Random matrix theory: applications to classical, quantum and statistical mechanics

• Grant number: 07/04579-2
• Support Opportunities: Scholarships in Brazil - Post-Doctoral
• Start date: October 01, 2007
• End date: February 03, 2009
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Domingos Humberto Urbano Marchetti
• Grantee: Tiago Pereira da Silva
• Host Institution: Instituto de Física (IF). Universidade de São Paulo (USP). São Paulo , SP, Brazil

Abstract

The purpose of this project is to analyze the spectrum of a matrix whose elements are random, as well as the spectral transitions in operators. In addition, we will apply the results about the spectra to investigate the collective behavior in complex networks. The project will be split in three main parts: (i) The study of the spectra of random matrices, when these are limited by an analytic curve whose equation is given in terms of the potential. (ii) The analysis spectral transitions in operators which are given by Jacobi matrices. (iii) The appearance of collective in complex networks. We will focus on complex neural networks where the couplings are chemical and electrical synapses. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

PEREIRA, TIAGO; MARCHETTI, DOMINGOS H. U.. Quantum States Allowing Minimum Uncertainty Product of phi and L-z. PROGRESS OF THEORETICAL PHYSICS, v. 122, n. 5, p. 1137-1149, NOV 2009. (07/04579-2)

VENEZIANI, A. M.; PEREIRA, T.; MARCHETTI, D. H. U.. Conformal deformation of equilibrium measures in normal random ensembles. Journal of Physics A-Mathematical and Theoretical, v. 44, n. 7, FEB 18 2011. (07/04579-2)