Banca de DEFESA: YGOR PARÁ SILVA

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : YGOR PARÁ SILVA
DATE: 23/08/2022
TIME: 09:30
LOCAL: Google Meet
TITLE:

Effects of Curvature in Two - Dimensional Condensed Matter Systems

KEY WORDS:

Curvature, two-dimensional, bi-orthogonal.

PAGES: 104
BIG AREA: Ciências Exatas e da Terra
AREA: Física
SUMMARY:

The influence of curved background on the properties of Condensed Matter systems is a significant question for a broad class of physical applications. They catch the curiosity of people 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 infinite sequence of exceptional points (EP), which depend on the radius (curvature) of the sphere. We employ quench dynamics to characterize curvature-dependent 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.

COMMITTEE MEMBERS:
Interno - 1674079 - LEO GOUVEA MEDEIROS
Interno - 1313663 - RODRIGO GONCALVES PEREIRA
Presidente - 2195232 - TOMMASO MACRI
Externo à Instituição - VAN SÉRGIO DA SILVA ALVES - UFPA
Externa à Instituição - VÍVIAN VANESSA FRANÇA HENN - UNESP