Cosmology in the laboratory: An analogy between hyperbolic metamaterials and the Milne universe

Figueiredo, David; Moraes, Fernando; Fumeron, Sébastien; Berche, Bertrand

doi:10.1103/physrevd.96.105012

Cited by 15 publications

(14 citation statements)

References 47 publications

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“…We also point out that our discussion of how to carry the interpretative postulates of Quantum Mechanics to R 3 1 is absent in the approach of reference 10 . Finally, as perspectives, we mention the extension of the present work to more complex situations like a surface of revolution with a light-like axis, for instance, and surfaces with a curvature singularity as the compactified Milne universe model studied recently by one of us and coworkers 42 . Besides, as commented in the Introduction, it is expected that the effect of the geometry-induced potential shall appear both in electronic and optical hyperbolic metamaterials.…”

Section: Discussionmentioning

confidence: 90%

Schrödinger formalism for a particle constrained to a surface in $\mathbb{R}_1^3$

Teixeira,

Leandro,

da Silva

et al. 2018

Preprint

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In this work it is studied the Schrödinger equation for a non-relativistic particle restricted to move on a surface S in a three-dimensional Minkowskian medium R 3 1 , i.e., the space R 3 equipped with the metric diag(−1, 1, 1). After establishing the consistency of the interpretative postulates for the new Schrödinger equation, namely the conservation of probability and the hermiticity of the new Hamiltonian built out of the Laplacian in R 3 1 , we investigate the confining potential formalism in the new effective geometry. Like in the well-known Euclidean case, it is found a geometryinduced potential acting on the dynamics V S = − 2 2m (εH 2 − K) which, besides the usual dependence on the mean (H) and Gaussian (K) curvatures of the surface, has the remarkable feature of a dependence on the signature of the induced metric of the surface: ε = +1 if the signature is (−, +), and ε = 1 if the signature is (+, +).Applications to surfaces of revolution in R 3 1 are examined, and we provide examples where the Schrödinger equation is exactly solvable. It is hoped that our formalism will prove useful in the modeling of novel materials such as hyperbolic metamaterials, which are characterized by a hyperbolic dispersion relation, in contrast to the usual spherical (elliptic) dispersion typically found in conventional materials.

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Section: Discussionmentioning

confidence: 90%

Schrödinger formalism for a particle constrained to a surface in $\mathbb{R}_1^3$

Teixeira,

Leandro,

da Silva

et al. 2018

Preprint

Self Cite

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“…Related to, but not really a model for spinning strings, is the case of a hyperbolic nematic-based metamaterial with a disclination which was addressed in [129]. Along the same line, in [130] it was proposed a disclination model for the compactified Milne model of a cyclic universe. More details on this model in Section III C. Among the gauge strings, a very interesting possibility is the semilocal string [131].…”

Section: B Beyond Cosmic Wedge Disclinationsmentioning

confidence: 99%

Geometric theory of topological defects: methodological developments and new trends

Fumeron

Berche

Moraes

2021

Liquid Crystals Reviews

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Liquid crystals generally support orientational singularities of the director field known as topological defects. These latter modifiy transport properties in their vicinity as if the geometry was non-Euclidean. We present a state of the art of the differential geometry of nematic liquid crystals, with a special emphasis on linear defects. We then discuss unexpected but deep connections with cosmology and high-energy-physics, and conclude with a review on defect engineering for transport phenomena.

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“…Metamaterials [55] are quite interesting because of their unique possibilities of investigations involving negative refractive indexes and technological developments [56]. Also, metamaterials allow the emulation of theoretical cosmology scenarios in the context of electrodynamics [57]. Thus, basically, it is possible to analyze the harmonic oscillator taking into account three different possibilities: i) an isotropic sample, where the helicoid is surrounded by the same material of the helicoidal surface, ii) an anisotropic material, and iii) an electronic analogue of a hyperbolic material.…”

Section: The Anisotropic Effective Mass and Schr öDinger Equation In ...mentioning

confidence: 99%

Quantum particle motion on the surface of a helicoid in the presence of harmonic oscillator

Ribeiro¹,

Cunha²,

Filgueiras³

et al. 2020

Preprint

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The geometric potential in quantum mechanics has been attracted attention recently, providing a formalism to investigate the influence of curvature in the context of low-dimensional systems. In this paper, we study the consequences of a helicoidal geometry in the Schrödinger equation dealing with an anisotropic mass tensor. In particular, we solve the problem of an harmonic oscillator in this scenario. We determine the eigenfunctions in terms of Confluent Heun Functions and compute the respective energy levels. The system exhibit several different behaviors, depending on the adjustment on the mass components.

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Cosmology in the laboratory: An analogy between hyperbolic metamaterials and the Milne universe

Cited by 15 publications

References 47 publications

Schrödinger formalism for a particle constrained to a surface in $\mathbb{R}_1^3$

Schrödinger formalism for a particle constrained to a surface in $\mathbb{R}_1^3$

Geometric theory of topological defects: methodological developments and new trends

Quantum particle motion on the surface of a helicoid in the presence of harmonic oscillator

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