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Questions tagged [phonons]

Collective excitations in periodic, elastic arrangements of atoms or molecules in condensed matter, like solids and some liquids. They are quasiparticle quantum modes of vibration of elastic structures of interacting particles.

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Why isn't the dispersion of the phonon spectrum of two atomic basis with equal masses the same as for the one atomic basis?

The solution for the two atomic basis is given by \begin{align*} \omega^{2}=\gamma\left(\frac{1}{M_{1}}+\frac{1}{M_{2}}\right) \pm \gamma\left[\left(\frac{1}{M_{1}}+\frac{1}{M_{2}}\right)^{2}-\frac{...
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Is it possible that gravitons don't exist, but are actually something like phonons? [on hold]

Why or why not? String theory says that gravity arises due to spin 2 closed strings. If gravitons were actually phonons, is it against the possibility that gravitons are actually closed strings? How ...
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Deriving effective interactions, e.g. phonon-mediated electron-electron interaction

Upshot of the question: how can I derive the effective electron-electron interaction brought about by the electron-phonon interaction? I've read derivations of the electron-phonon interaction and ...
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Why do purely harmonic interatomic interactions result in infinite thermal conductivity?

When interatomic interactions are purely harmonic, normal modes cannot interact, and therefore no phonon scattering occurs, thus resulting in infinite thermal conductivity. But why is anharmonicity ...
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Mossbauer effect: neglectable recoil or absolute no recoil?

I stumbled on the Mossbauer effect. From the wikipedia article, I cannot tell for sure if the momentum of recoil is really zero, or only neglectable. From what I do (think I) understand, the ...
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Should phonon energy be undefined at zero frequency?

The energy carried by phonons of frequency $\omega$ is given by $$ E = \hbar \omega n_b(\beta \hbar \omega) = \hbar \omega \frac{1}{exp(\beta \hbar \omega) - 1} $$ So when $\omega = 0 $, the energy ...
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The difference between optical phonons and acoustic phonons in terms of energy absorption

Why can the energy of a photon be directly absorbed by an optical phonon but not by an acoustic phonon?
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Heat capacity due to Phonon Vibrations

Why does the speed of sound come, in the expression of Heat capacity, from phonon vibrations?
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Calculate phonon density of states

I need to calculate phonon density of states for a cuprate superconductor. I know there is a general formula for the calculation of phonon density of states by Einstein models like this $$D(\omega)=(\...
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Optical and acoustic branch

Does a diatomic crystal posses both optical and acoustic branch simultaneously; Or, whether the vibration is either optical or acoustic?
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Why optical phonons are called “optical”? [duplicate]

In diatomic lattice vibration, acoustical phonons correspond to vibration. But I could not understand the relevance of term optical in this context.
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Vibrational Energy at T = 0 K using the Debye model

I mm trying to estimate the vibrational energy at $T=0$ for a 3-D lattice using the Debye model. My plan is to sum over all the frequencies using: $$U = \int_0^{\omega_D} d\omega D(\omega)\epsilon(...
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Approximations in article on phonon-assisted emission

I am trying to reproduce the calculations from an old article by J.J. Hopfield (J. Phys. Chem. Solids, vol.10, pp.110-119 (1959) - A theory of edge emission phenomena in CdS, ZnS and ZnO - found here)....
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Elastic X-ray diffraction: Where does the Photon Momentum go to?

lately I was discussing the following situation. Let's suppose you are doing X-Ray diffraction experiments on a crystal. So what you basically do is shooting a high energy photon with a wave vector $k$...
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Why phonon density of state depends on velocity autocorrelation?

We know that if we take the Fourier Transformation of velocity autocorrelation function, we will get the phonon density of state. But why phonon density of state depends on this? What is the physical ...
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Thermalizing bulk superconductors

I have been discussing with some friends whether or not (or how) bulk superconductors thermalize when placed in an environment far below their transition temperature. Suppose you have a cube of pure ...
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Derivation of the dynamical matrix

I am following a derivation of the dynamical matrix given at http://physik.uni-graz.at/~pep/Lehre/PP/DynMat.pdf. Here T and W are kinetic and potential energies. $T=\sum_{n\alpha i}\frac{M_{\alpha}}{...
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How does Bohmian Mechanics explain superconductivity?

