The adiabatic invariant of any harmonic oscillator : an unexpected application of Glauber's formalism

Martin Devaud (1) , Valentin Leroy (2) , Jean-Claude Bacri (1) , Thierry Hocquet (1)

1 MSC - Matière et Systèmes Complexes
2 LOA - Laboratoire Ondes et Acoustique (UMR 7587)

In this theoretical paper, we propose a general derivation of the adiabatic invariant of the n-degree-of-freedom harmonic oscillator, available whichever the physical nature of the oscillator and of the parametrical excitation it undergoes. This derivation is founded on the use of the classical Glauber variables and ends up with this simplest result: the oscillator's adiabatic invariant is just the sum of all the semiclassical quanta numbers associated with its different eigenmodes.

Mots clés: parametric excitation; adiabatic invariant; Glauber formalism

Domaines: Autre [cond-mat.other]

Martin Devaud, Valentin Leroy, Jean-Claude Bacri, Thierry Hocquet. The adiabatic invariant of any harmonic oscillator : an unexpected application of Glauber's formalism. 2007. ⟨hal-00197565⟩