Energy localisation (discrete breathers/superoscillations)

Optist,
I believe both indicate counterintuitive concepts of (a) localization of position, and energy, of an spatially extended (low frequency) wave, or (b) unexpected periods of high oscillatory frequencies in a low-bandwidth wave.

It requires some math, but a couple of references may be of interest --
First, the presentation "Faster than fourier: superoscillation and weak measurement"
http://ictp-saifr.org/webcast/notes/superoscillations 2013.pdf
or, the paper "Superoscillations: Faster Than the Nyquist Rate"
http://sweet.ua.pt/pjf/PDF/Ferreira2006a.pdf
There are many more references on the web.

One very interesting one I just found shows that superoscillatory waves can penetrate media that would normally be opaque to individual frequencies in their spectrum --
"Super-transmission: the delivery of superoscillations through the absorbing resonance of a dielectric medium"
https://www.eng.tau.ac.il/~alonb/JournalPapers/Eliezer, Super-transmission, Opt Exp 2014.pdf

Perhaps also worth noting is that when a potential barrier oscillates, tunneling probability can increase
- in some cases substantially, e.g., see --
"Selected elevation in quantum tunneling" http://cds.cern.ch/record/532809/files/0112167.pdf

So, maybe transient superoscillatory periods of potential barriers become important, even when the stimulus signal has a relatively low bandwidth, as long as it induces these transients, temporarily making a nearly insurmountable barrier temporarily more transparent.

Louis DeChiaro recently noted:

"[...]5. A departure from equilibrium must be established that will permit an external energy source (eg. the DC power supply in an electrolysis experiment and/or a pair of low power lasers as in the Letts/Hagelstein two laser experiment) to feed energy into the H-H or D-D stretching mode vibrations. The difference in chemical potential that is established in gas loading experiments can also serve very nicely; in this case the flux feeds energy into the stretching mode vibrations.

6. The nature of the lattice must permit these stretching mode vibrations to grow so large (over a period of perhaps many nanoseconds) that their amplitude becomes comparable to the lattice constant. When this occurs, the H atoms oscillate so violently that at the instants of closest approach, the curvature of the parabolic energy wells in which the atomic nuclei vibrate will become perturbed. Thus the curvature of the well oscillates as a periodic function of time. These very large amplitude vibrations are known as superoscillations in the Western literature and as “discrete breathers” in the Ukrainian literature. Under the right conditions, these oscillations can grow without impacting the atoms, which are much more massive than the hydrogens. We explored this computationally via Density Functional Molecular Dynamics runs.

7. When the curvatures of the parabolic energy wells of the nuclei are modulated at a frequency very near the natural resonant frequency, the quantum expectation value of the nuclear wave function spatial spread will oscillate with time in such a way that the positive-going peaks grow exponentially with time. Originally, I found this idea in the Ukrainian literature and was skeptical. So, we verified it by doing a direct numerical solution of the time-dependent Schrodinger Equation for a single nuclear particle in a parabolic energy well. These oscillations in spatial spread will periodically delocalize the nucleus and facilitate the tunneling of adjacent nuclei into the Strong Force attractive nuclear potential well, giving rise to nuclear fusion at rates that are several tens of orders of magnitude larger than what one calculates via the usual Gamow Factor integral relationship.

Almost none of this material was obvious back in 1989[...]"

http://www.e-catworld.com/2015…ing-pons-and-fleischmann/

Possibly, looking for multiple laser (or other stimuli) generating periodic superoscillations is worth examining.
Energetics' "Superwave" appears to be a good example.

I have a graduate background in physics, although I have worked in EE, rather than physics, for many years.

Much of the difficult work has already been done in mathematically describing discrete breathers and in general, making molecular modeling computationally tractable. Over the last 20 years the availability of ever more inexpensive compute power has made it possible to run MM programs on a PC. This should also be the case for modeling DBs.

Two key conditions must be met before DBs can be produced: these include a DB oscillation frequency that lies outside the metal matrix phonon spectrum, and a de-localized potential that takes into consideration the neighboring atoms. I believe the best (and perhaps the only) way to proceed is to utilize molecular modeling techniques to ascertain if a Ni/H + other metals system can generate the appropriate NAE environment. By NAE, I mean that P-P spacing can transiently approach 1E-12 meters.

Molecular modeling is a huge field, something that is becoming increasingly obvious as I attempt to find a modeling package that is suitable for simulating H2/metal systems. So called ab-initio modeling is not easy since all modeling tools must make approximations to be mathematically solvable and computationally tractable. Even constructing and simulating an isolated molecule and getting proper bond lengths is tricky. There are many parameters that need to be specified. Modeling must first define a basis set, which is, by necessity, incomplete and will inevitably produce some error. A complete basis set has an infinite number of vectors. For transition metals both the s and p electrons must be considered which increases the number of orbitals that must be evaluated. A quick literature search reveals literally dozens of basis sets, and there does not seem to be an easy way of selecting which set will give the best results.

