A Nonlinear Cause for the seasonal Predictability Barrier of SST

anomaly in the 2 tropical Pacific

Click to access 8b1ed053f271d2322cadb0c682a8386f.pdf

The Sample Entropy increases when there is more self-similarity within a time-series

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This new ψ satisfies the free-space Helmholtz equation (2.6) (with k0 = 1). AB physics is incorporated by ψ being non-singlevalued if the quantum flux is non-integer: under continuation around a circuit of the flux line, ψ acquires a phase shift −2πα. In this representation, kK(r) is simply the phase gradient as in (2.7). Gauge invariance implies [19] that AB observables in quantum physics must be periodic in the flux α. This is true of the wave (4.6) but is not true for the AB wave (4.3); although (4.3) is singlevalued under continuation around the flux line, the phase of this wave shifts by 2πα as α increases by unity. However, the kinetic momentum kK(r) is periodic in α, and so it is in principle observable; it is a gauge-invariant vector, which was the reason for studying its streamlines [16, 18]. However, the wave equation (4.1) also describes the classical physics of waves in a vortex flow, with α representing the strength of the vortex, in a medium flowing much more slowly than the wave [20]. For such cases, the phase, although not periodic in α, is directly observable, and it was observed for water waves encountering a bathtub vortex [20] (for an extension of this idea to fast flows, see [21]).

A superoscillation is like a delta-function or step change

5. Concluding remarks

The connection reported here, between zeros of the quantum potential and the boundaries of superoscillatory regions, can be seen in a wider context that would be useful in graduatelevel physics teaching: the intertwining of historical threads linking old ideas with current research. As I have explained elsewhere [22, 23], there is a sense in which the germ of the Madelung–Bohm representation of waves, incorporating the quantum potential, can be traced back to Isaac Newton’s speculations about edge diffraction at the beginning of the 18th century.

Superoscillations are especially strong near phase singularities, which were first discovered by William Whewell in the early 19th century in the patterns of tides in the world’s oceans[22, 24, 25], and are currently being extensively explored and applied, especially in optics[26, 27]. The modern exploration of superoscillations was triggered by Yakir Aharonov’s ‘weak measurements’ in quantum physics [9, 28], although there were anticipations in radar theory in world war II [29, 30]

https://iopscience.iop.org/article/10.1088/1367-2630/ac2bd7/pdf

Semiclassical superoscillations: interference, evanescence, post-WKB, MV Berry

Sean Carroll podcast with M.M. https://www.preposterousuniverse.com/podcast/2019/09/23/65-michael-mann-on-why-our-climate-is-changing-and-how-we-know/

MM: But under certain conditions, when the north-south temperature variations are just right, the atmosphere behaves as a wave guide, there’s basically a wall at sort of the subtropical end and at the subpolar end and these Rossby waves are funneled through a wave guide with minimum loss of energy. And it turns out the mathematics to solve for the dispersion relation, it requires the use of the same WKB approximation that was used in quantum mechanics in the early 20th century, yeah.

Roadmap on superoscillations, Berry, Aharanov, others

https://iopscience.iop.org/article/10.1088/2040-8986/ab0191/meta

The second early context was phase singularities (=wave vortices, nodal points and lines, or wave dislocations), understood as topologically stable features of waves of all kinds [5]. Around a circuit of such a singular point P in the plane, the phase changes by 2π; so, close to P, the local phase gradient can be arbitrarily larger than any of the wavevectors in the Fourier superposition representing the wave. Therefore, all band-limited waves, in particular monochromatic ones, are superoscillatory near their phase singularities. This understanding emerged belatedly, in 2007; since then, research in superoscillations and phase singularities have merged. Dennis calculated [6] that superoscillations in waves are unexpectedly common: for random monochromatic light in the plane (e.g. speckle patterns), 1/3 of the area is superoscillatory, with similar fractions for these ‘natural superoscillations’ in more dimensions. A monochromatic superoscillatory wave is illustrated in figures 1 and 2.

**interferometric phase
**

https://www.sciencedirect.com/science/article/pii/S0375960122006351

Generalizations of Berry phase and differentiation of purified state and thermal vacuum of mixed states

Instead of decomposing the density matrix to obtain a matrix-valued phase factor, a geometrical phase is directly assigned to a mixed state after parallel transport by an analogue of the optical process of the Mach-Zehnder interferometer. Hence, the geometrical phase generated in this way is often referred to as the interferometric phase. This approach can also be cast into a formalism by rewriting a mixed state as a purified state. The interferometric phase has been generalized to non-unitary processes [46], [47], [48], [49], [50], but the transformations are still on the system only.

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]]>Aren’t all wave profiles present in the real world?

MOD: There’s only one equation for E-M waves Maxwell Equations, here a wave is a wave, either trravelling or standing.

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]]>I appreciate the way you continue to push the boundaries of understanding.

Thanks Pukite

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