A molecule with half-Möbius topology
science.org
science.org
> The Half-Möbius electronic topology is a form of quantum topology in molecular science in which the π-orbital basis of a cyclic molecule undergoes a 90-degree phase twist per revolution around the ring, requiring four complete circuits to return to its starting phase. This is distinct from both the topologically trivial (Hückel) case, in which no net twist occurs, and the classical Möbius case, in which the orbital undergoes a 180-degree half-twist per loop.
I choose to believe that Hückel was not the one who characterized or discovered the trivial case, but instead a disliked graduate student who was once insulted at a party as "emotionally, intellectually, and topologically trivial", and it just cascaded from there into naming things after him.
Don't try to convince me otherwise.
describes the quantum-software-hardware co-design concept IBM is selling with that paper
It took my pea brain a while.. is this a joke or meant to teach something.. & I still don't get it.
Is the punch line "this is the first paper to name the concept Hueckel-orbitals", even planting their flag on Wikipedia to piss on a dead man?
That's a deep dismissal of Leo Gross
On the other hand, from these guys. I first learnt about Dyson orbitals, which are exactly the long-ranged blobs seen under the scanning tunneljng microscope! That was obvious in retrospect (for someone who has familiarity), so luckily all of us didn't get an urge to name the atom-sized unentangled NPC blobs you sometimes dont see in the STM after some grad student.
I am glad trivial--- for the sense of trivial that Leo Gross might think is different--- orbitals are named after nobody at all. and aptly has not one Wikipedia mention.
I suspect to acheive the 4D needed for construction without undesirable intersection, it will have to be implemented with a dynamic repeating 3D-Volume cycle, essentially rendering the 4D shape in time.
Much like time crystals.
https://en.wikipedia.org/wiki/4D_scanning_transmission_elect...
(Not in the sense that "time" is involved but in the sense that what distinguishes 3D from 4D is almost only software . The same way you can see 4D "all at once" on your 2D screen,but 4tuples coords!= code)
But then again IBM have claimed quantum software=quantum hardware (see above).. they might or might not understand what is or is not needed?
(It's easier if you get one that is not twisted. Something like https://www.sugarrushlane.com/products/filled-red-licorice-s... but with 4 instead of 5 parts. Also imagine each of the 4 parts has a different color. )
Now make a circle with it.
If you don't twist it, you get an horizontal surface that looks like a thick border of a circle, and a vertical surface that looks like the round wall of a cylinder.
If you twist half a turn, when you connect the extremes the top of the + in one extreme is glued to the bottom of the + in the other extreme. Something similar withe the left and right parts of the +. Now you have two overlapped copies of a Möbious strip, each perpendicular to the other.
If you twist a quarter of a turn, when you connect the extremes the top of the + goes to the right, the right to the bottom, the bottom to the left an the left to the top. So you get only one "strip?"