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I think OP's question is about the p-h symmetry in BdG equation of superconductivity. This is really an exact p-h symmetry (in mathematics), but it is however a redundancy of description. Since it doubles the degree of freedom.


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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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A simple way to see this is that due to the Meissner effect the magnetic field is expelled from the superconductor and field lines are deformed around the SC. Depending on the geometry of the superconductor the "density" of field lines on his surface is generally higher than the "density" of field lines away from the superconductor. This lead to an effective ...


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The principle behind STT is conservation of total angular momentum of the system. The equation that describes spin dynamics is called the LLG equation, named after Landau, Lifshitz and Gilbert. I will try to illustrate its physical meaning by using a general example. Consider an s-d model, where the sp-band electrons are itinerant and thus contribute to ...


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Under the substitution ℏk→ℏk−qA $ <p|x>=<0| a_{p} a_{x}^{+}|0>=exp(-ipx/ h) $ will become $ <p|x>=<0| a_{p} a_{x}^{+}|0>=exp(-i(p-qA)x/ h) $ effectively, the change in operator: $ a_{p} a_{x}^{+} \rightarrow a_{p} a_{x}^{+} e^{iqAx/h} $ Then it looks as if: $ a_{x}^{+} \rightarrow a_{x}^{+} e^{iqAx/h} $ $ ...


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On the deformation, I yet not know but the order is kept (see bellow). *GLASSY LIQUID-CRYSTALS - OBSERVATION OF A QUENCHED TWISTED NEMATIC Por: KESSLER, JO; RAYNES, EP PHYSICS LETTERS A Volume: A 50 Edição: 5 Páginas: 335-336 Publicado: 1974 * Stripe patterns in the magnetic reorientation of a glass-forming nematic liquid crystal Por: Grigutsch, M; ...


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I think a good introduction are these two talks: Roman Jackiw: "Fractional charge, Majorana fermions: the Physics of isolated zero modes" - 1 and Fabian Hassler Lecture 1: Topological quantum computing A short summary is that for 1D systems Majorana bound states can exist at domain walls. Let say you have a long wire and you can divide it in two ...


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In the Hall effect, the edge modes that possess an anomaly are connected to the bulk in such a way that the total system is gauge invariant and and has a conserved current. The Bardeen Zumino consistancy conditions arise from considering the current $J_{\mu {\rm consistent}}$ as the functional derivative with respect to $A_\mu$ of the edge effective action ...


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The film on the surface of the beaker forms by condensation from the saturated vapor above the helium bath. This, by itself, has nothing to do with superfluidity. What is speacial about superfluids is that the film, even though it is only a few dozen atomic layers thick, provides a capillary that the superfluid can flow through without resistance.


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There is an important distinction here which I feel the other answers have not addressed. One can check that the unitary $U$ as given in the question is indeed symmetric in the sense that $[U,W(g)] = 0$, where $W(g)$ is the representation of the symmetry. It is also a local unitary, in the sense that one can find a local (possibly time-dependent) Hamiltonian ...


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In superfluid helium-4, the phonon excitation spectrum includes a mode which has the same energy and momentum as a neutron with a speed of about 440 m/s (wavelength $\lambda \approx 9\,Å$). You can create a neutron beam which contains only 9 Å neutrons by starting with cold neutrons and being clever with diffraction from crystals. If you send these ...


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The Hamiltonian is given by \begin{equation} H=\frac{\mathbf{p}^2}{2m}+U\left(\mathbf{r}\right), \end{equation} where $U\left(\mathbf{r}\right)$ is the potential landscape due to the crystal lattice. The Bloch theorem asserts that the solution to the problem \begin{equation} H\Psi_{\mathbf{k}}=E\left(\mathbf{k}\right)\Psi_{\mathbf{k}}, \end{equation} is to ...


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Given that the title of the paper mentions valley contrasting physics, in the two cited paragraphs the authors try to motivate such a notion from basic principles, before delving into details. First they say that if a valley contrasting magnetic moment is to exist, it must be expressible in the form ${\frak m}=\chi\tau$ (where $\chi$ is an irrelevant ...


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I don't know nearly enough QFT to address the background or implications of your question. However, I'd basically answer yes to your first two questions, but it depends a little on your definition. A single phonon mode is not localized in space. However a wave packet can in principle be built up of a small range of frequencies, giving a fairly well defined ...


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Now I know why the Logarithmic discretization are take place in Anderson Model for low temperatures. We want to discretize the energy band-width $[-D,D]$ such that we can perform a numerical calculation. But we want to answering questions of low temperature, and we need to have very careful to apply the thermodynamic limit $N\rightarrow \infty$ before the ...


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They are two different things. "Springyness" is called elasticity. This is described by a modulus of elasticity, also for elongation called Young's modulus $Y$. Looking at a stress-strain curve [source] as below, the elasticity is the slope of the straight line in the elastic region. If you are not familiar with a stress-strain curve, consider it as a ...


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It is correct that if you proceed the way you describe it, you obtain a 4-local parent Hamiltonian $H=\sum h$, where $h\ge0$, and $h\vert\Psi\rangle=0$, where $\vert\Psi\rangle$ is the AKLT state. For a parent Hamiltonian constructed this way, one can show (for an arbitrary injective MPS) that the ground state is unique with a gap above. However, if you ...


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To understand what is going on, you need to understand something called unitarity. Unitarity basically just says that anything that can happen in forwards in time can also happen backwards in time. So in this case, unitarity means that if the particle can go from $\Psi_0$ to $\Psi_1$, then it can also go from $\Psi_1$ to $\Psi_0$. Now what does that have to ...


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I am not too familiar with KT transitions yet, but I would like to learn about them myself. I have read in the notes of Prof. Jensen (available online http://www.mit.edu/~levitov/8.334/notes/XYnotes1.pdf) in the end of chapter 4.2 that the divergence in the specific heat is so fast that it is experimentally not observable. Analytically (according to his ...


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If you are interested what happens in the energy spectrum, then this two papers could be very helpful for you: arXiv:1206.1736 and arXiv:1205.7054. The spin-orbit coupling splits the two spin bands (see in arXiv:1206.1736 Fig. 5a) and the Zeeman term mix them (see in arXiv:1206.1736 Fig. 5b). This looks then in the end like a p-wave pairing in the ...


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Angular momentum operator in quantum mechanics is defined as: $$\hat{L}=-i\hbar[r\times\nabla]$$ You just need to insert this definition of $\hat{L}$ to $\langle \psi|\hat{L}|\psi\rangle$ (or integral) to calculate. You need to use the integral form for the average of $\hat{L}$ and use numerical methods to evaluate. Also, angular momentum is not of the ...


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The definition in terms of LU transformations is more fundamental. In the general case, we believe that topological orders are described by modular tensor categories (MTC), and the equivalence of topological orders translates into the equivalence of MTCs. In the special case of boundary-gapped topological orders, they are all realized by quantum double (also ...


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It depends on what kind of pairing you are willing to include in the Hamiltonian. If only s-wave singlet pairing is present, and there is no spin-orbit coupling, the Hamiltonian has an additional $\mathrm{U}(1)$ symmetry (spin rotation around the direction of the Zeeman field), so falls into class A in the table. A bigger issue is that if $\alpha=0$, with ...



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