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Il Nuovo cimento della Società italiana di fisica. B/Il Nuovo cimento B

Quantum mechanics with only positive-time evolution for an isolated system

Alberto Barchielli, L. Lanz

Published Apr 1, 1978• 7 citations
Publisher
DOI
10.1007/bf02726791

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This note starts with a recapitulation of what people call the ``Measurement Problem'' of Quantum Mechanics (QM). The dissipative nature of the quantum-mechanical time-evolution of averages of states over large ensembles of identical isolated systems consisting of matter interacting with the radiation field is discussed and shown to correspond to a stochastic time-evolution of states of individual systems. The importance of dissipation for the successful completion of measurements is highlighted. To conclude, a solution of the ``Measurement Problem'' is sketched in an idealized model of a double-slit experiment.
A quantum system is a quantum system which is both isolated and non-time reversal invariant. This article presents precise definitions for those concepts and also a characterization of quantum systems within the class of completely posi- tive Markovian quantum systems in finite dimension (through a homogeneous linear equation for the non- Hamiltonian part of the system's Liouvillian). To set the framework, the basic features of quantum mechan- ics are reviewed focusing on time evolution and also on the theory of completely positive Markovian quantum systems, including Kossakowski-Lindblad's standard form for Liouvillians. After those general considera- tions, a simple two-dimensional example is presented and then applied to describe the neutrino oscillation, with the introduction of a new dispersive parameter.