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In a crystal, each electron polarizes its vicinity, meaning positive charges prefer to stay nearer to the electron while negative charges move away from it. As the electron traverses through the crystal, it has to drag the polarization cloud with it, which can effectively increase or decrease its mass. Actually, the system "electron+polarization cloud" can ...


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This is just a particle-in-a-box. You only have $\ell, m$ quantum numbers in a more complicated system like an atom--in particular, there needs to be a rotational symmetry and this just isn't that kind of system.


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In real life most fractures occur at defects. Even such everyday materials as cement can have their strength increased many times by reducing the defect density within them. You'll often see claims for the incredible strength of nanostructures, but the strength is just due to the fact that these structures are free of defects. It's a lot easier to make a ...


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DFT is based on two important theorems: (1) Hohenberg & Kohn: the potential and the density are connected by a one-to-one map (2) Kohn & Sham: there is always a non-interacting reference system (map: V_xc: non-interacting <-> interacting problem) having the same density as the interacting one. In a nutshell: the potential and the density of the ...


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As far as I understand. The effective mass is given by a lattice. There is a periodic field that makes electrons move differently in comparison to free electrons.


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Partition functions are a measure of the allowed volume in (microscopic-)configuration space for the system, and as such they are the normalizing function for probabilities expressed as volumes in configuration space (and assuming the applicability of the ergodic hypothesis). I know that this is very abstract, but it is also very general.


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But what is the physical interpretation of the partition function and it's significance to Thermodynamics? I'm seeking a simple yet understandable intuition. The partition function has one simple physical interpretation in terms of Thermodynamic functions: Its natural log is proportional to the Free Energy (the proportionality constant is the ...


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Start from the general definition, how this thing is set up in practice: You start from the mean energy of a system in contact with a thermal reservoir. The systems of the representative statistical ensemble are distributed over the entire number of possibilities, in accordance with the canonical ensemble $$P_i = C \exp(-\beta E_i) = \frac{\exp(-\beta ...


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Ok, finally solved it in a very simple geometrical way. IF we take a square slanted lattice in the hexagonal lattice, like in the image, which is $N$ particles along each side. Then the number of particles inside is $N^2$. The volume of that area is just $V=(Na)^2\cos(30)$, and so: $$\rho a^2=\frac{2}{\sqrt 3}$$. I'm sorry for asking, I was frustrating ...


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Imagine you have a string of irregularly placed (that is, not evenly spaced) christmas lights, and you want to calculate the total power emitted by all of them. There are two ways you can do this. One way is to sum over all lights the power emitted by a light. Another way would be divide the string of lights into segments of length $\Delta x$, and then sum ...


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Superconductors have both a critical temperature, at which they transition to the normal phase, and a critical applied magnetic field value. Once the applied magnetic field is at the critical value, a transition to normal occurs, regardless of the fact that the superconductor is below its critical temperature. The critical value of the applied magnetic ...


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Assuming that the expressions given for a 2D electron gas here are valid, there really is no contradiction. Remember that there is an implicit sum in a repeated index (Einstein summation convention). Equivalently, an inverse matrix need not be the component-by-component inverse of the original matrix. For example, we get: $$[\sigma\cdot\rho]_{xx} = ...


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The mathematics is okay but how does this makes sense from the physical point of view? How does the dimension of the system dictate that in 3D we have more states with high energy where as in a 1D the system we get fewer and fewer states for increasing the energy? The density of states just comes from counting the states with energy less that $E$ ...


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First, note that the way you have written the electrical wave-field isn't anything more than exactly a way to write a wave function in general. This is because the term $e^{i(kx-ωt)} $ can be written as: $$e^{i(kx-ωt)} = cos(kx-ωt) +i sin(kx-ωt) $$, and from here you can keep in general the real or the imaginary part as you wish. As for $κ$, the imaginary ...



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