2024/03/19 by Di Zhou, Zhou, Di
Engineering · Mathematics · #Algebraic and Geometric Analysis #Control and Stability of Dynamical Systems #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum Gases (cond-mat.quant-gas) #Robotic Mechanisms and Dynamics #Statistical Mechanics (cond-mat.stat-mech)
paper · pdf · doi:10.48550/arxiv.2403.12480
openalex publication_date 2024/03/19 · openalex created_date 2024/03/21 · openalex updated_date 2026/07/28
Particle-hole symmetry and chiral symmetry play a pivotal role in multiple areas of physics, yet they remain unstudied in systems with nonlinear interactions whose nonlinear normal modes do not exhibit U(1)-gauge symmetry. In this work, we establish particle-hole symmetry and chiral symmetry in such systems. Chiral symmetry ensures the quantization of the Berry phase of nonlinear normal modes and categorizes the topological phases of nonlinear dynamics. We show topologically protected static boundary modes in chiral-symmetric nonlinear systems. Our theoretical framework extends particle-hole and chiral symmetries to nonlinear dynamics, whose nonlinear modes do not necessarily yield U(1)-gauge symmetry.