Vantasner Coherence Model
[CODE]
01 SUMMARY 02 MODEL 03 DETAIL 04 SOURCE
A model crystal lattice of polished steel balls joined by rods, with smaller beads sitting in the gaps between them, lit from the right against a dark background. [Studio picture · a steel lattice with small beads in the gaps]

[Coherence model · summary of the report]

A coherence model, built in passes

The aim: build, in passes from coarse to fine, a model of a coherence domain in hydrogen-loaded nickel and palladium, a region where many hydrogen nuclei move in step, good enough to design experiments against.

[What this is not] It is not evidence that such domains produce heat or nuclear effects. That part of the chain was not modelled.

The findings in short Start with the method

The four stripes under the menu show the depth of the page. They run from Summary to Model to Detail to Source. Every claim links to the level below it.

[In short]

What the models show

Six models, each feeding the next, asked what could make many hydrogens in a metal move together, and how far that reaches. These are the results that matter. Each links to the page that shows how it was found.

0 ordered states from coupling to the electromagnetic field alone, at any strength 4–12% gap between computed and measured vibration energies, NiH, PdH and PdD 99.8% of the pumped NiH motion in one pattern, across all 110,592 simulated sites 1–2 nm: how far PdD stays in step under the same pump

  1. 01[The field]

    The field alone does not make them act together

    Coupled only to the electromagnetic field, with the field treated the same way everywhere it enters, the hydrogen nuclei form no ordered state at any coupling strength. Another ingredient is needed.

    Model 1 · protons and the field

  2. 02[The ingredients]

    Three ingredients that do

    The hydrogens' pull on each other through the metal, together with wells whose walls steepen faster than a spring's, gives a static route to order. A pump that makes every well stiffer and softer at twice the vibration frequency gives a driven route.

    Model 2 · the ingredients Model 4 · the pumped route

  3. 03[The wells]

    Stretch the metal and the wells soften, far more in PdD

    The pocket each hydrogen sits in was computed from the electrons up. Its stiffness responds to uniform stretch with a sensitivity of −22 in NiH and −113 in PdD, the relative change per unit strain: one percent of stretch softens the NiH well by about a fifth and takes the PdD well below zero.

    Model 3 · the wells

  4. 04[The vibration]

    Vibration energies close to the measured peaks

    For the vibration in which every hydrogen moves in step, the model gives 85.6 meV in NiH, 62.3 in PdH and 39.8 in PdD. Neutron experiments put the peaks at 89, 55.8 and 37 meV. Nothing was fitted to them.

    Model 4 · the oscillator

  5. 05[The lattice]

    Pumped and cold, NiH locks in step; PdD stays patchy

    At 0 K, 99.8 percent of the pumped NiH motion is one uniform pattern, in step across the entire simulated box of 110,592 sites. PdD stays in step over 0.82 to 1.75 nm only. At room temperature the pump adds nothing measurable in PdD.

    Model 5 · the lattice The two maps, below

  6. 06[Empty sites and interfaces]

    Empty sites and interfaces shape the response

    An empty neighbouring site softens a deuterium and pushes it off centre, and the arrangement of empty sites matters, not only their number. Nickel grown on palladium deuteride prints a mismatch pattern that, in a first estimate, lays a grid of soft lines into the wells, repeating every 1.73 nm.

    Model 3 · empty sites Model 6 · nickel on palladium

[One pump, two metals]

In step, or in patches

One layer of each simulated crystal, pumped the same way at 0 K: every well made 8 percent stiffer and softer at twice the frequency of the in-step vibration. Each dot is one hydrogen site, replaying its own computed swing.

In nickel hydride the whole layer brightens and darkens together. In palladium deuteride regions swing against each other a nanometre or so apart.

Brightness: how far a site swings, up to 0.110 Å, on one scale for both maps.

[FIG]Pumped motion in one layer, same scale

NiH110,592 sites · full loading

2 nm

In one uniform pattern
99.8%
In step over
3.85 nm = the box

PdD32,768 sites · loading 0.875

2 nm

In one uniform pattern
0.5%
In step over
1.38 nm
What to notice: in NiH every dot keeps the same colour as every other at each moment; in PdD neighbouring regions take opposite colours. Each map is one (001) layer of the simulated crystal, replayed from the fitted swing of every site at half the pump frequency over the second half of the run, slowed down for display. PdD at full loading has the same in-step length, 1.38 nm. g3_lattice/rerun/part2
MODEL Model 5: the full lattice results Loading, vacancy arrangement, stretch, temperature, and what the result leans on

[How it was done]

Cheapest whole model first

The work ran in passes. Pass 0 built the whole chain of six models from a few equations; each later pass replaced the guesses the answer depended on most with something computed, ending in electronic-structure calculations and a lattice simulation.

A small team of AI agents did the work: one lead and two specialists, one for the electronic-structure calculations and one for the physics models. Results were delivered as checksummed files, verified, and committed to a public repository.

Twice a cross-check exposed coarse settings behind an input: first the palladium deuteride wells, then the nickel hydride coupling, which came out 2.9 times its first value. Both were recomputed and the models that used them were rerun. This report states the corrected results.

