Modeling Kleinian cosmology with electronic metamaterials

TL;DR

This paper explores the analogy between Klein-Gordon particle propagation in spacetimes with signature changes and electron behavior at metamaterial interfaces, revealing mirror-like flux behavior and tunneling possibilities.

Contribution

It introduces a novel analogy between Kleinian cosmology and electronic metamaterials, analyzing particle dynamics and tunneling at boundary interfaces.

Findings

Mirror-like behavior of particle flux at boundaries

Potential for tunneling through double junctions

Calculated traversal times linking metamaterials and Kleinian slabs

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.