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Curie-Weiss model of the quantum measurement process | | Armen E. Allahverdyan
; Roger Balian
; Theo M. Nieuwenhuizen
; | | Date: |
22 Mar 2002 | | Journal: | Europhys.Lett. 61 (2003) 452-458 | | Subject: | Statistical Mechanics; Mesoscopic Systems and Quantum Hall Effect; Mathematical Physics | cond-mat.stat-mech cond-mat.mes-hall hep-th math-ph math.MP quant-ph | | Abstract: | 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 $Ngg 1$ 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. | | Source: | arXiv, cond-mat/0203460 | | Services: | Forum | Review | PDF | Favorites | |
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