2007/11/30 by Bruno Galvan
Computer Science · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum Information and Cryptography #Quantum Mechanics and Applications #quant-ph
paper · pdf · doi:10.1007/s10955-008-9530-2
published as J. Stat. Phys. 131, 1155-1167 (2008) · 16 pages, 1 figure. To appear in Journal of Statistical Physics, almost the published version
arxiv created 2008/03/21 · openalex publication_date 2008/04/07 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
An extension of the Born rule, the \it quantum typicality rule, has recently been proposed [B. Galvan: Found. Phys. 37, 1540-1562 (2007)]. Roughly speaking, this rule states that if the wave function of a particle is split into non-overlapping wave packets, the particle stays approximately inside the support of one of the wave packets, without jumping to the others. In this paper a formal definition of this rule is given in terms of \it imprecise probability. An imprecise probability space is a measurable space (Ω, \cal A) endowed with a \it set of probability measures \cal P. The quantum formalism and the quantum typicality rule allow us to define a set of probabilities \cal PΨ on (XT, \cal F), where X is the configuration space of a quantum system, T is a time interval and \cal F is the σ-algebra generated by the cylinder sets. Thus, it is proposed that a quantum system can be represented as the \it imprecise stochastic process (XT, \cal F, \cal PΨ), which is a canonical stochastic process in which the single probability measure is replaced by a set of measures. It is argued that this mathematical model, when used to represent macroscopic systems, has sufficient predictive power to explain both the results of the statistical experiments and the quasi-classical structure of the macroscopic evolution.