Harmonic and anharmonic oscillators in a linear chain: the Fermi, pasta, and Ulam problem

• Grant number: 17/18747-6
• Support Opportunities: Scholarships in Brazil - Scientific Initiation
• Start date: December 01, 2017
• End date: November 30, 2018
• Field of knowledge: Physical Sciences and Mathematics - Physics - General Physics
• Principal Investigator: Gustavo Garcia Rigolin
• Grantee: Gabriel Ruffolo
• Host Institution: Centro de Ciências Exatas e de Tecnologia (CCET). Universidade Federal de São Carlos (UFSCAR). São Carlos , SP, Brazil

Abstract

In this project we intend to study a linear (one dimension) chain of N coupled oscillators. Initially we will deal with the harmonic problem whose solution can be found analytically through appropriate coordinate transformations that lead us to the normal modes of oscillation. Then, we will study numerically the cases in which we add anharmonic interactions described by cubic and quartic potentials, as presented in the 1950s by Fermi, Pasta and Ulam. (AU)