Which Adiabatic Cycles Alter an Action Variable?

arXiv:2610.40671v1 Announce Type: new 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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