DISCIPLINAS DE PÓS-GRADUAÇÃO – 2022.1

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(*) compartilhada com FIS 1222, da Graduação. 
(**) compartilhada com FIS 1221, da Graduação.

Astrofísica
Topics: 1- Stellar spectra (Spectral lines, HR diagram, stellar atmosphere); 2- Stellar structure (Hydrostatic equilibrium, nucleosynthesis, energy generation and transport, thermodynamics of stars); 3- Stellar evolution (pre-main sequence, main-sequence, low and high mass stars); 4- Supernovae (mainly formation and evolution type II SNe); 5- White Dwarfs, neutron stars and Black holes; 6- Brief study of pulsars, binary stars and accretion; 7- More detailed study of Sun; 8- Solar neutrinos (propagation, MSW, detection); 9- Interstellar medium (Dust and gas, protostars); 10- Galaxies (morphology, classification, structure, dynamics); 11- Active Galactic Nuclei (Quasars, unified model); 12- Basic cosmology (Friedmann model, thermal history of universe, decoupling, BBN); 13- Brief overview of structure formation (growth of inhomogeneities, density perturbation); 14- Cosmic Microwave Background (anisotropies, spectral distortions); 15- Baryon Asymmetry (Sakharov conditions, Baryogenesis, Leptogenesis); 16- Cosmic rays (Galactic and extra-galactic, propagation and diffusion, possible sources, observation, ultra-high-energy CR, GZK); 17- Atmospheric neutrinos (production, oscillation, detection); 18- Dark Matter (theory and searches); 19- Inflation.

This course serves as an introduction to the vast area of knowledge about stars, galaxies, cluster of galaxies and Universe (collectively called Astrophysics) with an emphasis on theoretical aspects and its relation with particle physics. The course is intended for master and PhD students, although advanced undergrad students can enroll. A solid knowledge of special relativity, electrodynamics, statistical physics and quantum mechanics will be assumed. Also, concepts and techniques of fluid mechanics, plasma physics, radiative processes, nuclear physics and general relativity will be thoroughly used, though the required knowledge will be introduced when needed. Clearly, the enumerated topics barely fits even to a two-semester course. For a one-semester course, topics (1-8) and a selection of the rest (say, 12, 16, 17) can be covered, while none of the topics can be treated in depth. For a two-semester course topics (1-8) + (9-18) will be covered mostly, but not all, in depth, plus an overview of the topic (19). The format (one or two semesters) will be decided in the first session. Bibliography: no single textbook will be followed during the course since any topics required its own appropriate reference(s), which can be part of a textbook or a review paper. However, the following books contain most of the material:
1- Theoretical astrophysics, Volumes I, II and III, T. Padmanabhan, Cambridge University Press; 2- An Introduction to Modern Astrophysics, Bradley W. Carrol and Dale A. Ostlie, Cambridge University Press, 2nd edition; 3- High Energy Astrophysics, Malcolm S. Longair, Cambridge University Press, 3rd edition; 4- Fundamentals of Neutrino Physics and Astrophysics, C. Giunti and C. W. Kim, Oxford University Press.

Many-body physics
When applying quantum mechanics to understand the physical properties of solids, one often encounters many realistic issues that are beyond the description of usual single-particle quantum states, such as disorder and interactions. To see how these factors affect the experimental observables, the technique of many-body physics is developed, which is largely based on the aspects in field theory like propagators and perturbation theory. In this course, we will give an introduction to the many-body physics technique by starting from the Green’s function and linear response theory, and then see how disorder and interactions can be incorporated perturbatively to describe several experimental observables such as transport measurements, ARPES, STM, etc. The goal is to give the students some hands-on experience of calculating some experimental observables both theoretically and numerically, so we will do several small numerical projects to calculate experimental observables using simple programing tools like Mathematica or Python. The course will be in English, and grades will be entirely based on these projects and the homework. The topics that will be covered are listed below.

Green’s function and linear response theory at zero and finite temperature; Coherent state formalism, Wick’s theorem, and Feynman diagrams; Impurity scattering, electrical conductivity, and electron-phonon interaction; Dielectric and magnetic responses, electron-electron correlation; Electron-photon coupling, exciton absorption, Berry curvature, and quantum metric; Bogoliubov-de Gennes, normal and Josephson tunneling, strong coupling theory of superconductivity

References: [1] G. D. Mahan, Many-Particle Physics, 3rd edition (2000); [2] M. Tinkham, Introduction to Superconductivity, 2nd edition (2004); [3] G. Rickayzen, Green’s Functions and Condensed Matter (2013); [4] E. N. Economou, Green’s Functions in Quantum Physics, 3rd edition (2006); [5] J. W. Negele and H. Orland, Quantum Many-Particle Systems (1998); [6] N. Nagaosa, Quantum Field Theory in Condensed Matter Physics (1999).

Termodinâmica Estocástica
Fundamentos. Termodinâmica Estocástica. Teoremas de Flutuação. Termodinâmica de Informação. Teoria e Prática de Grandes Desvios (LDT). Aplicações Experimentais. Novos Desenvolvimentos.

Ótica Não Linear e Aplicações
Neste curso será introduzido o tema de ótica não linear e as diversas aplicações em fotônica. Serão abordados os mecanismos de geração de pulsos curtos, e os princípios básicos de ótica não linear em fibras óticas e aplicações.
Bibliografia: Nonlinear Optics, Robert W. Boyd. Nonlinear Fiber Optics, Govind Agrawal. Applications of Nonlinear Fiber Optics, Govind Agrawal