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Renormalization and quantum scaling of Frenkel-Kontorova models
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UNSPECIFIED. (2005) Renormalization and quantum scaling of Frenkel-Kontorova models. JOURNAL OF STATISTICAL PHYSICS, 121 (5-6). pp. 995-1014. ISSN 0022-4715
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Official URL: http://dx.doi.org/10.1007/s10955-005-8671-9
Abstract
We generalise the classical Transition by Breaking of Analyticity for the class of Frenkel-Kontorova models studied by Aubry and others to non-zero Planck's constant and temperature. This analysis is based on the study of a renormalization operator for the case of irrational mean spacing using Feynman's functional integral approach. We show how existing classical results extend to the quantum regime. In particular we extend MacKay's renormalization approach for the classical statistical mechanics to deduce scaling of low frequency effects and quantum effects. Our approach extends the phenomenon of hierarchical melting studied by Vallet, Schilling and Aubry to the quantum regime.
| Item Type: | Journal Article |
|---|---|
| Subjects: | Q Science > QC Physics |
| Journal or Publication Title: | JOURNAL OF STATISTICAL PHYSICS |
| Publisher: | SPRINGER/PLENUM PUBLISHERS |
| ISSN: | 0022-4715 |
| Date: | December 2005 |
| Volume: | 121 |
| Number: | 5-6 |
| Number of Pages: | 20 |
| Page Range: | pp. 995-1014 |
| Identification Number: | 10.1007/s10955-005-8671-9 |
| Publication Status: | Published |
| URI: | http://wrap.warwick.ac.uk/id/eprint/34236 |
Data sourced from Thomson Reuters' Web of Knowledge
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