Spectral taxonomy for quartic systems: fundamental clock, parity, and continuum
Abstract
A symmetric quartic potential is a physics model with expansive applications, ranging from broadband energy harvesters, quantum tunneling in molecules and the early universe, to torque-free spacecraft rotation. Its rich dynamics have been traditionally classified into regimes and expressed as disjointed time-domain solutions. Here we build a taxonomy for this broad class of motions and discover that their regimes exhibit a symmetrical spectral structure: they share a fundamental clock, obey parity selection, and dissolve into the separatrix through a discrete-to-continuum transition. Applied to the famous Dzhanibekov effect where a rotating body periodically undergoes rapid 180-degree flips in its attitude, the taxonomy reveals its spectral anatomy. The three principal-axis rotations share a common clock while occupying distinct parity channels, with stable-axis branches exchanging DC bias across the separatrix. We discuss a case study where the three spectral pillars: clock, parity, and continuum, survive the Wick rotation from real-time into imaginary-time kinematics.
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BibTeX
@misc{chachiyo2026spectral,
title = {{Spectral taxonomy for quartic systems: fundamental clock, parity, and continuum}},
author = {Teepanis Chachiyo},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.07731},
eprint = {2607.07731},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.07731},
}
RIS
TY - UNPB
TI - Spectral taxonomy for quartic systems: fundamental clock, parity, and continuum
AU - Teepanis Chachiyo
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2607.07731
UR - https://arxiv.org/abs/2607.07731
AB - A symmetric quartic potential is a physics model with expansive applications, ranging from broadband energy harvesters, quantum tunneling in molecules and the early universe, to torque-free spacecraft rotation. Its rich dynamics have been traditionally classified into regimes and expressed as disjointed time-domain solutions. Here we build a taxonomy for this broad class of motions and discover that their regimes exhibit a symmetrical spectral structure: they share a fundamental clock, obey parity selection, and dissolve into the separatrix through a discrete-to-continuum transition. Applied to the famous Dzhanibekov effect where a rotating body periodically undergoes rapid 180-degree flips in its attitude, the taxonomy reveals its spectral anatomy. The three principal-axis rotations share a common clock while occupying distinct parity channels, with stable-axis branches exchanging DC bias across the separatrix. We discuss a case study where the three spectral pillars: clock, parity, and continuum, survive the Wick rotation from real-time into imaginary-time kinematics.
ER -