One of the things that excites me about learning is the process of creating connections between different things. I believe, this is also the process of learning that is persistent throughout our lives, and in my opinion it can be as powerful as the process of learning in our childhood.
I therefore decided to start writing down notions that I read and which connect to notions I had read before. It’s funny how this can also be converted into a ‘computational’ network, and observe how clusters are formed between its nodes. The difference is that here I will not be connecting words between them, but rather presenting the same word, with the same conceptual meaning, used in different sub-domains in physics. Maybe the most appropriate measure here is when the network would ‘break down’. That is, when the meaning between different uses will change completely.
When I started using Density Functional Theory and, even more, when trying to re-create its results in a meaningful piece of material, like a nanoribbon or a nanowire, a lot of the problems came during geometry creation. This is natural, as DFT is a theory to derive quantities like eigenenergies, in a crystal lattice with periodicity. But when trying to switch to a model that is finite in one or more directions, you have to start a sort of mix and match procedure.
During this time (and assuming you are not the one who writes the software), visualizing vectors is maybe the less useful thing to do. Still, there are cases where you need it in order to get a better understanding of things, like visualizing Weyl points.
These are the books I’ve chosen to give a head start in quantum physics and strongly correlated systems. There may be more appropriate textbooks out there, but these are really clear and comprehensive, I thought they are worth sharing.
S. H. Simon. The Oxford Solid State Basics. OUP Oxford, 2013
S. Axler. Linear Algebra done right, third edition. Springer 2015
In microscopy, which is using microscopes to look at small things, you can’t separate things that are closer together than the wavelength used. This is why we use X-ray diffraction and electron microscopes with very short wavelengths to look at atoms and molecules. So if you want to measure the electron’s path with light, and measure it precisely on an atomic scale, you have to use a short wavelength of light. But if you use a short wavelength then it has a lot of energy (E = hν), enough to change the electron’s direction. This is the basis of the Uncertainty Principle.
A few months ago, after presenting my first year PhD results at the University of Southampton, I was asked “Are your results affected by the frequency of the incoming particle?” and the answer is very simply no. But here is a more detailed analysis of the physics involved one step before Total Ionizing Dose (TID) mechanisms for a gamma ray source – which is what we are using.
As is generally known, Total Ionizing Dose creates electron-hole pairs, and this is what device physics studies. The electron-hole pair generation rate is given through the following relationship,