Hi again, sorry for the long break since the last post, life has been busy. 🙂

I came across this recent article which allegedly describes notes by “Louis F. DeChiaro, Ph.D, a physicist with the US Naval Sea Systems Command (NAVSEA), Dahlgren Warfare Center”. (I say “allegedly” because the article is a third-hand account. It’s not Dr. DeChiaro’s own pen.) As usual for this blog, we skip over the fascinating experimental findings, and instead go straight to the discussion of microscopic mechanism. Here’s the relevant part:

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.

I don’t think point 7 is an obscure result from the Ukrainian literature. I think it is the first thing that every child learns about mechanical resonances: When you purturb a resonator at its resonant frequency, the oscillation amplitude grows and grows and grows.

**Think about pushing a child on a swingset**: If you give the kid a little push once per cycle (“if you purturb the potential at the resonant frequency”) then the kid can swing higher and higher. So I’m calling it the **“swingset method” of overcoming the Coulomb barrier**. It doesn’t particularly matter how exactly the potential is modified—you can shift it, you can change the curvature, whatever—if you modify the potential energy curve periodically at the resonant frequency, you really should not be surprised that a resonator will achieve extremely high amplitudes over time.

I think there are echoes of the “swingset method” idea in other cold fusion theorists’ accounts, like Edmund Storms’s.

**Problems with the “swingset method” in general:** Broadly speaking, I’m pretty skeptical that the “swingset” idea actually gets you any closer towards explaining cold fusion. There are two problems. First, the deuterium needs to get to ~10keV of energy before fusion occurs. But long, long before 10keV, it already has so much kinetic energy that you should not think of it as vibrating back and forth, you should imagine it flying through the crystal and occasionally bouncing off other atoms. Even 1keV is too much energy for an atom to vibrate back and forth in the same spot, as far as I know, and at 1keV you are only 10% of the way there. Second, it’s hard to see how a kinda diffuse energy source, like an electrochemically-induced current, would happen to drive a specific type of vibration more and more, rather than simply heating the material. Remember that the vibrational energy is always dissipating too, so unless you add energy to it *very* fast, it will not build up to a high level.

**Problems with this description in particular:** I’ll also say that I think the specifics discussed in the quote above (point 6) are mistaken. Let’s go back to the swingset. The child is going back and forth on the swingset, but now no one is pushing her anymore. Notice that the force on the child is changing over the course of the back-and-forth cycle, and that the changes are periodic (with period matching the cycle) and anharmonic (more complicated than a Hooke’s law restoring force, a.k.a. parabolic potential well).

Now someone who has diligently read this blog post will remember what I said a couple paragraphs above: “if you modify the potential energy curve periodically at the resonant frequency, you really should not be surprised that a resonator will achieve extremely high amplitudes over time.” This diligent reader will say: “Aha! The child on the swingset is experiencing a periodic anharmonic force (due to the mechanics of the swing itself), so even though she is not being pushed, she will probably achieve higher and higher amplitudes over time!” Sorry, diligent reader, but you didn’t get that quite right! We actually know (from common sense and conservation of energy) that if nobody is pushing a child on a swing, she does *not* go higher and higher. Indeed, the force is changing over the cycle, but it’s a position-dependent and conservative force. The force can be characterized by an abstract potential energy curve which is *not* changing over the course of the cycle. So it’s sort of an exception to our general expectations about what happens when something gets perturbed at its resonant frequency. This isn’t a “perturbation”, it’s the force that causes the resonance to occur in the first place.

Anyway, my impression is that the author of the quote above is making the same mistake as the “diligent reader”, who learns (correctly) that you can get high amplitudes by pushing an oscillator at its resonant frequency, but then mis-applies that lesson to conclude that a child on a swingset will swing higher and higher due to the force of the swing itself.

But I could be wrong, I’m just reading a brief third-hand account and some essential details might have been lost in translation. 🙂