Non-Euclidean Geometry, Nontrivial Topology and Quantum Vacuum Effects

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 excit...

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Bibliographic Details
Published in:Universe (Basel) 2018-02, Vol.4 (2), p.23
Main Authors: Sitenko, Yurii, Gorkavenko, Volodymyr
Format: Article
Language:English
Subjects:
Boundary conditions
Conflicts of interest
Defects
Geometry
ground state
nanocones
Phase transitions
Physics
quantum effects in monolayer crystals
Topology
Vortices
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Summary: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.
ISSN:2218-1997
2218-1997
DOI:10.3390/universe4020023