184 research outputs found
The quantum measurement process in an exactly solvable model
An exactly solvable model for a quantum measurement is discussed which is
governed by hamiltonian quantum dynamics. The -component of a
spin-1/2 is measured with an apparatus, which itself consists of magnet 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 of the tested spin. The quantum measurement goes
in two steps. On a timescale the off-diagonal elements of the
spin's density matrix vanish due to a unitary evolution of the tested spin and
the apparatus spins; on a larger but still short timescale this 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 a quantum process
which can already be understood from classical statistical mechanics. The von
Neumann collapse and the Born rule are derived rather than postulated.Comment: 7 pages revtex, 2 figure
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