I'm looking for sources that discuss how Bohmian Mechanics explains superconductivity. Are there still Cooper pairs? Phonons? I saw one vague reference to vortices, but no details. This is my first ...
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Is this equation for the density of states of an elastic isotropic material an approximation?

The density of states of phonons can be calculated with $$ Z(\omega)=\frac{V}{(2\pi)^3}\int_{\omega=\text{const}}\frac{d\vec{f}_\omega}{|\vec\nabla\omega|} $$ where $\omega$ is the phonon frequency ...
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Doppler shift in Acousto-Optic modulators

The interaction between a beam of light and an acoustic wave is commonly modelized as a photon-phonon scattering phenomenon. Applying the conservation of energy we have that $$ \hbar\nu_1=\hbar\nu_0\...
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Long-ranged Coulomb Interaction $\Rightarrow$ Longitudinal Plasmon Modes?

I am currently taking a lecture on quantum theory of condesed matter systems. In the lecture notes it is stated that For long-ranged Coulomb interactions only longitudinal plasmon modes are ...
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Can we consider oscillation of air column in the wind instruments as phonons subject to Bose- Einstein statistics ?

A flute is a wind instrument, which could be modelled as a resonance cylinder open at both ends. Any cylinder resonates at multiple frequencies. A skilful player produces a standing wave in the flute ...
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Why the chemical potential of phonon gas in Einstein 's solid model is not zero

In Einstein’s model of solid, each atom in the solid is considered to be an independent three-dimensional quantum harmonic oscillator with characteristic frequency $ω$ that is constant. Each degree of ...
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Understanding what the Bose-Einstein distribution

I'm currently studying Kittel's Solid State Physics and in his chapter on Phonon heat capacity, we need to first calculate the total energy $U$. Phonons have energy $E_n = (n+1/2)\hbar\omega$ and he ...
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Understanding the technical bits of quantising elastic waves

I'm reading Kittel's Solid State book and I have a number of 'simple-ish' questions regarding phonons. He starts with the hamiltonian $$H=\sum_{s=1}^N\left[\dfrac{1}{2M}p_s^2+\dfrac{1}{2}C(q_{s+1}-q_s)...
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Spontaneous symmetry breaking in fluids

BACKGROUND: One can think of solids as spontaneously breaking translational symmetries in the sense that each atom in a lattice has to pick a particular position. Yet, as with everything in our ...
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What is the phonon/lattice interaction?

To my understanding, phonons in solids are an excited state of a lattice, i.e., a lattice of atoms oscillate at a certain frequency. Phonons are quasipartices. But what should the phonon/lattice ...
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Debye Temperature for Copper

I am trying to calculate the Debye temperature, $\theta_D$, of copper using the following: $$ \theta_D = \frac{\hbar v_s}{k_B} \left( \frac{6\pi^2N}{V} \right)^{1/3} $$ I have the following values: $...
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Why does acoustic imepdance increase when mass density and bulk modulus increaes?

If we take some material and (somehow) increase its mass density or bulk modulus then its acoustic impedance will increase as $z = \sqrt{\rho \kappa}$. That is, it What is the physical reasoning ...
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Allowed k value for maximum and minimum phonon frequency in a diatomic lattice

I've got an expression for the phonon frequency in a diatomic lattice where the atoms are of mass $m$ and $5m$. The expression is $\omega^2=(12Cm\pm\sqrt{(144C^2m^2-20m^2C^2(1-\cos(ka)})))/(10m^2)$. I ...
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Can light cool down materials?

I was studying Raman scattering and I computed the probability of anti-Stokes scattering (with density of states n, at the numerator) over Stokes (n+1 at denominator). The densities are based on the ...
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In phonon theory, what is the physical significance of the force constants tensors?

I want to compute phase equilibria of crystalline solids using First-principle methods (DFT in particular). The methodology for this computation is described in this chapter. In order to calculate ...
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Can the periodicity in k-space of the electronic band structure be understood as a result of aliasing?

