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arXiv · 1711.00450

Non-Euclidean geometry, nontrivial topology and quantum vacuum effects

Yurii A. Sitenko·Volodymyr M. Gorkavenko
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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.

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Yurii A. Sitenko, Volodymyr M. Gorkavenko. 2018-05-24. Non-Euclidean geometry, nontrivial topology and quantum vacuum effects. https://doi.org/10.3390/universe4020023

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