dorsal/arxiv
View SchemaPhase transitions and quantum measurements
| Authors | Armen E. Allahverdyan, Roger Balian, Theo M. Nieuwenhuizen |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/0508162 |
| URL | https://arxiv.org/abs/quant-ph/0508162 |
| DOI | 10.1063/1.2158710 |
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.
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"abstract": "In a quantum measurement, a coupling $g$ between the system S and the\napparatus A triggers the establishment of correlations, which provide\nstatistical information about S. Robust registration requires A to be\nmacroscopic, and a dynamical symmetry breaking of A governed by S allows the\nabsence of any bias. Phase transitions are thus a paradigm for quantum\nmeasurement apparatuses, with the order parameter as pointer variable. The\ncoupling $g$ behaves as the source of symmetry breaking. The exact solution of\na model where S is a single spin and A a magnetic dot (consisting of $N$\ninteracting spins and a phonon thermal bath) exhibits the reduction of the\nstate as a relaxation process of the off-diagonal elements of S+A, rapid due to\nthe large size of $N$. The registration of the diagonal elements involves a\nslower relaxation from the initial paramagnetic state of A to either one of its\nferromagnetic states. If $g$ is too weak, the measurement fails due to a\n``Buridan\u0027s ass\u0027\u0027 effect. The probability distribution for the magnetization\nthen develops not one but two narrow peaks at the ferromagnetic values. During\nits evolution it goes through wide shapes extending between these values.",
"arxiv_id": "quant-ph/0508162",
"authors": [
"Armen E. Allahverdyan",
"Roger Balian",
"Theo M. Nieuwenhuizen"
],
"categories": [
"quant-ph",
"cond-mat.mes-hall",
"cond-mat.stat-mech"
],
"doi": "10.1063/1.2158710",
"title": "Phase transitions and quantum measurements",
"url": "https://arxiv.org/abs/quant-ph/0508162"
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