Non-Euclidean geometry, nontrivial topology and quantum vacuum effects

TL;DR

This paper investigates quantum vacuum effects induced by non-Euclidean geometry in topological defects like nanocones, revealing conditions where these effects are independent of boundary parameters and defect size.

Contribution

It introduces a continuum model for quantum effects in monolayer nanocones considering disclination size and boundary conditions, highlighting cases of boundary-independent quantum effects.

Findings

Quantum effects are independent of boundary parameters in certain nanocone configurations.

The model accounts for disclination size in quantum ground state calculations.

Quantum vacuum effects are induced by non-Euclidean geometry in topological defects.

Abstract

Space out of a topological defect of the Abrikosov-Nielsen-Olesen vortex type is locally flat but non-Euclidean. If a spinor field is quantized in such a space, then a variety of quantum effects is induced in the vacuum. Basing on the continuum model for long-wavelength electronic excitations, originating in the tight-binding approximation for the nearest neighbor interaction of atoms in the crystal lattice, we consider quantum ground state effects in monolayer structures warped into nanocones by a disclination; the nonzero size of the disclination is taken into account, and a boundary condition at the edge of the disclination is chosen to ensure self-adjointness of the Dirac-Weyl Hamiltonian operator. In the case of carbon nanocones, we find circumstances when the quantum ground state effects are independent of the boundary parameter and the disclination size.