Geometric influences of a particle confined to a curved surface embedded in three-dimensional Euclidean space

Wang, Yong-Long; Jiang, Hua; Zong, Hong-Shi

doi:10.1103/physreva.96.022116

Cited by 39 publications

(29 citation statements)

References 72 publications

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“…(10). Unlike the scalar geometrical field κ 2 /4, which results from the action of normal derivatives on the rescale factor [32], the other two additional terms −iτŜ 1 and −iκŜ 3 relate to the parallel transport of the electric field vector along a curve and act as effective gauge terms within the effective dynamics. These two effective gauge terms result in a number of geometry-induced SOI of light.…”

Section: Effective Equationmentioning

confidence: 99%

Geometrical phase and Hall effect associated with the transverse spin of light

et al. 2019

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By analyzing the vectorial Helmholtz equation within the thin-layer approach, we find that light acquires a novel geometrical phase, in addition to the usual one (the optical Berry phase), during the propagation along a curved path. Unlike the optical Berry phase, the novel geometrical phase is induced by the transverse spin along the binormal direction and associated with the curvature of the curve. Furthermore, we show a novel Hall effect of light induced by the torsion of the curve and associated with the transverse spin along the binormal direction, which is different from the usual spin Hall effect of light. Finally, we demonstrate that the usual and novel geometrical phase phenomena are described by different geometry-induced U(1) gauge fields in different adiabatic approximations. In the nonadiabatic case, these gauge fields are united in one effective equation by SO(3) group.

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Section: Effective Equationmentioning

confidence: 99%

Geometrical phase and Hall effect associated with the transverse spin of light

et al. 2019

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“…When the free particle is confined to a curved surface, the effective dynamics would be affected by the geometrical properties 13,18 . In the spirit of the thin-layer quantization scheme, to obtain the effective quantum dynamics describing a particle confined to a curved surface, the Schrödinger equation Eq.…”

Section: Quantum Dynamics Of a Particle Confined On A Periodicallmentioning

confidence: 99%

“…According to the above results, using the formula of the geometric influence 18,35,36 , we can calculate the effective Hamiltonian as…”

Section: Quantum Dynamics Of a Particle Confined On A Periodicallmentioning

confidence: 99%

The geometric potential of a double-frequency corrugated surface

Cao

Wang

Chen³

et al. 2019

Physics Letters A

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For an electron confined to a surface reconstructed by double-frequency corrugations, we give the effective Hamiltonian by the formula of geometric influences, obtain an additive scalar potential induced by curvature that consists of attractive wells with different depth. The difference is generated by the multiple frequency of the double-frequency corrugation. Subsequently, we investigate the effects of geometric potential on the transmission probability, and find the resonant tunneling peaks becoming rapidly sharper and the transmission gaps being substantially widened with increasing the multiple frequency. As a potential application, double-frequency corrugations can be employed to select electrons with particular incident energy, as an electronic switch, which are more effective than a single-frequency ones.

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“…This momentum can be obtained by many different ways including: the hermiticity requirement on derivative part −i ∇ Σ [3], and compatibility of constraint condition n · p + p · n = 0 which means that the motion is perpendicular to the surface normal vector n [4,5], and thin-layer quantization or confining potential formalism which instead considers that particle is confined onto the surface Σ N −1 by means of introduction of a confinement potential along the normal direction of the the surface [6], and dynamical quantum conditions (DQCs) [7], etc. [9,10] It was demonstrated that this momentum (2) satisfies last one of the FQCs (1), when it explicitly takes following simplest form [7],…”

Section: Introductionmentioning

confidence: 99%

“…Experimental justification was performed by comparison of the interference spots formed by the surface plasmon polariton propagating on a cylindrical surface, predicted by the introduction of the geometric momentum or not [8], respectively. Some of previous discussions deal with quite general case [5,7,10], some of them [3,4,6,9] are mainly for a particle on Σ 2 . The geometric momentum (2) suffices to act on state function that has a single component.…”

Section: Introductionmentioning

confidence: 99%

Generally covariant geometric momentum, gauge potential and a Dirac fermion on a two-dimensional sphere

Liu

Zhou

et al. 2019

Eur. Phys. J. C

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For a particle that is constrained on an (N −1)-dimensional (N ≥ 2) curved surface, the Cartesian components of its momentum in N -dimensional flat space is believed to offer a proper form of momentum for the particle on the surface, which is called the geometric momentum as it depends on the mean curvature. Once the momentum is made general covariance, the spin connection part can be interpreted as a gauge potential. The present study consists in two parts, the first is a discussion of the general framework for the general covariant geometric momentum. The second is devoted to a study of a Dirac fermion on a two-dimensional sphere and we show that there is the generalized total angular momentum whose three cartesian components form the su(2) algebra, obtained before by consideration of dynamics of the particle, and we demonstrate that there is no curvature-induced geometric potential for the fermion. PACS numbers: 03.65.Pm Relativistic wave equations; 04.60.Ds Canonical quantization; 04.62.+v Quantum fields in curved spacetime; 98.80.Jk Mathematical and relativistic aspects of cosmology * Electronic address: quanhuiliu@gmail.com

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Geometric influences of a particle confined to a curved surface embedded in three-dimensional Euclidean space

Cited by 39 publications

References 72 publications

Geometrical phase and Hall effect associated with the transverse spin of light

Geometrical phase and Hall effect associated with the transverse spin of light

The geometric potential of a double-frequency corrugated surface

Generally covariant geometric momentum, gauge potential and a Dirac fermion on a two-dimensional sphere

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