Hot answers tagged

4

It is definitely a Kronecker sum. Take the case where there are only two different states $+$ and $-$, then, for example, $$ \hat H =E_+ \hat a^\dagger_+ \hat a_++E_- \hat a^\dagger_- \hat a_- .$$ What does $\hat a_+$ means ? Well, if we label the states with the number of excitations in the states $+$ and $-$ by $|n_+,n_-\rangle$, then we understand $\hat ...


4

It's a good question and I don't think there is a simple way of seeing it from the action. I just checked Fradkin (section 7.7 and 7.8) and through an RG analysis he shows that any half-integer spin behaves the same as the spin-$\frac{1}{2}$ case. But for the latter he then refers to the exact Bethe ansatz solution to show it is gapless! However, I wanted ...


2

The torque exerted by $\vec B$ is perpendicular to it, so the $z$ component of angular momentum is conserved.


2

Chiral $p$-wave superconductor and He A phase can be considered being equivalent phases of matter, for the following reason: The fact that the superconductor is charged does not make too much difference in this regard, because it only affects the electromagnetic response (one has Meissner effect, the other does not), but electromagnetic field is an external ...


2

Sputtering deposition is not normally preformed at ultra high vacuum pressures, thus the films tend to be polycrystalline while e-beam evaporated metal films could be done at much lower pressures resulting in a more uniform film, even single crystalline depending on other conditions like the substrate, lattice mismatch and so on. This is just one difference. ...


2

Glass is a typical amorphous solid. Amorphous materials typically show no melting point but do have a Glass Transition Point ($T_g$). Below it, the material behaves like a solid, with a glass-like fracture surface when fractured. Typical amorphous materials include several types of elastomer (rubber) like natural rubber (NR), with a $T_g$ of around ...


2

The criterion for the Fermi liquid theory to be justified is that the imaginary part of the self-energy must be vanishingly small around the Fermi surface (both in the energy scale and in the momentum deviation). $$-2\Im\Sigma_\text{el}(k,\omega)\to 0\text{ as }k\to k_F\text{ and }\omega\to 0.$$ The broadening of the quasi-particle peak in the spectral ...


2

It depends a little on what you mean by "extreme" electric current, but the answer is probably no. The energy scales are wrong. Electric current in a metal is a sub-electron-volt process: a potential difference of much less than a volt can displace electrons all the way through a piece of metal. The weak interaction is a keV- or MeV-scale process. And ...


1

I'll start by saying that correctly stating Kirchhoff's law is quite tricky. "Emissivity equals absorptivity" in a certain sense, but they may depend on wavelength, and angle of incidence (or emission), and polarization. In magneto-optic materials, you can have high absorptivity from one direction balancing high emissivity into a different direction!! (This ...


1

The ratio of emissive power to the absorbitity is constant when the substance is at thermal equilibrium with surrounding. Or The emissive power of a substance is equal to its absorbtivity under the same conditions.


1

I don't think we need Sokhotski-Plemelj for this. Think of $E_j - E_i$ as a fixed value $E$. Then the formula is re-written as $$\frac{\hbar \omega}{E - \hbar \omega - i \eta}\, .$$ Now let $x \equiv \hbar \omega$ and you get $$\frac{x}{E -x - i \eta} \, .$$ This integral is dominated by the part where $x \approx E$ so let's try shifting the variables $y ...


1

Noting the simple relation $$ \frac{\Delta E_{i,j}}{\Delta E_{i,j}-\hbar\omega-i\eta}-\frac{\Delta E_{i,j}-\hbar\omega-i\eta}{\Delta E_{i,j}-\hbar\omega-i\eta}=\frac{\hbar\omega+i\eta}{\Delta E_{i,j}-\hbar\omega-i\eta} $$ and by Sokhotski-Plemelj theorem $$ \lim_{\eta\rightarrow 0^+} \frac{i\eta}{\Delta E_{i,j}-\hbar\omega-i\eta}=0 $$ because, if the limit ...


1

Confinement is usually discussed in the context of gauge theories. Here you do not have any specific information about the properties of the insulator, so it is not clear why you put "confined states" and "localized states" on the same footing. Insulating states must have a gap for charge carriers. The gap can come in two types: 1) in a clean system, or ...



Only top voted, non community-wiki answers of a minimum length are eligible