> "we can consider the Atmosphere as a single quasi-particle, and the Earth as an interacting quasi-particle."
Since Planck, the concept of a standing wave and a quantum state have been tied together. The major climate indices such as ENSO, IOD, QBO, etc are characterized by their standing-wave wavenumber, which is the number of wavelengths that will fit around the circumference of the earth. All these wavenumbers are non-zero except for QBO which has a wavenumber of 0. ENSO and IOD are essentially dipole standing waves that stretch across the Pacific and Indian ocean respectively. The QBO has a wavenumber of 0 because it encircles the earth uniformly at any one time and shows a collective motion that is either all easterly or all westerly. Outside of these indices, the collective motion breaks up into travelling waves such as the MJO and meandering waves that show less of a pattern.
This video shows the transition into standing waves of varying wavenumbers based on a stimulating frequency. You can see that one frequency almost creates a perfect wavenumber 0 formation.
Fluids are more a collective motion rather than quasiparticles, even though quasiparticles as described elsewhere *"are not elementary particles, but are instead collective excitations of many electrons in solid devices"*