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6

A quick answer The bottom line is the spontaneous breakdown of a global U(1) symmetry and the concomitant rigidity of this U(1) phase. By rigidity, I mean something reminiscent of a restoring force felt when one tries bending or distorting a solid stick, which, fundamentally, originates from the translational symmetry breaking in a typical crystalline ...


1

Taking a step back, I'd suggest a look at Ashcroft and Mermin's "Solid State Physics" where they treat the harmonic crystal modes (chapter 22 in my edition). Nowhere do they suggest that LO-TO splitting occurs only in ionic solids. Instead, they make it clear that a Bravais lattice with a mono-atomic basis has acoustic modes only. Once a poly-atomic ...


5

In all theories (London, Ginzburg-Landau, Bardeen-Cooper-Schrieffer, Bogoliubov-Gennes) the Meissner effect is accounted for as the constitutive relation $j\propto A$ : the current is proportional to the vector-potential. (The proportionality factor depends on the system of units, so let us forget about that here.) For the London's phenomenological theory, ...


2

Some materials can occur in several crystal structures if the formation energy is similar. In fact, what matters is the formation energy (difference) at the temperature, where synthesis is performed (typically at higher temperature). Depending on the particular composition, some materials exhibit phase transitions, when brought back to ambient conditions. ...


0

This has to be true by construction, either in the real space or in the reciprocal space. There is one primitive parallelepiped and one Wigner-Seitz cell per lattice point, and both of them tile the whole space.


0

It is by definition, and it is defined that way because of convenience. For a single (but not very complete, explanation you check http://en.wikipedia.org/wiki/Brillouin_zone


1

It is true that the lattice structure will determine the symmetries of the band structure. However, this alone cannot determine the low energy excitations because those are determined by the number of mobile electrons in the unit cell, i.e. the Fermi energy (at least in the case of a metal). This is why elements in the periodic table tend to have similar ...


111

For organic matter, such as bread and human skin, cutting is a straightforward process because cells/tissues/proteins/etc can be broken apart with relatively little energy. This is because organic matter is much more flexible and the molecules bind through weak intermolecular interactions such as hydrogen bonding and van der Waals forces. For inorganic ...


12

It depends on what's being cut. When metal is cut, what happens is that, on a small or not so small scale, it shears. That means layers slide over each other. The mechanism by which they slide over each other is that there are imperfections in the crystal structure called dislocations, and the crystal layers can move by making the dislocations move in the ...


1

Since the superconductor is not dissipative (at least for very low frequencies), it will not generate thermal noise the same way a resistor does. However, every superconductor of finite length forming a loop of non-zero area has an inductivity L. Just like capacitors held at a finite temperature will generate charge fluctuations for a charge measurement of ...


2

Well, the local work function depends heavily on the surface topography, e.g. dense step concentration causes dramatic reduction of the local work function. a good read can be found here. Look at it this way: Just as the energy levels in the bulk are determined by the lattice's potential energy (which is determined by the structure and dopants in the bulk), ...


0

When an electron gains enough energy from a photon of light, it can leave the surface of the metal - leaving the metal with a positive charge. But this positively charged piece of metal will attract an electron to become neutral again. Often, if 'left to itself' the photo electron will just fall back to the metal surface it came from. If there is a ...


0

If atoms have well defined energy levels and those differences correspond to the frequencies of light that can be absorbed, how is it that opaque objects absorb all or most visible light frequencies get absorbed Photons in almost all frequencies hitting an object are absorbed in different ways (absorbed, reflected, refracted, scattered, ...


2

If atoms have well define energy levels and the differences correspond to the frequencies of light that can be absorbed, This is correct how is it that opaque objects absorb all or most visible light frequencies get absorbed and you basically don't have any visible light coming out on the other end? The crux of the matter is the word "objects". ...


1

Well, when did you want it to be written down? As it is, it was pretty much simultaneously and independently arrived at by Hubbard, Kanamori, and Gutzwiller an awful long time ago. Probably others too. The point is, it was written down when there were experimental phenomena that justified including interactions in the model. It wasn't some great conceptual ...


1

min Zhang, The Hubbard model (offen reffered to as the U and J terms in ab-initio DFT or tight-binding models) is a little bit more complicated than it looked like. It is indeed an additional energy that you add locally to some states (d or f bands usually) to locallized them. Usually you want to do this because DFT tends to spouriously delocallize ...


2

Do you understand that the electric field within a conductor is zero? The charge is mobile, so the internal charge rearranges itself until there is no longer any force to move them: there is no field in the interior. If you understand that, then you will realize that a test particle within the conductor will feel no force, so no work will be done in ...



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