ADIABATIC DYNAMICS IN LINEAR AND NONLINEAR SYSTEMS

Abstract

This thesis explores the dynamics of linear and nonlinear systems during adiabatic evolution. It consists of four projects: 1) investigating adiabatic pumping in a non-abelian system, demonstrating non-commutative features and interband coherence effects; 2) utilizing Bloch oscillation to modify the behavior of Floquet systems, enabling quantized pumping and discovering new Floquet phases with large Chern numbers; 3) studying the dynamical phase, Berry phase, and Aharonov-Bohm phase around a Dirac cone induced by power-law nonlinearity, explaining the π-quantization of the Aharonov-Bohm phase for Kerr nonlinearity and distinguishing it as a critical case among power-law nonlinearities; 4) analyzing soliton dynamics in the Ablowitz-Ladik model, deriving 1-, 2-, and N-soliton solutions with time-varying hopping coefficients, as well as discovering novel soliton shapes and solutions in various models.