Modeling Kleinian cosmology with electronic metamaterials

Abstract

This paper deals with the propagation of Klein-Gordon particles in flat background spacetime exhibiting discontinuous metric changes from a Lorentzian signature (-,+,+,+) to a Kleinian signature (-,+,+,-). A formal analogy with the propagation of electrons at a junction between an anisotropic semiconductor and an electronic metamaterial is presented. From that analogy, we study the dynamics of these particles falling onto planar boundary interfaces between these two families of media and show a mirror-like behavior for the particle flux. Finally, the case of a double junction of finite thickness is examined and the possibility of tunneling through it is discussed. A physical link between the metamaterial and the Kleinian slabs is found by calculating the time of flight of the respective traversing particles.

arXiv comment9 pages, 9 figures

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Cited by in corpus (10)

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• Eisenhart lift of Koopman-von Neumann mechanics
• Schrödinger formalism for a particle constrained to a surface in ${\mathbb{R}}_1^3$
• Geometric theory of topological defects: methodological developments and new trends
• Implications of Kleinian relativity
• Curved non-interacting two-dimensional electron gas with anisotropic mass
• The wiggly cosmic string as a waveguide for massless and massive fields
• Diamonds in Klein geometry
• A simple light-trapping device from a hyperbolic metamaterial on a catenoid
• Metamaterial branes