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Non-Euclidean Geometry, Nontrivial Topology and Quantum Vacuum Effects

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Bogolyubov Institute for Theoretical Physics, National Academy of Sciences of Ukraine, 14-b Metrologichna street, 03143 Kyiv, Ukraine
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Department of Physics, Taras Shevchenko National University of Kyiv, 64 Volodymyrs’ka Street, 01601 Kyiv, Ukraine
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Author to whom correspondence should be addressed.
Universe 2018, 4(2), 23; https://doi.org/10.3390/universe4020023
Received: 3 November 2017 / Revised: 13 December 2017 / Accepted: 25 December 2017 / Published: 31 January 2018
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. View Full-Text
Keywords: nanocones; ground state; quantum effects in monolayer crystals nanocones; ground state; quantum effects in monolayer crystals
MDPI and ACS Style

Sitenko, Y.A.; Gorkavenko, V.M. Non-Euclidean Geometry, Nontrivial Topology and Quantum Vacuum Effects. Universe 2018, 4, 23.

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