Berry’s phase, locally inertial frames, and classical analogues

Kügler, M.; Shtrikman, S.

doi:10.1103/physrevd.37.934

Cited by 99 publications

(41 citation statements)

References 11 publications

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“…The role of the Frenet torsion in solutions of the scalar Helmholtz equation in coordinates adapted to non-planar curves has been noted before in a number of different contexts [15][16][17]. …”

Section: Wavetubes Of Circular Cross-sectionmentioning

confidence: 99%

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Geometry, Sagnac ring lasers and twisted EM modes

2005

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A new geometric approximation scheme, designed to solve the covariant Maxwell equations inside a rotating hollow slender conducting cavity (modelling a ring-laser) on a background spacetime, is constructed. It is shown that for well-defined conditions the electromagnetic spectrum splits into TE-and TM-type modes. A twisted mode spectrum is found to depend on the integrated Frenet torsion of the cavity and this in turn may affect the Sagnac beat frequency induced by a non-zero rotation of the cavity.

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Section: Wavetubes Of Circular Cross-sectionmentioning

confidence: 99%

“…A class of embeddings with Darboux frames that satisfy (16) and (17) are based on torus knots (see Fig. 1).…”

Section: Wavetubes Of Circular Cross-sectionmentioning

confidence: 99%

Geometry, Sagnac ring lasers and twisted EM modes

2005

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“…If one considers the fiber to be a curve described by the vector R(s), the direction of the propagation vector k is simply the tangent vector e 1 . The E, B vectors acquire a phase depending on the geometry of the fiber, which has been experimentally observed [Haldane, 1986;Berry, 1987;Shapere and Wilczek, 1989;Kugler and Shtrikman, 1988;Chiao and Wu, 1986].…”

Section: Geometric Phase In Classical Opticsmentioning

confidence: 99%

“…In these transformed coordinates the propagation of the wave, described by the wave equation for a field ψ, ∇ 2 ψ = −Eψ, is just that along a straight fiber to second order in κ [Kugler and Shtrikman, 1988]. Thus the only difference in propagation, between a straight fiber and a curved one, is the phase factor φ − θ = s τ ds ′ .…”

Section: Geometric Phase In Classical Opticsmentioning

confidence: 99%

Nonlinear Dynamics of Moving Curves and Surfaces: Applications to Physical Systems

Murugesh

Lakshmanan

2005

Int. J. Bifurcation Chaos

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The subject of moving curves (and surfaces) in three dimensional space (3-D) is a fascinating topic not only because it represents typical nonlinear dynamical systems in classical mechanics, but also finds important applications in a variety of physical problems in different disciplines. Making use of the underlying geometry, one can very often relate the associated evolution equations to many interesting nonlinear evolution equations, including soliton possessing nonlinear dynamical systems. Typical examples include dynamics of filament vortices in ordinary and superfluids, spin systems, phases in classical optics, various systems encountered in physics of soft matter, etc.Such interrelations between geometric evolution and physical systems have yielded considerable insight into the underlying dynamics. We present a succinct tutorial analysis of these developments in this article, and indicate further directions. We also point out how evolution 1 equations for moving surfaces are often intimately related to soliton equations in higher dimensions.

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“…[1,2,4] Related geometries such as crossed wires [5] and elbows [3] have also been studied extensively. The primary focus has been on the existence of unanticipated bound states and on the "adiabatic" limit where the radius of curvature is always much greater than the width of the tube.…”

Section: Introductionmentioning

confidence: 99%

Bound states and threshold resonances in quantum wires with circular bends

Kang

1996

Phys. Rev. B

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We study the solutions to the wave equation in a two-dimensional tube of unit width comprised of two straight regions connected by a region of constant curvature. We introduce a numerical method which permits high accuracy at high curvature. We determine the bound state energies as well as the transmission and reflection matrices, T and R and focus on the nature of the resonances which occur in the vicinity of channel thresholds. We explore the dependence of these solutions on the curvature of the tube and angle of the bend and discuss several limiting cases where our numerical results confirm analytic predictions. † Present address:

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Berry’s phase, locally inertial frames, and classical analogues

Cited by 99 publications

References 11 publications

Geometry, Sagnac ring lasers and twisted EM modes

Geometry, Sagnac ring lasers and twisted EM modes

Nonlinear Dynamics of Moving Curves and Surfaces: Applications to Physical Systems

Bound states and threshold resonances in quantum wires with circular bends

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