Measurement and ergodicity in quantum mechanics

DOI10.1088/1751-8113/48/18/185302zbMATH Open1314.81027arXiv1312.6907OpenAlexW2080762587MaRDI QIDQ5251077

P. A. Mello, Mariano Bauer

Publication date: 22 May 2015

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Abstract: The experimental realization of successive non-demolition measurements on single microscopic systems brings up the question of ergodicity in Quantum Mechanics (QM). We investigate whether time averages over one realization of a single system are related to QM averages over an ensemble of similarly prepared systems. We adopt a generalization of von Neumann model of measurement, coupling the system to $N$ "probes" --with a strength that is at our disposal-- and detecting the latter. The model parallels the procedure followed in experiments on Quantum Electrodynamic cavities. The modification of the probability of the observable eigenvalues due to the coupling to the probes can be computed analytically and the results compare qualitatively well with those obtained numerically by the experimental groups. We find that the problem is not ergodic, except in the case of an eigenstate of the observable being studied.

Full work available at URL: https://arxiv.org/abs/1312.6907

zbMATH Keywords

quantum ergodicitynon-demolition measurementsvon Neumann model of measurement

Mathematics Subject Classification ID

Entropy and other invariants (28D20) Quantum optics (81V80) Quantum measurement theory, state operations, state preparations (81P15) Dynamical systems and their relations with probability theory and stochastic processes (37A50)

Related Items (2)

Energy fluctuation relations and repeated quantum measurements ⋮ Title not available (Why is that?)

This page was built for publication: Measurement and ergodicity in quantum mechanics

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q5251077)