*Europhys. Lett.*,

**61**(4), pp. 452-458 (2003)

## 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

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.

PACS: 03.65.Ta – Foundations of quantum mechanics; measurement theory / 03.65.Yz – Decoherence; open systems; quantum statistical methods / 05.30.-d – Quantum statistical mechanics

*© EDP Sciences, 2003*