1,137 research outputs found
Cosmic strings and the topological theory of defects
No full textTreballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2017, Tutor: Oleg BulashenkoA mathematical characterization of topological defects is provided, with a discussion of topological stability and the necessary conditions for stable defects to appear. Defect formation in symmetry-breaking phase transitions of the Universe is discussed, and a simple model for the formation of cosmic strings is given. Geodesics in a cosmic string spacetime are calculated for the study of gravitational lensing phenomen
Analogue Gravity in Hyperbolic Metamaterials
No full textTreballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2017, Tutor: Oleg BulashenkoMetamaterials are artificial materials whose electromagnetic parameters can be properly designed to achieve many interesting properties not found in natural materials. With a convenient design they demonstrate an analogy between their electrodynamics and general relativity phenomena. In this work we discuss the unusual optical properties of hyperbolic metamaterials and show that the wave equation for light propagation in these media is formally equivalent to the Klein-Gordon equation for a scalar field. Based on these results, the analogue gravity in hyperbolic metamaterials is considered to model an expanding Universe in a (2+1)-dimensional de Sitter spacetime
Analogue Gravity in Hyperbolic Metamaterials
No full textTreballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2017, Tutor: Oleg BulashenkoMetamaterials are artificial materials whose electromagnetic parameters can be properly designed to achieve many interesting properties not found in natural materials. With a convenient design they demonstrate an analogy between their electrodynamics and general relativity phenomena. In this work we discuss the unusual optical properties of hyperbolic metamaterials and show that the wave equation for light propagation in these media is formally equivalent to the Klein-Gordon equation for a scalar field. Based on these results, the analogue gravity in hyperbolic metamaterials is considered to model an expanding Universe in a (2+1)-dimensional de Sitter spacetime
Thermal cloaking via heat ux transformation
No full textTreballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2018, Tutor: Oleg BulashenkoThe methods used in Transformation optics could be extrapolated to thermal cloaking studies thanks to invariance of Heat Conduction Equation under mappings. On this basis, we study different transformations looking for the most suitable mapping for our interests. Then, we apply an asymptotic homogenization and diverse experimental constraints with the aim to implement a thermal cloak using exclusively homogeneous isotropic materials
Dynamics of a quantum particle constrained to a circle
No full textTreballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2022, Tutor: Oleg BulashenkoIn this work, we study the tunneling of a quantum particle using the instanton method.
As a starting point, we consider the double well potential, then we extend the results to a periodic potential and compare them to a particle constrained to a circle. Lastly, we test the non-perturbative approach of the method, and we discuss the coupling through a specific, parameter-dependent, periodic potentia
Non-Hermitian systems with PT symmetry
No full textTreballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2018, Tutor: Oleg BulashenkoWe discuss the possibility to build the formalism of quantum mechanics based on Parity-Time (PT ) symmetry, rather than on the Hermiticity of operators. We consider the simple analytically tractable case of a PT -symmetric 2 x 2 Hamiltonian matrix and analyse the conditions for the eigenvalues to be real and for time evolution to be unitary. Lastly, we review and reproduce the results of an experiment involving PT symmetry in optic
Instanton approach to the decay of a metastable quantum state
No full textTreballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2021, Tutor: Oleg BulashenkoThe escape transition due to quantum tunnelling of a particle from a metastable region, created by a cubic potential, is studied. Finding this amplitude is reduced to the computation of a Feynman path integral. This calculus has been carried out using the instanton method, which demands to rotate the time coordinate along the imaginary plane. The results obtained show that the ground state energy has actually an imaginary part (fact that is actually related to the metastability of the system) and allows to find the decaying rate of the metastable stat
Spontaneous pattern formation in Turing systems
No full textTreballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Any: 2015, Tutor: Oleg BulashenkoWe give a general description of pattern forming systems and describe the linear stability analysis that allows to determine whether a system in a uniform state will spontaneously evolve to a patterned state. Such an analysis is performed on Turing systems and conditions for pattern formation are derived. As an example of a Turing system, we consider the Brusselator
model, for which a variety of patterns are found numerically for different values of the bifurcation parameters
Probing dark matter halos by gravitational waves
No full textTreballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Curs: 2023, Tutor: Oleg BulashenkoGravitational waves open a new possibility in the detection of small dark matter halos. In this study we examine the gravitational lensing properties of the Navarro-Frenk-White (NFW) density profile, which is the most used model to describe cold dark matter halos. We also analyze the influence of the NFW halos on gravitational waves and, lastly, we study the effects of this interaction on the detection of the already mentioned waves. By exploring this effects, our objective is to understand better the interaction of gravitational waves and dark matter, two subjects shrouded in mistery
Spontaneous pattern formation in Turing systems
No full textTreballs Finals de Grau de Física, Facultat de Física, Universitat de Barcelona, Any: 2015, Tutor: Oleg BulashenkoWe give a general description of pattern forming systems and describe the linear stability analysis that allows to determine whether a system in a uniform state will spontaneously evolve to a patterned state. Such an analysis is performed on Turing systems and conditions for pattern formation are derived. As an example of a Turing system, we consider the Brusselator
model, for which a variety of patterns are found numerically for different values of the bifurcation parameters
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