The next step is to select a so called pseudo-potential. Again, there are a huge number of these to choose from. DBs require a potential model that properly models the higher order (cubic and quartic) non-linearities and properly describes large amplitude motion of a pair of hydrogen nuclei. The so called Morse potential or a variant thereof is a good place to start. I could go on, but it should be clear that molecular modeling, while I think is the only method of obtaining meaningful predictive results, entails a good bit of black magic. Nevertheless, if time permits, I plan to get hold of an open source software package like CP2K and see if I can get any meaningful results.

Jeff

Jeff,
Probably most simulations will be mathematically intractable, but maybe you are restricting your analysis to discrete breathers in lattices. I would be interested if you could analyze whether electron-capture reactions can also be driven by transient super-oscillating em-fields in other settings. Just speculating, of course, but it appears that unexpected photo-nuclear reactions can occur in x-ray fields, e.g., see --

"THE POTENTIAL USES OF X-RAY FELS IN NUCLEAR STUDIES"
http://accelconf.web.cern.ch/A…L2013/papers/thocno03.pdf
"Cooperative effects in nuclear excitation with coherent x-ray light"
http://iopscience.iop.org/arti…1367-2630/14/8/085025/pdf
Viewpoint: Free-Electron Lasers Trigger Nuclear Transitions - https://physics.aps.org/articles/v7/20

Maybe, the anomalously strong em-fields in super-oscillating regions (triggered by the fairly recently considered issue of random lasing) could drive inner K-shell electrons into the nucleus of certain atoms.
If this is even possible, finding correct parameters is the-needle-in-the-hay-stack, or curse-of-dimensionality problem.

Yo, I am the author of this paper

http://arxiv.org/abs/cond-mat/9704118

back in the day. At that time Albert Sievers at Cornell was very interested in the question of localization, connected with this idea that was called "two-level systems".

Anyway when we are talking about classical mechanics, localization is easy to find. The trouble is finding it in real systems and in quantum mechanical theory.

Here is an idea I talked about with Al but it never went anywhere.

Back in the old days with the Bohr Atom you had the amount of "action" that was quantized like (n+1/2) hbar. In the case of an anharmonic localized exception there are two things to think about at the semiclassical limit. When I was working with Al's group one could differentiate between the "periodic orbit" which the core of the anon, vs. the excitations around that periodic orbit. In the paper above the situation was constrained such that a single momentum-position manifold exists to leak out of the anon mode.

The nexts step, which we never did, would be to try the simulation with a realistic potential AND check if (1) we couid make an anon with (n+1/2) hbar worth of action, and (2) if the stable region around the anon has a surface area < hbar. If (1) and (2) are both the case the classical version has some validity, but if they are not true, the graininess of quantum mechanics would make the anon state impossible to find. That's my take.

What you state in your last sentence pretty much describes what I intend to do using MM software. Most MM packages support DFT which solves exactly the electrons' correlation and exchange components of the potential. It should not be that difficult to construct a 1-D model of alternating metal and hydrogen cores and utilize a realistic potential, either an equation-based potential like L-J or Morse potentials or one empirically measured for each species of atom. Most MM packages also comprehend phonon interactions, so DFT + the implicit B-O approximation should be sufficient to model discrete breathers.

Jeff

Perhaps of interest - some additional items on concentrating energy into "hot spots" as superoscillations, or energy focused in time, or by "bunching" em-waves into steep rogue waves -

"New methods for creating superoscillations"
http://arxiv.org/pdf/1608.03121v1.pdf

"Anderson localization in the time domain"
http://arxiv.org/pdf/1603.05827v2.pdf

"Self-accelerating Airy-Ince-Gaussian and Airy-Helical-Ince-Gaussian light bullets in free space"
https://www.osapublishing.org/DirectPDFAccess/9ED9215A-E227-A7E2-005BCE5F3A493712_348396/oe-24-17-18973.pdf?da=1&id=348396&seq=0&mobile=no

"Abruptly autofocusing waves"
https://www.researchgate.net/p…ruptly_autofocusing_waves
ABSTRACT: [...]new class of (2+1)D spatial and (3+1)D spatiotemporal waves that tend to autofocus in an abrupt fashion. While the maximum intensity of such a radial wave remains almost constant during propagation, it suddenly increases by orders of magnitude right before its focal point [...]

All related to a (now unavailble) 1990 paper with the intriguing title -
"How can an infra-red photon behave as a gamma ray? "

The Breathers are important for
Molecular Biology, but in LENR research , what's important is their
counterpart : « The Freezers »

« Freezers » are hypothetical zones of quasicrystals
with NO thermal oscillation of atoms. Atoms in these part can undergo
quantum behaviour like Bose-Einstein-Condensates :

https://www.researchgate.net/p…1_Le_feu_sous_la_banquise