Geometric phase and topology of elastic oscillations and vibrations in model systems: Harmonic oscillator and superlattice

P. A. Deymier; K. Runge; J. O. Vasseur

doi:10.1063/1.4968608

Geometric phase and topology of elastic oscillations and vibrations in model systems: Harmonic oscillator and superlattice

P. A. Deymier, K. Runge, J. O. Vasseur

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21 Scopus citations

Abstract

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.

Original language	English (US)
Article number	121801
Journal	AIP Advances
Volume	6
Issue number	12
DOIs	https://doi.org/10.1063/1.4968608
State	Published - Dec 1 2016

ASJC Scopus subject areas

General Physics and Astronomy

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10.1063/1.4968608

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abstract = "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.",

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AU - Vasseur, J. O.

PY - 2016/12/1

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AB - 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.

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Geometric phase and topology of elastic oscillations and vibrations in model systems: Harmonic oscillator and superlattice

Abstract

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