# Non-Euclidean Geometry, Nontrivial Topology and Quantum Vacuum Effects

@article{Sitenko2018NonEuclideanGN, title={Non-Euclidean Geometry, Nontrivial Topology and Quantum Vacuum Effects}, author={Yu. A. Sitenko and Volodymyr M. Gorkavenko}, journal={Universe}, year={2018}, volume={4}, pages={23} }

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…

## One Citation

### Finite temperature charge and current densities around a cosmic string in AdS spacetime with compact dimension

- Physics
- 2022

For a massive scalar ﬁeld with a general curvature coupling parameter, we investigate the ﬁnite temperature contributions to the Hadamard function and to the charge and current densities in the…

## References

SHOWING 1-10 OF 19 REFERENCES

### Vacuum polarization in graphene with a topological defect

- Physics
- 2008

The influence of a topological defect in graphene on the ground state of electronic quasiparticle excitations is studied in the framework of the long-wavelength continuum model originating in the…

### Vacuum polarization effects on graphitic nanocones

- Physics
- 2008

Theory of vacuum polarization by singular background fields is applied to the study of electronic properties of the graphitic monolayer (graphene) with a topological defect. Graphene in the…

### Dirac materials

- Physics
- 2014

A wide range of materials, like d-wave superconductors, graphene, and topological insulators, share a fundamental similarity: their low-energy fermionic excitations behave as massless Dirac particles…

### The rise of graphene.

- PhysicsNature materials
- 2007

Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of 'relativistic' condensed-matter physics, where quantum relativistic phenomena can now be mimicked and tested in table-top experiments.

### Constraints on brane inflation and cosmic strings

- Physics
- 2008

By considering simple, but representative, models of brane inflation from a single brane–antibrane pair in the slow roll regime, we provide constraints on the parameters of the theory imposed by…

### Two- and one-dimensional honeycomb structures of silicon and germanium.

- PhysicsPhysical review letters
- 2009

First-principles calculations of structure optimization, phonon modes, and finite temperature molecular dynamics predict that silicon and germanium can have stable, two-dimensional, low-buckled, honeycomb structures, which show remarkable electronic and magnetic properties, which are size and orientation dependent.

### Cosmic Strings and Other Topological Defects

- Physics
- 1985

Preface 1. Introduction 2. Phase transitions in the early universe 3. Topological defects 4. String field theory 5. Superconducting strings 6. String dynamics 7. String gravity 8. String interactions…