Curie-Weiss model of the quantum measurement process

Details Curie-Weiss model of the quantum measurement process Curie-Weiss model of the quantum measurement process

2002-03-22

arxiv.org/abs/cond-mat/0203460v2

Europhys.Lett. 61 (2003) 452-458

Physics

Condensed Matter

Statistical Mechanics

5 pages Revtex

Scientific paper

10.1209/epl/i2003-00150-y

A hamiltonian model is solved, which satisfies all requirements for a realistic ideal quantum measurement. The system S is a spin-$\half$, whose $z$-component is measured through coupling with an apparatus A=M+B, consisting of a magnet $\RM$ formed by a set of $N\gg 1$ spins with quartic infinite-range Ising interactions, and a phonon bath $\RB$ 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.

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