Topological phase dynamics described by overtone-synthesized classical and quantum Adler equations

Fuente: arXiv
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Main Authors: Yamaguchi, Hiroshi, Asano, Motoki
Format: Preprint
Published: 2026
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author Yamaguchi, Hiroshi
Asano, Motoki
author_facet Yamaguchi, Hiroshi
Asano, Motoki
contents The Adler equation is a well-known one-dimensional model describing phase locking and synchronization. Motivated by recent experiments using optomechanical oscillators, we extend the model to include overtone-synthesized sinusoidal coupling with adiabatic temporal modulation. This extension gives rise to unique topological features such as winding-number quantization, discontinuous phase-slip transitions, and hysteretic and non-reciprocal phase dynamics. We further extend the analysis to the quantum regime, where we find a counterintuitive result: the breakdown of winding-number quantization. This arises from the superposition of different winding-number states in a closed-space Thouless pump. Moreover, hysteretic dynamics, once eliminated in quantum adiabatic approximation, is recovered in non-adiabatic calculations, as the superposition of two Floquet states with different PT eigenvalues becomes the quantum counterpart of phase trajectory.
format Preprint
id arxiv_https___arxiv_org_abs_2602_21451
institution arXiv
publishDate 2026
record_format arxiv
spellingShingle Topological phase dynamics described by overtone-synthesized classical and quantum Adler equations
Yamaguchi, Hiroshi
Asano, Motoki
Quantum Physics
Mesoscale and Nanoscale Physics
The Adler equation is a well-known one-dimensional model describing phase locking and synchronization. Motivated by recent experiments using optomechanical oscillators, we extend the model to include overtone-synthesized sinusoidal coupling with adiabatic temporal modulation. This extension gives rise to unique topological features such as winding-number quantization, discontinuous phase-slip transitions, and hysteretic and non-reciprocal phase dynamics. We further extend the analysis to the quantum regime, where we find a counterintuitive result: the breakdown of winding-number quantization. This arises from the superposition of different winding-number states in a closed-space Thouless pump. Moreover, hysteretic dynamics, once eliminated in quantum adiabatic approximation, is recovered in non-adiabatic calculations, as the superposition of two Floquet states with different PT eigenvalues becomes the quantum counterpart of phase trajectory.
title Topological phase dynamics described by overtone-synthesized classical and quantum Adler equations
topic Quantum Physics
Mesoscale and Nanoscale Physics
url https://arxiv.org/abs/2602.21451