A Dynamical Theory of Quantum Measurement and Spontaneous Localization

Abstract

We develop a rigorous treatment of discontinuous stochastic unitary evolution for a system of quantum particles that interacts singularly with quantum "bubbles" at random instants of time. This model of a "cloud chamber" allows to watch and follow with a quantum particle along the trajectory in the cloud chamber by sequential unsharp localization of spontaneous scatterings of the bubbles. Thus, the continuous reduction and spontaneous localization theory is obtained as the result of quantum filtering theory, i.e., a theory describing the conditioning of the a priori quantum state by the measurement data. We show that in the case of indistinguishable particles the a posteriori dynamics is mixing, giving rise to an irreversible Boltzmann-type reduction equation. The latter coincides with the nonstochastic Schroedinger equation only in the mean field approximation, whereas the central limit yields Gaussian mixing fluctuations described by stochastic reduction equations of diffusive type.

arXiv comment25 pages. See also related papers at http://www.maths.nott.ac.uk/personal/vpb/research/mes_fou.html and http://www.maths.nott.ac.uk/personal/vpb/research/evo_equ.html

References in corpus (1)

• Measurements continuous in time and a posteriori states in quantum

Cited by in corpus (4)

• The Stochastic Representation of Hamiltonian Dynamics and The Quantization of Time
• Quantum Stochastics, Dirac Boundary Value Problem, and the Ultra Relativistic Limit
• A Variance Inequality for Meromorphic Measurement Functions under Exterior Probability
• On Stochastic Schroedinger Equation as a Dirac Boundary-value Problem, and an Inductive Stochastic Limit