> How is there more than an analogy between QM and ENSO waves?

There's this paper "Topological origin of equatorial waves"


>That unity reaches beyond materials science, according to Pierre Delplace and Antoine Venaille of the École Normal Supérieure de Lyon in France, working with Brad Marston of Brown University in Rhode Island. They say that two types of long-recognized wavelike flow in the atmosphere and oceans, called Kelvin and Yanai waves, also have a topological origin, which is mathematically analogous to the surface-conducting states of topological insulators.

> This equivalence shows up in the mathematics of the problem, the researchers say. In condensed-matter physics, electron states are described by the wavelike Schrödinger equation. Orbits are created by the fact that an applied magnetic field breaks time-reversal symmetry: the solutions to the Schrödinger equation change when time t is replaced by –t. The surface electron flows then arise from a breakdown of translational symmetry that occurs at the surface.

>Coriolis force

> All these features, say Delplace and colleagues, are mimicked in the wave equations for flows in the atmosphere and oceans, where the Coriolis force – an effective force due to the Earth’s rotation that displaces flows to the right and left in the northern and southern hemispheres, respectively – plays the role of a magnetic field. These equations produce waves trapped close to the equator, always compelled to travel eastward, which are known as equatorial Kelvin and mixed Rossby-gravity (Yanai) waves.

> Other such waves also exist, such as the long-period pure Rossby waves, but these are not “topologically protected” in the same way. Kelvin and Rossby waves can act as precursors to the quasi-periodic ocean-atmosphere oscillation called the El Niño Southern Oscillation, which produces significant climatic effects such as drought or high rainfall in some equatorial regions.



Related, just published in Physical Review Letters

https://arxiv.org/abs/2002.10607 "Non-Newtonian Topological Mechanical Metamaterials Using Feedback Control"

> "we focus on the quantum Haldane model, which is a two-band system with directional complex coupling terms, **violating Newton's third law** "