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A study undertaken by Nutting and Nuttall at the University of Leeds found that "gold is not inherently more ductile than other face-centered cubic metals", such as copper. The authors found by experimentation that "gold is considerably less ductile in tension than silver." But when beaten foil becomes very thin, other metals tend to fragment, whereas gold ...


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You are referring to different models, not different electrons. Like saying Newton's gravity and Einstein's gravity - it doesn't mean, that there's more than one type of gravity in the nature.


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I found the answer to my question myself. Simply put, the answer is 'no'. The reason lies in the definition of the lattice sum (equation 2 in Beenakkers original paper 'Ewald sum of the Rotne-Prager Tensor' from 1986). Due to the symmetry of the system, it can be reduced to a 3Nx3N matrix that includes the hydrodynamic interactions of the entire system, ...


0

I think you should get Altland's book. Fradkin's book is more advanced and covers more modern (and important) topics. It also provides an excellent bibliography. However if you try to follow the derivation and reproduce the result you are likely to be disappointed. I have read in detail the Quantum Hall effect chapter, so far I have found numerous mistakes, ...


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I am not sure thermal expansion is much greater in polycrystals than in single crystals (http://nvlpubs.nist.gov/nistpubs/jres/14/Jresv14n5p523_A1b.pdf, Fig. 13). Wikipedia article that you quote says that single crystals have higher creep strength at high temperatures, so they can provide higher turbine efficiency.


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Single crystal jet turbine blades are grown in a substantially different way than most crystals. The following article gives details of some of the R&D and large scale production process that is used. http://www.tms.org/superalloys/10.7449/1980/superalloys_1980_205_214.pdf


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Okay so admittedly I know nothing about jet turbines, however I know a little something about crystals. The occupied lattice points of a single crystal are interacting with good overlap of atomic orbitals. If you have a d-block metal then you get the standard d-d and d-p interactions as predicted by tight binding and Hubbard models. Grain boundaries are ...


5

They are all identical electrons. Its just that for the purpose of the paper or whatever they are behaving according to the rules of Dirac's equation, etc, because of the circumstances the electron is in. 'Free electron' means an electron flying about on its own, while a bound electron is in an atom and a Dirac electron is one that needs to be modelled using ...


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Your argument is correct, in fact you can use it to show that the Hall conductivity is set by the density. However, there is an underlying assumption when you apply Galilean transformation, that is translation invariance. In reality there are impurities that can backscatter electrons and cause the current to dissipate. So your argument immediately fails for ...


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Earlier theoretical works have generally employed the classical approach where the exciton "hops" from one lattice site to another, the so called exciton hopping model. In more recent years, this model has been replaced by modern approaches based on the quantum coherence properties of the exciton. In the coherent propagation scheme, the exciton is modelled ...


1

The fractional dimensional space approach (FDSA) can be adopted to introduce flexibility in examining optoelectronic properties in anisotropic systems (quantum dot, wells etc). Here the material are fitted to models that utilize a variable dimension, (alpha) which has provided good agreement with experimental results in many works. This is because the ...


0

One of the most important attribute of an exciton is its binding energy. This energy is calculated by subtracting the exciton energy from the difference in energy levels of the conduction and valence bands. The binding energy is NOT the same as the exciton energy. So the exciton is stable when its binding energy exceed zero. When Pauli blocking mechanism ...


4

In the long run I don't think it matters much which of the two you study now. If you truly understand calculus in 2-3 dimensions, you won't have too much trouble generalizing your understanding to $N$ dimensions. On the other hand, if you want to do research in condensed matter, you will need linear algebra anyway, so there's no harm in picking up that topic ...


0

I figured it out myself. The complex function used in the summation is $$g(z) = e^{-z\tau}\left[\frac{1}{z-\Omega}-\frac{1}{z+\Omega}\right]$$ One can then write $$\sum_{i\omega_n}g(i\omega_n) = \sum_{i\omega_n}\text{Res}[g(z)n_B(z)]_{z=i\omega_n} = \oint\mathrm dz\ g(z)n_B(z)$$ Then, one flips the contour and evaluates it as a sum over the poles of $g$. ...


2

The relevant part of the sum as $\sum_{k^*,s_1,s_2}\delta_{k^*,s_1s_2}d_{s_1}d_{s_2}B^k_P$ Let me assume that the fusion category has no multiplicities, so $N_{ab}^c=0,1$, which I think Levin and Wen also assumed. We can write the sum as $\sum_{k^*,s_1}d_{s_1}B^k_P\sum_{s_2\in s_1\times \bar{k}}d_{s_2}$ This is because if $\delta_{k^*,s_1s_2}=1$, it ...


0

resistor is an electric component which is used for the purpose to restrict the electron flow. if you run with 10Km/hour speed now i will stop you is it possible to stop you suddenly. No it is not possible. so that resistor dissipate some energy in the form of heat.


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It "runs out" when it reaches thermal equilibrium with it's environment. In that case, as @Kevin points out, the dissipation equals the absorption from the environment. If you pass a current through the resistor, it will heat up and that will drive extra current/voltage noise in the resistor. FYI: Resistive cooling of ions in a Penning trap uses a cooled ...


1

You can find an excellent description of what a topological insulator is in this brief presentation from the Yazdani Group at Princeton: Topological Insulators. To answer your question on the meaning of negative effective mass: The effective mass is actually determined by the behavior of the energy levels $E({\bf k})$ as functions of the crystal wave ...


