Curie-Weiss model of the quantum measurement process

¹ SPhT, CEA Saclay - 91191 Gif-sur-Yvette cedex, France
² Yerevan Physics Institute - Alikhanian Brothers St. 2, Yerevan 375036, Armenia
³ Institute for Theoretical Physics - Valckenierstraat 65 1018 XE Amsterdam, The Netherlands

Received: 1 July 2002
Accepted: 11 December 2002

Abstract

A Hamiltonian model is solved, which satisfies all requirements for a realistic ideal quantum measurement. The system S is a spin-, whose z-component is measured through coupling with an apparatus , consisting of a magnet M formed by a set of spins with quartic infinite-range Ising interactions, and a phonon bath B at temperature T. Initially A is in a metastable paramagnetic phase. The process involves several time-scales. Without being much affected, A first acts on S, whose state collapses in a very brief time. The mechanism differs from the usual decoherence. Soon after its irreversibility is achieved. Finally, the field induced by S on M, which may take two opposite values with probabilities given by Born's rule, drives A into its up or down ferromagnetic phase. The overall final state involves the expected correlations between the result registered in M and the state of S. The measurement is thus accounted for by standard quantum-statistical mechanics and its specific features arise from the macroscopic size of the apparatus.