Topological adiabatic dynamics in classical mass-spring chains with clamps

TL;DR

This paper explores how adiabatic evolution in classical mass-spring chains with clamps depends on the path taken, revealing phenomena like mode braiding and adiabatic pumping of invariants, with implications for classical and quantum systems.

Contribution

It demonstrates that chain modifications can braid normal mode frequencies and induce adiabatic pumping, extending understanding of adiabatic invariants in classical and quantum systems.

Findings

Adiabatic path dependence causes mode braiding.

Adiabatic cycles pump action variables.

Edge modes can be manipulated via clamps.

Abstract

The path dependence of adiabatic evolution in classical harmonic chains with clamps is examined. It is shown that cutting and joining a chain may braid adiabatic normal mode frequencies. Accordingly, different adiabatic paths with the same endpoints may transport a normal mode to a different one, and an adiabatic cycle pumps action variables, i.e., the adiabatic invariants of integrable classical systems. Another adiabatic pump for artificial edge modes induced by clamps is shown as an application. Extensions to completely integrable systems and quantum systems are outlined.