the sense of Everett [H. Everett III, Rev. Mod. Phys. 29(3), 454 (1957)]}, encoding all events occurring in the system space. An algorithm introduced by Dalibard et al. [Phys. Rev. Lett. 68(5), 580 (1992)] to numerically solve quantum master equations is interpreted in the context of unraveling, and the trajectories of expected values of system observables are calculated.