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Phase transitions and quantum measurements | | Armen E. Allahverdyan
; Roger Balian
; Theo M. Nieuwenhuizen
; | | Date: |
22 Aug 2005 | | Subject: | Quantum Physics; Statistical Mechanics; Mesoscopic Systems and Quantum Hall Effect | quant-ph cond-mat.mes-hall cond-mat.stat-mech | | Abstract: | In a quantum measurement, a coupling $g$ between the system S and the apparatus A triggers the establishment of correlations, which provide statistical information about S. Robust registration requires A to be macroscopic, and a dynamical symmetry breaking of A governed by S allows the absence of any bias. Phase transitions are thus a paradigm for quantum measurement apparatuses, with the order parameter as pointer variable. The coupling $g$ behaves as the source of symmetry breaking. The exact solution of a model where S is a single spin and A a magnetic dot (consisting of $N$ interacting spins and a phonon thermal bath) exhibits the reduction of the state as a relaxation process of the off-diagonal elements of S+A, rapid due to the large size of $N$. The registration of the diagonal elements involves a slower relaxation from the initial paramagnetic state of A to either one of its ferromagnetic states. If $g$ is too weak, the measurement fails due to a ``Buridan’s ass’’ effect. The probability distribution for the magnetization then develops not one but two narrow peaks at the ferromagnetic values. During its evolution it goes through wide shapes extending between these values. | | Source: | arXiv, quant-ph/0508162 | | Services: | Forum | Review | PDF | Favorites | |
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