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This photo from a proposal for stainless steel stents ( to be used in humans) is enlightening stainless steel scanning electron microscope (SEM) photo The crystallization is obviously random, with a lot of pores at that size ( which is what they try to increase for the purposes of the study). This means that the facets of the crystals are not on a ...


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The entanglement of any region in a matrix product state of bond dimension $D$ is bounded by $S\le 2\log D$. Thus, in order to simulate a system with a lot of entanglement, the bond dimension (and thus the memory and time of the computation) will grow exponentially with the entropy. Conversely, we know that if for a state $\vert\psi\rangle$ the ...


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If there is only one band maximum in the BZ, this point is one of the high-symmetry points of the BZ. However, there can be cases where there are many points which are a band maximum and they are not at one of the high-symmetry points of the BZ. These points however are all connected by a symmetry operation. An example of a system with band minima away ...


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$\renewcommand{ket}[1]{|#1\rangle}$ The basic logical connection here is $$\text{symmetry} \rightarrow \text{degeneracy} \rightarrow \text{avoided crossing} \rightarrow \text{band gap} \, .$$ $\textrm{symmetry}\rightarrow \textrm{degeneracy}$ Consider an operator $S$ and let $T(t) = \exp[-i H t / \hbar]$ be the time evolution operator. If $$ [ T(t), S] = 0 ...


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There is no resistance is this scenario. You need a scattering mechanism like electron-phonon scattering or electron-defect scattering to obtain a non-infinite conductivity.


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These are two different problems. What Jon was saying is correct. However, it does not explain LO-TO splitting. Like Jon said, because you can tell when you are on a Ga or As atom, the degeneracy of the optical modes are lifted at the Gamma point. This is in regards of 3 different optical modes separating. However, the phenomena Cardona is refers to involves ...


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This is interesting! Just want to ask a few questions for clarification: (1) Which geometry did you use for the states? disk, sphere, torus? (2) Which set of Slater determinants did you computed overlaps with? for example, did you use a fixed single particle basis and did the optimization over occupation numbers only, or did you allow for changes of the ...


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I'll comment on the second issue that $E_F$ should always be greater than zero, which leads to a finite scattering rate. However, that's beside the point because in an ideal Fermi liquid at $T\rightarrow 0, |E_F-E|\rightarrow0$, the scattering rate becomes zero, which leads to an infinite lifetime. If in graphene, as you say, the independent particle picture ...



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