Rodrigo Bissacot Proença

• Multidimensional symbolic dynamics and lattice models of quasicrystals, AR.EXT
• First Joint Meeting Brazil-France in Mathematics, AO.R

• Abstract

  We will investigate the existence (or not) of one or multiple KMS states for suitable potentials on the setting of Countable Markov Shifts. (AU)

  Thermodynamic formalism and KMS states on Countable Markov shifts, AV.BR

(Only some records are available in English at this moment)

• Abstract

  The research project will focus on studying the 8-vertex model and how it is connected to other lattice systems. I am especially interested in understanding its relation to Kitaev's toric code model, one of the greatest examples of topological quantum codes. The project therefore intends to research in detail the 8-vertex model, the toric code, and its correlation inequalities, which were…

  The 8-vertex model, the toric code and quantum information, BP.IC

• Abstract

  The project will be based on the theme of Surface Tension in Statistical Mechanics. The main objective is to comprehend the concept above by reading two papers: the first gives general properties of the surface tension in ferromagnetic systems, while the other makes an approach in more general systems using Pirogov-Sinai theory. After both papers are read and if there is time remaining, a…

  The concept of surface tension in statistical mechanics, BP.MS

• Abstract

  Present the algebraic formulation and main thermodynamic properties of spin and fermionic quantum lattice systems. Apply these notions to some concrete models as Hubbard and Falicov-Kimball ones. In particular, make use of the Pirogov-Sinai theory to study the phase diagrams at low temperatures given by perturbations in the hamiltonian, as done in two papers by Borgs and Kotecky. (AU)

  Spin and fermionic lattice systems in low temperature, BP.MS

(Only some records are available in English at this moment)

• Abstract

  The notion of equilibrium is central in statistical mechanics. In the classical case, the DLR equations describe all the possible equilibrium states for a spin lattice system. In the quantum case, where the appropiate notion of equilibrium is the KMS condition, the very notion of boundary condition is not well understood, even though some proposals already exist. In this project, using th…

  Boundary conditions and KMS states, BE.EP.DD

• Abstract

  The goal of this project is to find general conditions for subshifts in order to guarantee that any equilibirum measure on that is a Gibbs measure. (AU)

  Gibbs and equilibrium measures on subshifts, BE.EP.DR

• Abstract

  During the visit, we will discuss projects concerning to Gibbs Measures, phase transitions in Ising Model type and chaotic behavior around critical points.

  Gibbs Measures and Phase Transitions, BE.PQ

(Only some records are available in English at this moment)