On the interplay between Noether's theorem and the theory of adiabatic invariants
Abstract
This article focuses on an important quantity that will be called the Rund-Trautman function. It already plays a central role in Noether's theorem since its vanishing characterizes a symmetry and leads to a conservation law. The main aim of the paper is to show how, in the realm of classical mechanics, an 'almost' vanishing Rund-Trautman function accompanying an 'almost' symmetry leads to an 'almost' constant of motion within the adiabatic assumption, that is, to an adiabatic invariant. To this end, the Rund-Trautman function is first introduced and analysed in detail, then it is implemented for the general one-dimensional problem. Finally, its relevance in the adiabatic context is examined through the example of the harmonic oscillator with a slowly varying frequency. Notably, for some frequency profiles, explicit expansions of adiabatic invariants are derived through it and an illustrative numerical test is realized.
Fichier principal
On the interplay between Noether's theorem and the theory of adiabatic invariants.pdf (333.67 Ko)
Télécharger le fichier
iopart12.clo (4.59 Ko)
Télécharger le fichier
Origin | Files produced by the author(s) |
---|