Extended Adiabatic Invariance

Breakdown of adiabatic invariance in spherical tokamaks

Thermal ions in spherical tokamaks have two adiabatic invariants: the magnetic moment and the longitudinal invariant. For hot ions, variations in magnetic-field strength over a gyro period can become sufficiently large to cause breakdown of the adiabatic invariance. The magnetic moment is more sensitive to perturbations than the longitudinal invariant and there exists an intermediate regime, su...

Adiabatic invariance in volume-preserving systems

Adiabatic invariance along the reaction coordinate.

In a two-dimensional space where a point particle interacts with a diatomic fragment, the action integral contour integral of p(theta) d theta (where theta is the angle between the fragment and the line of centers and p(theta) its conjugate momentum) is an adiabatic invariant. This invariance is thought to be a persistent dynamical constraint. Indeed, its classical Poisson bracket with the Hami...

Adiabatic Invariance and the Regularity of Perturbations

A loss in smoothness of a switching process decreases the accuracy of an adiabatic invariant. Here we show that for classical Hamiltonian systems the degree of smoothness can be observed in the signal.

Resonances and adiabatic invariance in classical and quantum scattering theory

We discover that the energy-integral of time-delay is an adiabatic invariant in quantum scattering theory and corresponds classically to the phase space volume. The integral thus found provides a quantization condition for resonances, explaining a series of results recently found in non-relativistic and relativistic regimes. Further, a connection between statistical quantities like quantal reso...