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Symplectic geometry and quantum systems: questions on symbol correspondences

Grant number: 13/04630-9
Support Opportunities:Scholarships abroad - Research
Effective date (Start): August 13, 2013
Effective date (End): August 04, 2014
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Geometry and Topology
Principal Investigator:Pedro Paulo de Magalhaes Rios
Grantee:Pedro Paulo de Magalhaes Rios
Host Investigator: Alan David Weinstein
Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Research place: University of California, Berkeley (UC Berkeley), United States  


Research Project divided in three parts. The first part investigates a problem posed in a previous work of mine, on the possibility of breakdown of linear unitary evolution of certain pure-state Wigner functions, in the semiclassical asymptotic limit. The second part aims at developing a complete treatment of symbol correspondences and their symbol products, in the context of the group SU(1,1) and its coadjoint orbits, in particular the hyperbolic plane. The third part focus on developing a better treatment of some twisted products of symbols for spin systems, in a particular asymptotic limit. Both parts 2 and 3 of this project rely on another previous work of mine (this one a research monograph in collaboration with Eldar Straume, in attachment). (AU)

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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)
CRAIZER, MARCOS; DOMITRZ, WOJCIECH; RIOS, PEDRO DE M.. Even dimensional improper affine spheres. Journal of Mathematical Analysis and Applications, v. 421, n. 2, p. 1803-1826, . (13/04630-9)
DOMITRZ, W.; RIOS, P. DE M.; RUAS, M. A. S.. SINGULARITIES OF AFFINE EQUIDISTANTS: PROJECTIONS AND CONTACTS. JOURNAL OF SINGULARITIES, v. 10, p. 15-pg., . (10/15179-8, 13/04630-9, 08/54222-6, 14/00304-2)

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