Convite à Física 2018
Colóquios dedicados ao público geral, em especial aos alunos ingressantes da USP.
Organizados pelo Departamento de Física Matemática
“Stephen Hawking: Uma breve biografia científica”
Palestrante: Prof. Alberto Saa - IMECC - UNICAMP
Data: dia 08 de agosto, quarta-feira às 18h
Local: Auditório Abrahão de Moraes, Instituto de Física
Riemann hypothesized that the zeta function ζ(s) has (non-trivial) zeroes only on the line Re(s) = 1/2 in the complex s-plane. Hilbert and Polya suggested that the position of these zeroes might be related to the spectrum of a `Hamiltonian'. It has been known for some time that the statistical properties of the eigenvalue distribution of an ensemble of random matrices resemble those of the zeroes of the zeta function. We construct a unitary matrix models (UMM) for the zeta function, however, our approach to the problem is `piecemeal'. That is, we consider each factor in the Euler product representation of the zeta function to get a UMM for each prime. This suggests a Hamiltonian (of the type proposed by Berry and Keating) from its phase space description. We attempt to combine this to get a matrix model for the full zeta function.
Local: Sala Jayme Tiomno
The rate of entropy production in a classical dynamical system is characterized by the Kolmogorov-Sinai entropy rate given by the sum of all positive Lyapunov exponents of the system. I will present a quantum version of this result valid for bosonic systems with unstable quadratic Hamiltonians: the entanglement entropy of squeezed coherent states grows linearly for large times, with a rate determined by the Lyapunov exponents and the choice of the subsystem. I will discuss the application of this result to quantum field theory and its conjectured implications for the behaviour of chaotic quantum systems prepared in a semiclassical state.
*Local: Sala Jayme Tyomno
Descreverei, de maneira não técnica, resultados que obtive com diversos co-autores nos últimos anos, explorando a ideia de que modelos ferromagnéticos, quando na presença de campos externos, podem ter o comportamento do mesmo modelo com campo nulo ou com campo uniforme não-nulo, dependendo da velocidade com que este decai a zero. O exemplos são modelos de Ising na rede e em árvores, e, também, modelos de Dyson na rede unidimensional Z. Neste último caso, obtemos o primeiro exemplo de uma medida de Gibbs que não é uma g-medida.
Local: Sala Jayme Tiomno
Discutir-se-á localização dinâmica para perturbações de operadores de Schrödinger discretos unidimensionais com campos elétricos uniformes. Os principais argumentos são baseados no processo iterativo KAM.
Local: Sala Jayme Tiomno
Demonstramos que funções geratrizes de Gaertner-Ellis associadas a estados de equilíbrio de férmions na rede, fracamente interagentes, podem ser vistas como limites de logaritmos de integrais de Berezin Gaussianas, cujas covariâncias são uniformemente absolutamente somáveis e possuem cotas uniformes para seus Pfaffianos. Disto segue que, por intermédio de expansões em árvore de Brydges-Kennedy, tais integrais de Berezin podem ser utilizadas para obter-se representação da função geradora de Gaertner-Ellis como série de potências de seu argumento. Tal resultado tem aplicações imediatas à teoria das "flutuações quânticas normais" e, portanto, à teoria do transporte, assim como ao estudo da entropia relativa de Rényi de estados de Gibbs fermiônicos.
Local: Sala Jayme Tiomno
Lensing in cosmology is usually discussed in terms of the Cosmic Shear, a 2-point correlation statistic. The lensing probability distribution functions (PDF) of convergence, shear and magnification, on the other hand, carry extra information which can be recovered in a different way. I will discuss some challenges in extracting this signal, which requires an accurate modelling of the cosmological dependence of the PDFs. I will focus on the effect of baryons, computed using the Magneticum suite of simulations, which have a significant impact on the high magnification and high convergence regions of the PDFs. I will also discuss how the angular resolution of the observations must be taken into account when modelling the PDFs.
Local: Sala Jayme Tiomno
In this talk we will study the behaviour of the Wigner measures of solutions to the Schrödinger equation with potentials presenting conical singularities. These measures are related to the concentration of the solutions in the limit where a parameter in the equation (e.g. the Planck's constant) goes sufficiently small, and represent a mass density over the phase space, which may be a classical particle or a continuum of mass. The situation becomes particularly interesting with conical singularities, since they give rise to problems of non-unicity in the Hamiltonian flows that ultimately dismiss the existence of any selection principle allowing one to study the measures' time evolution within a pure classical framework.
Local: Sala Jayme Tiomno