Nonlinear effects in one-dimensional collective modes

• Grant number: 11/23386-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: March 01, 2012
• End date: December 31, 2012
• Field of knowledge: Physical Sciences and Mathematics - Physics - Condensed Matter Physics
• Principal Investigator: Rodrigo Gonçalves Pereira
• Grantee: Millena Logrado dos Santos
• Host Institution: Instituto de Física de São Carlos (IFSC). Universidade de São Paulo (USP). São Carlos , SP, Brazil

Abstract

Nonlinear effects that represent interactions between collective modes are important to explaining the dynamical properties of one-dimensional quantum fluids beyond the Luttinger liquid paradigm. In this project, we propose to study how interaction affects the excitation spectrum of a simple boson model. This study should serve as an introduction to concepts of many-body theory while applying methods of quantum mechanics, such as the formalism of creation and annihilation operators for harmonic oscillators and degenerate or time-dependent perturbation theory.(AU)