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Non-Euclidean Geometry, Nontrivial Topology and Quantum Vacuum Effects

By Yurii A. Sitenko and Volodymyr M. Gorkavenko

Abstract

Space out of a topological defect of the Abrikosov–Nielsen–Olesen (ANO) vortex type is locally flat but non-Euclidean. If a spinor field is quantized in such a space, then a variety of quantum effects are induced in the vacuum. On the basis of 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 Dirac materials with two-dimensional 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. We show that the quantum ground-state effects are independent of the disclination size, and we find circumstances in which they are independent of parameters of the boundary condition

Topics: nanocones, ground state, quantum effects in monolayer crystals, Elementary particle physics, QC793-793.5
Publisher: MDPI AG
Year: 2018
DOI identifier: 10.3390/universe4020023
OAI identifier: oai:doaj.org/article:6d416b9e1da04dcc9b3d990d760edfce
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