Ballistic Conduction in Graphene & Other Cool Quantum Effects in Ripple Tank

Currently, as I’m starting to write this, I’m relaxing and sitting at the porch of our hunting club’s cottage. My girlfriend and I made a hole in the ice, soon we will heat up the sauna, black woodpecker is calling nearby, and a juicy roast is waiting us in an oven. I think I will also continue my bow project at some point.

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It’s a beautiful day! It is sad how rare these clear, really cold days are nowadays. Maybe that is the climate change 🙁

During the week I made a hell of a work as I wrote a nice looking funding application, like I promised that I’ll try to become a more independent researcher. That’s because I have the best figure about my farsighted ideas, logically, why I want to have a good grip on how the research is made and what will be the quality of it. I have the best aspect to determine what is fundamental and what is not for advancing the visions. My ideas are high-flying, why the projects need determination, sustainability, and a lot of reasoning. As an inventor I want to have the responsibility, but not to exclude the kind support of the nice and clever people in our scientific institutions. I’m pretty excited because this kind of an arrangement is totally new to me. Hopefully I don’t bother the other people too much with my stupid questions 😀 Well, now we’ll just have to wait and see what will happen after I sent the application 🙂

The funding application I made have nothing to do with quantum mechanics nor ballistic conduction in graphene, but once again I had a time to wonder the beauty of the surrounding world and its phenomena. Seriously, sometimes I use a big, flat dish for studying how waves behave, but today I bought a nice wave simulator for my MacRipple Tank. I give it 4,5 stars. Basically, the software produces 2D waves, from one or multiple different sources, with one or two different frequencies. The interactions of the waves with the walls and mediums can be studied. I wish the software could support more simultaneous frequencies, for studying phenomena seen with polychromatic waves. It would be even more fun, if quantum mechanical waves could be simulated somehow, but I believe it would be quite demanding to compute. I mean like if one pulse of a probability wave is released, it would become absorbed somewhere according to its heights of the amplitudes, and during the absorption the wave would disappear from all the other places. Anyhow, for example, one can still study how mirages are formed on hot asphalt (try the setup of Temperature Gradient 2), how lenses work (biconvex lens), how surface plasmons travel in an interface (internal reflection), doppler effect (Doppler), or try the famous double slit experiment (Double Slit).

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Relaxing and playing with the new app, Ripple Tank.

The main reason I bought the software was to simulate ballistic conduction in a thin wire. For example, ballistic conduction in graphene. If the dimensions of conducting medium are relatively small to the wavelength of an electron, the electron might travel through it almost like a classical particle, from point A to B to C and so on. Instead, if the dimensions are too spacious, the probability waves might “echo” back and forth from the walls, and the movement of the electron would not be so straightforward anymore. At least this is what I have understood as a biochemist! So, I wanted to see the effect by my own eyes. I took two wave sources with the same frequency, and put each between two walls. See the following figure. The other source was in a thinner space (right), while the other had more space (left). In the right hand case the probability waves flowed nicely from top to bottom, but in the left side there was a big mess. The electron could “pop out” here and there, because the most probable positions (high wave amplitudes) were scattered all around. Thus, in the left hand case the electron would wander through a longer road, and in the right hand case it will move much more straightforward. A nice real life example of ballistic conduction can be seen in graphene. I believe one good reason for the good conduction in graphene is the low amount of scattering of electrons. That is why graphene is even better conductor than a copper wire. Because the freely moving electrons are trapped in the 2D lattice of carbon atoms, the probability waves of electrons do not echo and scatter so easily. Instead, they go straightforward.

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A screen shot from the Ripple Tank app for Mac. A source of “probability waves” is placed between close walls (right) or distant walls (left). In the left hand case, the probability waves “echo” from the walls and produce a diffraction mess. An electron, carrying its part of current, can be found here and there, and its movement is not straightforward. This means a bad conduction. In the right hand case the probability waves flow straightly from point A to B to C and so on. This is an example visualization of ballistic conduction in graphene, a thin sheet of conducting carbon atoms, same stuff which is used in pencils.

In graphene, there is also small, but a freaking cool effect which has its part for keeping the graphene sheets together. Casimir effect. It is related to the popping-out of virtual photons out of nowhere, which I don’t yet understand pretty well, and the larger set of acceptable wavelengths outside of two graphene sheets than between them. The outside infinity of different sets of wavelengths is bigger than the infinity inside, because photons with wrong wave lengths cannot produce standing waves between the close graphene sheets and would go elsewhere. I tried to demonstrate this one also with the software, but without polychromatic sources it is somewhat difficult. Instead, look at this interesting demonstration from YouTube. It shows how Casimir effect works on practical level.

*Yawn*, I’m getting tired 🙂 Here are some photos taken under the frozen night, on a lake right next to the cottage. Look at how beautiful our galaxy is. Good night!

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Big dipper, my guide in darkness 🙂 Sometimes I wonder. If a photon starts its travel from a distant star, as a probability wave, should it encounter earth as a large, spatially coherent plane wave? If it does, could the same photon be absorbed either into my eye or somewhere else in a distant place, equally likely? Just before the much debated wave function collapse, could the photon become seen in someone’s eye almost as likely as someone’s else?

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Mesmerizing.

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Big dipper points at the cottage and yells “back inside, it’s cold outside my children!” 🙂

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