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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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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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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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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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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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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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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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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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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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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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