Topological Equatorial Waves and Violation (or not) of the Bulk Edge Correspondence

TL;DR

This paper investigates the applicability of the bulk-edge correspondence principle to atmospheric and oceanic equatorial waves, revealing conditions under which it can be violated due to specific Coriolis force profiles.

Contribution

It demonstrates that the bulk-edge correspondence may not hold for certain differential Hamiltonian models of equatorial wave transport, challenging previous assumptions.

Findings

Bulk-edge correspondence can be violated with discontinuous Coriolis profiles.

Quantized asymmetries are achievable beyond traditional topological insulator models.

Numerical simulations support the theoretical analysis.

Abstract

Atmospheric and oceanic mass transport near the equator display a well-studied asymmetry characterized by two modes moving eastward. This asymmetric edge transport is characteristic of interfaces separating two-dimensional topological insulators. The northern and southern hemispheres are insulating because of the presence of a Coriolis force parameter that vanishes only in the vicinity of the equator. A central tenet of topological insulators, the bulk edge correspondence, relates the quantized edge asymmetry to bulk properties of the insulating phases, which makes it independent of the Coriolis force profile near the equator. We show that for a natural differential Hamiltonian model of the atmospheric and oceanic transport, the bulk-edge correspondence does not always apply. In fact, an arbitrary quantized asymmetry can be obtained for specific, discontinuous, such profiles. The results are based on a careful analysis of the spectral flow of the branches of absolutely continuous spectrum of a shallow-water Hamiltonian. Numerical simulations validate our theoretical findings.