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PreprintCC BY 4.0arXiv

Which Adiabatic Cycles Alter an Action Variable?

  • Atushi Tanaka
  • Taksu Cheon
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Abstract

Action variables are adiabatic invariants: their values are preserved during adiabatic time evolutions in completely integrable classical Hamiltonian systems. Nevertheless, an adiabatic cycle can alter how an action variable depends on phase-space variables that are independent of adiabatic parameters. Such a change, which we call action variable holonomy, induces adiabatic torus pumping in phase space. For a family of completely integrable kicked-top systems, a homotopy classification of adiabatic cycles identifies which adiabatic cycles induce action variable holonomy and adiabatic torus pumping. A physical example is also provided.

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Cite

BibTeXRIS
BibTeX
@misc{tanaka2026which,
  title = {{Which Adiabatic Cycles Alter an Action Variable?}},
  author = {Atushi Tanaka and Taksu Cheon},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.40671},
  eprint = {2610.40671},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.40671},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Which Adiabatic Cycles Alter an Action Variable?
AU  - Atushi Tanaka
AU  - Taksu Cheon
PY  - 2026
DA  - 2026/10/19
PB  - arXiv
DO  - 10.48550/arxiv.2610.40671
UR  - https://arxiv.org/abs/2610.40671
AB  - Action variables are adiabatic invariants: their values are preserved during adiabatic time evolutions in completely integrable classical Hamiltonian systems. Nevertheless, an adiabatic cycle can alter how an action variable depends on phase-space variables that are independent of adiabatic parameters. Such a change, which we call action variable holonomy, induces adiabatic torus pumping in phase space. For a family of completely integrable kicked-top systems, a homotopy classification of adiabatic cycles identifies which adiabatic cycles induce action variable holonomy and adiabatic torus pumping. A physical example is also provided.
ER  -