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With Bloch electrons, the Brillouin zone and all bands comprises a complete space. This means that while it is possible to write down and speak of states outside the Brillouin zone, these states are actually duplicates of the ones inside. In short, the Brillouin zone must be defined with a width in k-space of $2\pi/a$, with $a$ being the lattice constant. ...

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The answer probably lies in what are called Rayleigh–Bénard convection cells that often form hexagonal structures. Buoyancy, and hence gravity, is responsible for the appearance of convection cells. The initial movement is the upwelling of lesser density fluid from the heated bottom layer.[3] This upwelling spontaneously organizes into a regular ...

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A sum-frequency system with a "hot" mirror could act something like an optical switch: Unlike a switch, the output frequency will be different from either of the inputs. Edit: For an example of sum-frequency generation crystals see: Thorlabs Introduction To Periodically Poled Lithium Niobate (PPLN) (PDF) Thorlabs also sells hot mirrors.

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Z3 or Z1, Z2 excitons are labelled according to the locations of the peaks in the emission spectra of materials. These emission peaks are superimposed on the main band spectra linked to transitions between the conduction and valence bands. The occurrence of the various excitons can be attributed to the properties of the material system, such as the strength ...

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Kramers theorem is a very general result that in fermionic systems with time-reversal symmetry, energy levels are at least double degenerate. Circularly polarized light is an eigenstate of angular momentum. Angular momentum is odd under time reversal ($T$), since $\mathbf x\times\mathbf p$ is an angular momentum and $\mathbf p \mapsto -\mathbf p$ under $T$. ...

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You are right that the Einstein model will break down if you are looking at low temperature. The next level of approximation, which does better, would be the Debye model. If you look in any intro. statistical physics book (I recommend Schroeder, Introduction to Thermal Physics if you are undergrad, or Kittel's Intro. to Solid State Physics) you will find a ...

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