Remnants of the nonrelativistic Casimir effect on the lattice

Abstract

The Casimir effect is a fundamental quantum phenomenon induced by the zero-point energy for a quantum field. It is well-known for relativistic fields with a linear dispersion relation, while its existence or absence for nonrelativistic fields with a quadratic dispersion is an unsettled question. Here, we investigate the Casimir effects for various dispersion relations on the lattice. We find that Casimir effects for dispersions proportional to an even power of momentum are absent in a long distance but a remnant of the Casimir effect survives in a short distance. Such a remnant Casimir effect will be experimentally observed in materials with quantum fields on the lattice, such as thin films, narrow nanoribbons, and short nanowires. In terms of this effect, we also give a reinterpretation of the Casimir effect for massive fields.

6+4 pages, 5+2 figures; published version

References in corpus (4)

• The electronic properties of bilayer graphene
• Lattice-fermionic Casimir effect and topological insulators
• Casimir effect for lattice fermions
• Non-relativistic Casimir effect at finite temperature

Cited by in corpus (9)

• Dirac/Weyl-node-induced oscillating Casimir effect
• Topologically protected Casimir effect for lattice fermions
• Casimir effect in axion electrodynamics with lattice regularizations
• Non-Hermitian Casimir effect of magnons
• Dual chiral density wave induced oscillating Casimir effect
• Quantum vacuum effects in non-relativistic quantum field theory
• Lifshitz formulas for finite-density Casimir effect
• Casimir effect in magnetic dual chiral density waves
• Casimir effect for fermions on the lattice