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arXiv:hep-th/9409189 · Annalen der Physik

Event‐enhanced quantum theory and piecewise deterministic dynamics

Ph. Blanchard, Arkadiusz Jadczyk

Published Jan 1, 1995• 60 citations
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Abstract

Abstract The standard formalism of quantum theory is enhanced and definite meaning is given to the concepts of experiment, measurement and event. Within this approach one obtains a uniquely defined piecewise deterministic algorithm generating quantum jumps, classical events and histories of single quantum objects. The wave‐function Monte Carlo method of Quantum Optics is generalized and promoted to the level of a fundamental process generating all the real events in Nature. The already worked out applications include SQUID‐tank model and generalized cloud chamber model with GRW spontaneous localization as a particular case. Differences between the present approach and quantum measurement theories based on environment‐induced master equations are stressed. Questions: what is classical, what is time, and what observers are addressed. Possible applications of the new approach are suggested, among them connection between the stochastic commutative geometry and Connes' noncommutative formulation of the Standard Model, as well as potential applications to the theory and practice of quantum computers.

DOI
10.1002/andp.19955070605

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Abstract The standard formalism of quantum theory is enhanced and definite meaning is given to the concepts of experiment, measurement and event. Within this approach one obtains a uniquely defined piecewise deterministic algorithm generating quantum jumps, classical events and histories of single quantum objects. The wave‐function Monte Carlo method of Quantum Optics is generalized and promoted to the level of a fundamental process generating all the real events in Nature. The already worked out applications include SQUID‐tank model and generalized cloud chamber model with GRW spontaneous localization as a particular case. Differences between the present approach and quantum measurement theories based on environment‐induced master equations are stressed. Questions: what is classical, what is time, and what observers are addressed. Possible applications of the new approach are suggested, among them connection between the stochastic commutative geometry and Connes' noncommutative formulation of the Standard Model, as well as potential applications to the theory and practice of quantum computers.
The standard formalism of quantum theory is enhanced and definite meaning is given to the concepts of experiment, measurement and event. Within this approach one obtains a uniquely defined piecewise deterministic algorithm generating quantum jumps, classical events and histories of single quantum objects. The wave-function Monte Carlo method of Quantum Optics is generalized and promoted to the level of a fundamental process generating all the real events in Nature. The already worked out applications include SQUID-tank model and generalized cloud chamber model with GRW spontaneous localization as a particular case. Differences between the present approach and quantum measurement theories based on environment-induced master equations are stressed. Questions: what is classical, what is time, and what observers are addressed. Possible applications of the new approach are suggested, among them connection between the stochastic commutative geometry and Connes' noncommutative formulation of the Standard Model, as well as potential applications to the theory and practice of quantum computers.
We review what we call \event-enhanced formalismof quantum theory. In this approach we explicitly assume classical nature of events. Given a quantum system, that is coupled to a classical one by a suitable coupling, classical events are being triggered. The trigerring process is partly random and partly deterministic. Within this new approach one can modelize real experimental events, including pointer readings of measuring devices. Our theory gives, for the rst time, a unique algorithm that can be used for computer generation of experimental runs with individual quantum objects.
Abstract This chapter contains the foundations of the stochastic formulation of continuous measurements carried out on an open quantum system. It shows that the time evolution of the state vector, conditioned on the measurement record, is given by a piecewise deterministic process in Hilbert space involving continuous time-evolution periods which are broken by randomly occurring, sudden quantum jumps. This so-called unravelling of the quantum master equation in the form of a stochastic process is based on a close relation between quantum dynamical semigroups and piecewise deterministic processes. The general theory is illustrated by means of a number of examples, such as direct, homodyne, and heterodyne photodetection. The chapter also treats the corresponding description of continuous measurements through stochastic Schr ö dinger equations and stochastic differential equations for the density matrix, as well as the stochastic representation of multitime correlations functions.
The law of track formation in cloud chambers is derived from the Liouville equation with a simple Lindblad's type generator that describes coupling between a quantum particle and a classical, continuous medium of two-state detectors. Piecewise deterministic random process (PDP) corresponding to the Liouville equation is derived. The process consists of pairs (classical event, quantum jump), interspersed with random periods of continuous (in general, non-linear) Schrödinger-type evolution. The classical events are flips of the detectors – they account for tracks. Quantum jumps are shown, in the simplest, homogeneous case, to be identical to those in the early spontaneous localization model of Ghirardi, Rimini and Weber (GRW). The methods and results of the present paper allow for an elementary derivation and numerical simulation of particle track formation and provide an additional perspective on GRW's proposal.