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

Research output: Contribution to journalArticle

10 Citations (Scopus)

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 languageEnglish (US)
Article number121801
JournalAIP Advances
Volume6
Issue number12
DOIs
StatePublished - Dec 1 2016

Fingerprint

elastic systems
harmonic oscillators
topology
vibration
oscillations

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Geometric phase and topology of elastic oscillations and vibrations in model systems : Harmonic oscillator and superlattice. / Deymier, Pierre A; Runge, Keith A; Vasseur, J. O.

In: AIP Advances, Vol. 6, No. 12, 121801, 01.12.2016.

Research output: Contribution to journalArticle

@article{750eded796bc48bf95a2af06eb8e37ff,
title = "Geometric phase and topology of elastic oscillations and vibrations in model systems: Harmonic oscillator and superlattice",
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.",
author = "Deymier, {Pierre A} and Runge, {Keith A} and Vasseur, {J. O.}",
year = "2016",
month = "12",
day = "1",
doi = "10.1063/1.4968608",
language = "English (US)",
volume = "6",
journal = "AIP Advances",
issn = "2158-3226",
publisher = "American Institute of Physics Publising LLC",
number = "12",

}

TY - JOUR

T1 - Geometric phase and topology of elastic oscillations and vibrations in model systems

T2 - Harmonic oscillator and superlattice

AU - Deymier, Pierre A

AU - Runge, Keith A

AU - Vasseur, J. O.

PY - 2016/12/1

Y1 - 2016/12/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=84999232945&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84999232945&partnerID=8YFLogxK

U2 - 10.1063/1.4968608

DO - 10.1063/1.4968608

M3 - Article

AN - SCOPUS:84999232945

VL - 6

JO - AIP Advances

JF - AIP Advances

SN - 2158-3226

IS - 12

M1 - 121801

ER -