Efeitos de curvatura em sistemas bidimensionais de matéria condensada
The influence of curved background on the properties of Condensed Matter systems is a significant question for a broad class of physical applications, catching the curiosity because of their interesting features in a rich interface between many research areas. In this thesis, we introduce an anal...
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| Formato: | doctoralThesis |
| Idioma: | pt_BR |
| Publicado em: |
Universidade Federal do Rio Grande do Norte
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| Endereço do item: | https://repositorio.ufrn.br/handle/123456789/54567 |
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| Resumo: | The influence of curved background on the properties of Condensed Matter systems is a
significant question for a broad class of physical applications, catching the curiosity because
of their interesting features in a rich interface between many research areas. In this thesis, we
introduce an analytically solvable model of Dirac fermions with imaginary mass on the sphere.
We show the existence of an in nite sequence of exceptional points (EP), which depend on
the radius (curvature) of the sphere. We employ quench dynamics to characterize curvaturedependent Non-Hermitian phase transitions. We demonstrate that the existence of singular
points of the Loschmidt echo and the fidelity are an unambiguous signature of geometric EPs
that distinguish between different phases of the model. Also, we use numerical techniques to
solve the Bose-Hubbard hamiltonian that simulates the hyperbolic geometry. In this system,
we attempt to verify whether we can observe a bound-states comprising a pair of atoms in
the presence of repulsive interactions in a hyperbolic lattice. This system is a playground
to simulate a space with negative curvature, that is difficult to simulate in a euclidean space
without distortions. |
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