Hannay Angle: Yet Another Symmetry Protected Topological Order Parameter in Classical Mechanics

Abstract

Topological way of thinking now goes beyond conventional solid materials, and topological characterization of classical mechanical systems governed by Newton's equation of motion begins to attract much attention. To have a deeper insight on physical meaning of topological numbers in mechanical systems, we demonstrate the use of the Hannay angle, a classical counterpart of the Berry phase, as a symmetry protected topological order parameter. We first derive the Hannay angle using a canonical transformation that maps the Newton's equation to the Schrödinger type equation. The Hannay angle is then used to characterize a simple spring-mass model topologically with a particular focus on the bulk-edge correspondence and new aspects of the symmetry in a classical system.

5 pages

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Cited by in corpus (9)

• Classification of topological phonons in linear mechanical metamaterials
• Square-root topological semimetals
• Nonlinearity-induced transition in nonlinear Su-Schrieffer-Heeger model and nonlinear higher-order topological system
• Duality of Topological Edge States in a Mechanical Kitaev Chain
• Strain topological metamaterials
• Quench dynamics and bulk-edge correspondence in nonlinear mechanical systems
• Asymptotically exact photonic analogues of chiral symmetric topological tight-binding models
• Nonlinear topological phase diagram in dimerized sine-Gordon model
• Differences between quantum and classical adiabatic evolution