Discrete sampling in the case of phonons In the case of phonons in periodic solids, the picture is quite intuitive. The motion of the atoms in the lattice is described as a continuous wave (amplitude ...
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How many types of phonons are there, and what are their characteristics?

I've skimmed through Wikipedia's article, as well as as PSE question What is a phonon?, but I am still entirely left in confusion as to the types of phonons and their corresponding characteristics and ...
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Pauli principle for “Phonons”

I'm reading in Feynman's "Statistical Mechanics" Chap. 6.4 about a system of $M$ interacting particles, they may be bosons or fermions. Let the hamiltonian be $$ H=\sum_i^{3M}p_i^2+\sum_{ij}^{3M}U_{...
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Phonons to solve solid mechanics problems?

From what I understand, phonons can be used to solve acoustics or optics problems, but can we used phonons to solve a solid mechanics problem? The first answer I expect is :"Acoustics wave are solid ...
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In a material, how does the heat equation arise from phonons? And from electrons?

What would be the starting point to derive the heat equation in a material? Generally, in insulators the heat is mediated via phonons while in metals (conductors), electrons are the main responsible ...
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Phase-shifting by Acousto-Optic modulators

I am working on a project where I need to be able to introduce a phase-shift to a light pulse, without any mechanical parts involved. One of the options is to use an acousto-optic modulator: ...
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How do phonons impact the way heat is transferred between two solids?

If we assume that in a system heat is only transferred by conduction (between two different solid of different materials), what role do phonons play in this phenomenon?
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Perowskit: Why is oxygen moving “up”?

I have a question concerning the "Perowskit Structure". First of all, a displacement of positively and negatively charged ions happens. So far, so good. But why is oxygen considered to move upwards? ...
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Quasi-elastic electron-phonon scattering

When does electron-phonon interaction become quasi-elastic as opposed to inelastic and why does this happen at high temperatures? Also, which factors influence the temperature at which this crossover ...
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Misunderstood of wave-particle dualism? [duplicate]

Reading about dual nature of light, and atomic transitions, it seems to me, maybe wrongly, that the dual nature depends on the way we look at the phenomena. Suppose a water wave travels and reach ...
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D-peak of Raman Spectra of Graphite explanation

The D peak in the Raman Spectrum of Graphite is attributed to the breathing mode of $A_{1g)$ symmetry involving phonons near zone boundary. The explanation is the following: The change of bond ...
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Energy and momentum conservation argument for electron-phonon transitions in Bilayer Graphene

I'm reading a paper which says that the interband transitions ($\pi_1^* \rightarrow \pi_2^*$) involving phonons at $q= 0 $ and $ q = K$ in Bilayer Graphene are prohibited by energy and momentum ...
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Fourier transform to decouple pairwise interacting harmonic oscillators

To solve a Hamiltonian below $$H=\sum_{i}\frac{p^{2}_{i}}{2m_{i}}+\frac{1}{2}\sum_{j}k_{jj+1}(x_{j}-x_{j+1})^{2} $$ one can do fourier transform to decouple the harmonic oscillators. $$p_{m}=\sum_{q=1}...
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Solid State Phonons at the edge of Brillion zone

Bose-Einstein statistics tell us that the number of phonons with energy k at temperature T via the bose einstein distribution. My question is regarding phonons in the low energy regime. My notes ...
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Velocity changes due to crystal anharmonicity?

What is the effect of cubic and higher anharmonicities of a phonon hamiltonian on the velocity of phonons?
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Difference between Phonons and heat?

1, if these two were the different then how we differentiate with one another?. 2, if these two were the same, then what is really vibrating?, atom in the lattice or electron in the atom or the bond ...
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Lattice to continuum transformation in one dimension (arbitrary range interaction)

Please help me convert the ionic displacement $u_l$ of the $l^{th}$ ion to a continuous field $u'(y)$ in the following problem. I am trying to derive the Hamiltonian of a 1-D lattice (spacing $=n_0^{-...
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Beyond the frequency cutoff in Debye model

I understand when wavelength is smaller than the atom interval, sound waves can't travel; hence, we need a frequency cutoff in the Debye Model. But surely when it is the case, atoms are still ...