Geometric phase and topology of elastic oscillations and vibrations in model systems: Harmonic oscillator and superlattice
We illustrate the concept of geometric phase in the case of two prototypical elastic systems, namely the one-dimensional harmonic oscillator and a one-dimensional binary superlattice. We demonstrate formally the relationship between the variation of the geometric phase in the spectral and wave numbe...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIP Publishing LLC
2016-12-01
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| Series: | AIP Advances |
| Online Access: | http://dx.doi.org/10.1063/1.4968608 |
| _version_ | 1811262513420959744 |
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| author | P. A. Deymier K. Runge J. O. Vasseur |
| author_facet | P. A. Deymier K. Runge J. O. Vasseur |
| author_sort | P. A. Deymier |
| collection | DOAJ |
| description | We illustrate the concept of geometric phase in the case of two prototypical elastic systems, namely the one-dimensional harmonic oscillator and a one-dimensional binary superlattice. We demonstrate formally the relationship between the variation of the geometric phase in the spectral and wave number domains and the parallel transport of a vector field along paths on curved manifolds possessing helicoidal twists which exhibit non-conventional topology. |
| first_indexed | 2024-04-12T19:28:00Z |
| format | Article |
| id | doaj.art-f2813b52d5e84865a70cf561df5b3a78 |
| institution | Directory Open Access Journal |
| issn | 2158-3226 |
| language | English |
| last_indexed | 2024-04-12T19:28:00Z |
| publishDate | 2016-12-01 |
| publisher | AIP Publishing LLC |
| record_format | Article |
| series | AIP Advances |
| spelling | doaj.art-f2813b52d5e84865a70cf561df5b3a782022-12-22T03:19:26ZengAIP Publishing LLCAIP Advances2158-32262016-12-01612121801121801-1510.1063/1.4968608003694ADVGeometric phase and topology of elastic oscillations and vibrations in model systems: Harmonic oscillator and superlatticeP. A. Deymier0K. Runge1J. O. Vasseur2Department of Materials Science and Engineering, University of Arizona, Tucson, AZ 85721, USADepartment of Materials Science and Engineering, University of Arizona, Tucson, AZ 85721, USAInstitut d’Electronique, de Micro-électronique et de Nanotechnologie, UMR CNRS 8520, Cité Scientifique, 59652 Villeneuve d’Ascq Cedex, FranceWe illustrate the concept of geometric phase in the case of two prototypical elastic systems, namely the one-dimensional harmonic oscillator and a one-dimensional binary superlattice. We demonstrate formally the relationship between the variation of the geometric phase in the spectral and wave number domains and the parallel transport of a vector field along paths on curved manifolds possessing helicoidal twists which exhibit non-conventional topology.http://dx.doi.org/10.1063/1.4968608 |
| spellingShingle | P. A. Deymier K. Runge J. O. Vasseur Geometric phase and topology of elastic oscillations and vibrations in model systems: Harmonic oscillator and superlattice AIP Advances |
| title | Geometric phase and topology of elastic oscillations and vibrations in model systems: Harmonic oscillator and superlattice |
| title_full | Geometric phase and topology of elastic oscillations and vibrations in model systems: Harmonic oscillator and superlattice |
| title_fullStr | Geometric phase and topology of elastic oscillations and vibrations in model systems: Harmonic oscillator and superlattice |
| title_full_unstemmed | Geometric phase and topology of elastic oscillations and vibrations in model systems: Harmonic oscillator and superlattice |
| title_short | Geometric phase and topology of elastic oscillations and vibrations in model systems: Harmonic oscillator and superlattice |
| title_sort | geometric phase and topology of elastic oscillations and vibrations in model systems harmonic oscillator and superlattice |
| url | http://dx.doi.org/10.1063/1.4968608 |
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