Speaking of solitons there's a recent paper in PRL, which I just caught because it referenced an old paper of ours for a key finding.

Hafke, B. et al. [Thermally Induced Crossover from 2D to 1D Behavior in an Array of Atomic Wires: Silicon Dangling-Bond Solitons in Si(553)-Au](https://www.researchgate.net/publication/338522710_Thermally_Induced_Crossover_from_2D_to_1D_Behavior_in_an_Array_of_Atomic_Wires_Silicon_Dangling-Bond_Solitons_in_Si553-Au). Physical Review Letters 124, (2020).

This is fascinating in the how the solitons are triggered by increasing thermal energy applied to the step-edge danging bonds. The “standing waves” of the bonding arrangement release a soliton (the equivalent of a traveling wave) which makes it free to slide along the 1D wire defined by the step edge.

![](https://imagizer.imageshack.com/img924/2396/YUzMNx.gif)

A couple of points here. One is in that how similar this arrangement is to the 1D behavior of the standing-wave ENSO and the traveling wave MJO. In the solid state situation, the (N-S/Euler/Laplace) wave equation of a fluid is replaced by Schrödinger's wave equation of the lattice considering the electron occupancy level of unsaturated dangling bonds. The stable low-T state shows a 3-fold periodicity in occupancy (analogous to the main ENSO dipole) but at higher T it starts triggering solitons that fuzz up the periodicity. This is where they incorporate [our analysis for detecting order/disorder transitions in periodicity](https://www.sciencedirect.com/science/article/pii/0039602885907277).

Another point is in the concept that condensed matter physics and ideas in particular based on topological insulators of low-dimensional structures are useful. This is *a la* the work of [Delplace, Marston, Venaille](https://science.sciencemag.org/content/358/6366/1075.abstract), who also claim that equatorial waves have a topological origin, borrowed from ideas of the quantum Hall effect. This is such cool stuff and in which most climate scientists, save for these guys and what we are working on here, are unaware. So there is hope.

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1D molecular chain

https://newscenter.lbl.gov/2020/11/12/charges-cascading-molecular-chain/

![](https://newscenter.lbl.gov/wp-content/uploads/sites/2/2020/11/STM-1D-array-graphene-1200x800-1-628x419.png)

Hafke, B. et al. [Thermally Induced Crossover from 2D to 1D Behavior in an Array of Atomic Wires: Silicon Dangling-Bond Solitons in Si(553)-Au](https://www.researchgate.net/publication/338522710_Thermally_Induced_Crossover_from_2D_to_1D_Behavior_in_an_Array_of_Atomic_Wires_Silicon_Dangling-Bond_Solitons_in_Si553-Au). Physical Review Letters 124, (2020).

This is fascinating in the how the solitons are triggered by increasing thermal energy applied to the step-edge danging bonds. The “standing waves” of the bonding arrangement release a soliton (the equivalent of a traveling wave) which makes it free to slide along the 1D wire defined by the step edge.

![](https://imagizer.imageshack.com/img924/2396/YUzMNx.gif)

A couple of points here. One is in that how similar this arrangement is to the 1D behavior of the standing-wave ENSO and the traveling wave MJO. In the solid state situation, the (N-S/Euler/Laplace) wave equation of a fluid is replaced by Schrödinger's wave equation of the lattice considering the electron occupancy level of unsaturated dangling bonds. The stable low-T state shows a 3-fold periodicity in occupancy (analogous to the main ENSO dipole) but at higher T it starts triggering solitons that fuzz up the periodicity. This is where they incorporate [our analysis for detecting order/disorder transitions in periodicity](https://www.sciencedirect.com/science/article/pii/0039602885907277).

Another point is in the concept that condensed matter physics and ideas in particular based on topological insulators of low-dimensional structures are useful. This is *a la* the work of [Delplace, Marston, Venaille](https://science.sciencemag.org/content/358/6366/1075.abstract), who also claim that equatorial waves have a topological origin, borrowed from ideas of the quantum Hall effect. This is such cool stuff and in which most climate scientists, save for these guys and what we are working on here, are unaware. So there is hope.

---

1D molecular chain

https://newscenter.lbl.gov/2020/11/12/charges-cascading-molecular-chain/

![](https://newscenter.lbl.gov/wp-content/uploads/sites/2/2020/11/STM-1D-array-graphene-1200x800-1-628x419.png)