Quantum chaos, matrix integrals and combinatorics

• Grant number: 12/00699-1
• Support Opportunities: Regular Research Grants
• Start date: April 01, 2012
• End date: October 31, 2013
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Marcel Novaes
• Grantee: Marcel Novaes
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

The main conjecture in the area known as quantum chaos says that all spectral correlation functions of generic chaotic systems coincide with those predicted by an adequate random matrix theory. Until now, this has only beenproved for the simplest two point function. This project aims at extending this result to all $n$-point correlation functions. We believe we know the route to this ambitious objective. That routeinvolves matrix integrals, which are notoriously related to combinatorial problems, such as counting maps or factorizations of permutations. (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)

NOVAES, MARCEL. A semiclassical matrix model for quantum chaotic transport. Journal of Physics A-Mathematical and Theoretical, v. 46, n. 50, DEC 20 2013. (12/00699-1)