The concept of quasi-integrability

• Grant number: 13/21598-1
• Support Opportunities: Research Grants - Visiting Researcher Grant - International
• Start date: March 22, 2014
• End date: April 27, 2014
• Field of knowledge: Physical Sciences and Mathematics - Physics - Elementary Particle Physics and Fields
• Principal Investigator: Luiz Agostinho Ferreira
• Grantee: Luiz Agostinho Ferreira
• Visiting researcher: Wojtek Zakrzewski
• Visiting researcher institution: Durham University (DU), England
• Host Institution: Instituto de Física de São Carlos (IFSC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 09/16982-1 - Solitons, infinite symmetries and integrable field theories, AP.TEM

Abstract

During the visit of Prof. Zakrzewski we will investigate the so-called quasi-integrability phenomenon. We have found that some field theories present solutions which behave very similarly to solitons in exactly integrable theories. There exist an infinite number of quantities which are asymptotically conserved during the scattering process of two of such quasi-solitons, i.e despite the fact they are not conserved their values after the scattering return to those values they had prior the scattering. The interesting fact is that such quantities vary a lot during the scattering process. We have already understood that from the mathematical point of view such thing happens due to a PT symmetry (space-time parity). The issue now is to understand the non-linear physical processes responsible for it. Such effect has a great potential of applicability in several realistic non-linear phenomena. In addition we will also investigate the Skyrme model we recently proposed and that possesses a self-dual sector. (AU)