The quantum measurement process: an exactly solvable model

Details The quantum measurement process: an exactly solvable model The quantum measurement process: an exactly solvable model

2003-09-08

arxiv.org/abs/cond-mat/0309188v2

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

4 pages, presented at the conference "Anomalies and Strange Behavior in Physics: Challenging the conventional", Napels, April,

Scientific paper

An exactly solvable model for a quantum measurement is discussed, that integrates quantum measurements with classical measurements. The z-component of a spin-1/2 test spin is measured with an apparatus, that itself consists of magnet of N spin-1/2 particles, coupled to a bath. The initial state of the magnet is a metastable paramagnet, while the bath starts in a thermal, gibbsian state. Conditions are such that the act of measurement drives the magnet in the up or down ferromagnetic state, according to the sign of s_z of the test spin. The quantum measurement goes in two steps. On a timescale 1/\sqrt{N} the collapse takes place due to a unitary evolution of test spin and apparatus spins; on a larger but still short timescale this collapse is made definite by the bath. Then the system is in a `classical' state, having a diagonal density matrix. The registration of that state is basically a classical process, that can already be understood from classical statistical mechanics.

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