dorsal/arxiv
View SchemaClassical Dynamics of the Quantum Harmonic Chain
| Authors | Todd A. Brun, James B. Hartle |
|---|---|
| Categories | |
| ArXiv ID | quant-ph/9905079 |
| URL | https://arxiv.org/abs/quant-ph/9905079 |
| DOI | 10.1103/PhysRevD.60.123503 |
| Journal | Phys.Rev. D60 (1999) 123503 |
Abstract
The origin of classical predictability is investigated for the one dimensional harmonic chain considered as a closed quantum mechanical system. By comparing the properties of a family of coarse-grained descriptions of the chain, we conclude that local coarse-grainings in this family are more useful for prediction than nonlocal ones. A quantum mechanical system exhibits classical behavior when the probability is high for histories having the correlations in time implied by classical deterministic laws. But approximate classical determinism holds only for certain coarse-grainings and then only if the initial state of the system is suitably restricted. Coarse-grainings by the values of the hydrodynamic variables (integrals over suitable volumes of densities of approximately conserved quantities) define the histories usually used in classical physics. But what distinguishes this coarse-graining from others? This paper approaches this question by analyzing a family of coarse-grainings for the linear harmonic chain. At one extreme in the family the chain is divided into local groups of $N$ atoms. At the other extreme the $N$ atoms are distributed nonlocally over the whole chain. Each coarse-graining follows the average (center of mass) positions of the groups and ignores the ``internal'' coordinates within each group, these constituting a different environment for each coarse-graining. We conclude that noise, decoherence, and computational complexity favor locality over nonlocality for deterministic predictability.
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"abstract": "The origin of classical predictability is investigated for the one\ndimensional harmonic chain considered as a closed quantum mechanical system. By\ncomparing the properties of a family of coarse-grained descriptions of the\nchain, we conclude that local coarse-grainings in this family are more useful\nfor prediction than nonlocal ones. A quantum mechanical system exhibits\nclassical behavior when the probability is high for histories having the\ncorrelations in time implied by classical deterministic laws. But approximate\nclassical determinism holds only for certain coarse-grainings and then only if\nthe initial state of the system is suitably restricted. Coarse-grainings by the\nvalues of the hydrodynamic variables (integrals over suitable volumes of\ndensities of approximately conserved quantities) define the histories usually\nused in classical physics. But what distinguishes this coarse-graining from\nothers? This paper approaches this question by analyzing a family of\ncoarse-grainings for the linear harmonic chain. At one extreme in the family\nthe chain is divided into local groups of $N$ atoms. At the other extreme the\n$N$ atoms are distributed nonlocally over the whole chain. Each coarse-graining\nfollows the average (center of mass) positions of the groups and ignores the\n``internal\u0027\u0027 coordinates within each group, these constituting a different\nenvironment for each coarse-graining. We conclude that noise, decoherence, and\ncomputational complexity favor locality over nonlocality for deterministic\npredictability.",
"arxiv_id": "quant-ph/9905079",
"authors": [
"Todd A. Brun",
"James B. Hartle"
],
"categories": [
"quant-ph",
"gr-qc"
],
"doi": "10.1103/PhysRevD.60.123503",
"journal_ref": "Phys.Rev. D60 (1999) 123503",
"title": "Classical Dynamics of the Quantum Harmonic Chain",
"url": "https://arxiv.org/abs/quant-ph/9905079"
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