1

It works just like every other kind of thermal energy. If a resistor can give out energy to the environment, it can also receive it. For example, if it gives it out by radiating, it can also absorb radiation; if it gives it out by having its fast-moving atoms smash into air molecules, then fast-moving air molecules can also smash into it. When it's in ...


2

Your equation $$ v_F (\sigma \cdot k)\psi(k) = E \psi(k) $$ seems to be the "momentum representation" via Fourier transform of the envelope function equation for graphene. In this case $k$ is just the wavevector introduced by the Fourier transform, not a "crystal wave vector" as in the Bloch ansatz, and the $\psi_k$-s are the Fourier coefficients for the ...


3

The most truthful answer, to my mind, to this is simply "because it often works in practice." It is not obvious, a priori, that band structure should apply to any realistic solid. The Coulomb interaction is typically of the order of the Fermi energy. Nonetheless, thanks to the magic of Fermi liquid theory, this strong interaction somehow only results in ...


0

Here is a partial answer that depends on a particular choice of local gauge constraint. In a U(1) gauge theory, the usual gauge constraint is just Gauss' Law, $$ \nabla \cdot \mathbf{E} = \rho. $$ This in turn implies Coulomb's Law $\mathbf{E} \sim 1/r$ for the electric field surrounding a deconfined point charge. Such a long-range interaction ought to be ...


4

Usually, when talking of the "band structure" of such a system one either refers to the non-interacting band structure (which relates to the free Green functions occuring in many methods to handle the interactions, like perturbation expansions or DMFT), or to the sharp features usually visible in the spectral function (which is more or less experimentally ...


0

Yes, the ions carry charge. However, the substrate is grounded so that current flows to keep the substrate neutral (and to measure the implanted dose). Otherwise a potential would rapidly build up (possibly up to the accelerating potential), changing the implant profile and/or causing arcing. (As an aside, this causes some difficulties when implanting or ...


1

Is the existence of deconfined gauge charges a sufficient condition to ensure gaplessness? I think the answer is NO, such as the $Z_2$ gauge theory in 2+1D and 3+1D. I believe that the existence of deconfined gauge charges of a continuous gauge group is a sufficient condition to ensure gaplessness? Hastings and I have a paper ...


1

In the continuum limit the lattice spacing $a$ goes to zero, therefore the Brillouin zone grows to infinity. If the Fermi velocity shall remain constant, the hopping parameter has to be rescaled as $t \propto 1/a$ (remember that the bandwidth is on the scale of $t$ and $v_F = \nabla_k E(\vec k)$), therefore only the features close to the Dirac points remain ...


-1

I'm not sure if I can help you on the part concerning the Weyl fermions. But your question seems to deal rather with what is a geometrical phase. Parallel transport and geometrical phase Maybe the more intuitive thing to do first is to draw a parallel between geometrical phase and parallel transport. As shown in the image of this wikipedia article, ...


2

First of all, the expression for the magnetic length that you give is wrong: there is a square root missing: $l_B=\sqrt{\frac{\hbar c}{eB}}$. Secondly, to understand the meaning, you don't really need to think about lattices or phases of the electron wavefunction as the previous answers would have it. Instead, begin by thinking about a motion of a classical ...


0

There are a bunch of subtleties about the measurements and the conditions that define an “ideal” measurement. But here is the basic idea. One of the most common measurement geometries is the "Hall bar" geometry. See Fig 4 here: http://www.sp.phy.cam.ac.uk/research/fundamentals-of-low-dimensional-semiconductor-systems/lowD Ideally, the source and the ...


1

I highly recommend Richard D. Mattuck A Guide to Feynman Diagrams in the Many-Body Problem. You can read some pages here. It's a very surface level introduction, but the first 3 or so chapters are presented at what he calls a "kindergarten" level so you shouldn't have any problems understanding it. However, the last part is most definitely not ...


1

There are many resources on many-body Green's functions (propagators) both on-line and in print. You may want to search "quantum field methods in many-particle systems" or "quantum field methods for condensed matter systems" or variations thereof. In any case, I personally recommend the oldie-but-goodie book by Fetter and Walecka, Quantum Theory of ...


2

Fundamentally it is that the $1/N!$ for the classical system only correctly compensates for overcounting of indistinguishable states if the particles are always in different states. For a system of Bosons at low temperature, where it is quite likely that many particles are in the same state, this breaks down. For a very understandable introduction to this ...


1

Every phase transition has an order parameter: something that vanishes above the transition temperature and is finite below. In superconductors, the order parameter is a complex quantity related to the superconducting gap: $\Delta = |\Delta| e^{i \phi}$. In BCS theory, there is a self-consistent equation for the gap: $\Delta_k = -\sum_q V_{kq} ...


3

In condensed matter "bulk" does not refer to the dimensionality of the problem but the location in the material. It refers to the volume of the crystal, as opposed to, e.g., surface effects. Many organic conductors behave as 1D systems, yet you can talk about bulk properties. Copper oxide superconductors have a 2D physics. However, often you will find ...


1

Does this mean that there are two different fields, one static field and one induced by a laser? Yes, that is exactly right. There is a static (meaning not time dependent) electric field $\vec{E}_\text{static}$ $(*)$ and there is also a time-varying electric field $\vec{E}_\text{laser}$ from the laser. Since we are told the laser field is linearly ...


0

Previous discussions were all performed at the quantum mechanical level. However, the same question can obviously be asked about classical systems. For example, can the viscosity of liquids (e.g. water) arise solely from the interactions between the constituents? The answer could be found in Boltzmann's transport theory. Clearly, if only that type of ...



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