  • [Passes]0→3sized by compute, from a few equations to the electrons of the metal
  • [Models]6in a chain, each one's output the next one's input
  • [Team]1+2a lead agent and two specialist agents
  • [Corrections]2inputs recomputed after cross-checks, models rerun

[FIG] Four passes, six models. The step height shows the compute tier

  1. Pass 0 · Negligible

    A few equations

    NumPy

  2. Pass 1 · Light

    Sweeps and a ranking of the unknowns

    NumPy

  3. Pass 2 · Moderate

    Compute the top of the ranking

    GPAW, 164 core-minutes

  4. Pass 3 · Heavier

    Scale, layers, loading

    GPAW, about 2,870 core-minutes for loading and 200 for strain; NumPy lattice

MODEL 01 · The method: passes, models, team and tools Why the cheapest whole model came first, how the unknowns were ranked, and what each step cost in compute

[The report]

Nine chapters

Each chapter opens with the same kind of short summary as this page, then goes into the equations, the method and the tables. Read them in order, or start where a finding caught your eye.

  1. One small bracket made three times: in clay, in wire and in machined steel 01 The method Cheapest whole model first, then resolution where it matters. Two agents, one lead, compute sized in passes. [What you will find] The four passes, the chain of six models, the team of agents and what each step cost in compute.
  2. Facing mirrors with a light beam crossing a row of still beads 02 Model 1: protons and the field Coupling protons to the electromagnetic field alone does not make them act together. [What you will find] An exact calculation of nuclei coupled to light, and why it gives no ordered state.
  3. Springs, steel balls, magnets and a tuning fork laid out on a bench 03 Model 2: what could make them order Five candidate ingredients, tested in every combination, and the two routes that survive. [What you will find] Five ingredients switched on and off in all 32 combinations, and the two routes to order that remain.
  4. A steel ball resting at the bottom of a glass watch glass 04 Model 3: the proton wells, computed The shape of the pocket each hydrogen sits in, from electronic-structure calculations. [What you will find] The pocket each hydrogen sits in, computed from the electrons up, and how stretch, shear and empty sites change it.
  5. A row of pendulums, a group in the middle swinging together 05 Model 4: the anharmonic oscillator One proton in its real well, coupled to its neighbours: a static route under stretch and a pumped route. [What you will find] Vibration energies against the measured peaks, the stretch at which hydrogens shift together, and the pumped route.
  6. Steel beads on a dark plate gathered into lines, patches and rings 06 Model 5: many sites together Lattices of up to a million sites, with loading, arrangement, stretch, temperature and pump as sliders. Do the hydrogens move in step? [What you will find] Maps of a pumped crystal: nickel hydride in step, palladium deuteride in patches, with loading, empty sites and temperature.
  7. Two wire meshes of slightly different spacing laid one over the other 07 Model 6: nickel on palladium The natural mismatch pattern at a layered interface and what it does to the wells beneath it. [What you will find] The mismatch pattern nickel prints on palladium, the soft lines it lays into the wells, and where pumped motion gathers.
  8. A stack of thin metal foils bowed in a small steel clamp 08 Engineered strain A forward look: how layered metals could tune the d band, the wells and collective behaviour. [What you will find] A forward look at layered metals: why a stretched metal binds hydrogen differently, and ways to put strain to work.
  9. A lens focusing a thin beam of light onto a metal foil 09 What an experiment could test The predictions, the open inputs and the next pass. [What you will find] Six predictions a measurement could look for, what the team trusts, and the seven steps of the next pass.

[How much to trust it]

Firm, conditional, extrapolated

The results are not equally solid. The two specialists reviewed them and the lead sorted them into three kinds.

Firm

Computed directly, for the inputs as stated.

  • The field result. Coupled to the field alone, the nuclei do not order. This rules out that one route.
  • The computed wells and couplings, at the geometries stated.
  • The vibration energies: 85.6, 62.3 and 39.8 meV for NiH, PdH and PdD.

Conditional

Computed, but the size rests on an unmeasured input or a finite simulation.

  • Every pump threshold. The loss rate of the hydrogen vibration has not been measured, and nothing yet connects a real drive to the stiffness modulation. Across two loss scenarios the threshold runs from 1.7 to about 23 percent.
  • The NiH in-step length. At 3.85 nm it equals the box. Larger boxes and room temperature have not been run on the corrected inputs.

Extrapolated

Uses laws well outside the range they were computed on.

  • The ordering strains, 5.3 to 8.8 percent, carried from calculations at ±1 percent.
  • The interface well map. Its local strains run from −18 to +8 percent, outside the computed range at every site.
  • Loading below 0.75, which uses the loading law beyond the cells it was fitted on.

[What comes next]

The next pass

The specialists named seven steps. Three of them decide the most.

  1. 1[First priority · moderate to heavy compute]

    Let the hydrogens settle

    Relax the hydrogen positions in a few strained, thin-film and partially loaded cells and compute the wells where the hydrogens come to rest. This decides which of the soft spots are real.

    Step 1

  2. 4[Light compute]

    Run NiH in a larger box, and at 300 K

    Find the true reach of the in-step motion in NiH, now capped by the box at 3.85 nm, and whether it survives room temperature.

    Step 4

  3. 7[Needs a measurement]

    Establish the pump path and the loss rate

    Find which physical drive makes the wells stiffer and softer at twice the vibration frequency, how strongly per unit field, and how fast the vibration loses energy. Until both are known, no threshold is an experimental number.

    Step 7

Start with the method, or go straight to what an experiment could test.

01 · The method 09 · What an experiment could test The repository