Position dependent non-commutativity in two dimensions

• Grant number: 13/25579-1
• Support Opportunities: Scholarships in Brazil - Master
• Start date: April 01, 2014
• End date: January 31, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Applied Mathematics
• Principal Investigator: Vladislav Kupriyanov
• Grantee: Armand Idárraga López
• Host Institution: Centro de Matemática, Computação e Cognição (CMCC). Universidade Federal do ABC (UFABC). Ministério da Educação (Brasil). Santo André , SP, Brazil

Abstract

The combination of the arguments of quantum mechanics with general relativity indicates that at distances of the order of the Planck wavelength, the space-time loses its structure of continuous and smooth manifold and should be replaced by some kind of non-commutative structure. The main objective of this project is to study the physical consequences of non-commutative, when the commutator between the space coordinates depends on these coordinates. Using as a base the mathematical model of non-commutative quantum mechanics recently proposed by Kupriyanov (2013) we intend to analyze the effects caused by the non-commutativity in exactly solvable models in two dimensions as the harmonic oscillator and the Landau problem. (AU)