Lévy-Leblond fermions on the wormhole

Abstract

We propose a simple model of entanglement generated by geometry, studying non-relativistic massive Lévy-Leblond fermions in the $1+2$ geometry of a Bronnikov-Ellis wormhole. The model is equivalent to that of relativistic massless Dirac fermions in $1+3$ dimensions, where one spatial direction is flat. The effect of the wormhole is to generate quantum states that, far from the throat, are approximated by entangled particles on two flat, separated spacetime regions. An appealing feature of the model is that it has a condensed matter analogue, the regime of intermediate energies for two planes of bilayer graphene linked by a bilayer carbon nanotube. Therefore we expect that it might be possible to realize in the laboratory the entangled states studied here. We argue that generalisations of our solvable model which preserve the topology will have similar quantum behaviour.

15 pages, 3 figures. V2 references added

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Cited by in corpus (6)

• Traversable wormholes in Einstein-Dirac-Maxwell theory
• Traversable Wormholes in General Relativity
• Einstein-Dirac-Maxwell wormholes: ansatz, construction and properties of symmetric solutions
• Rotational influence on fermions within negative curvature wormholes
• Morris-Thorne Wormhole in the Vector-Tensor theories with Abelian gauge symmetry breaking
• On the Lévy-Leblond-Newton equation and its symmetries: a geometric view