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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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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1answer
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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
$$ \hbar\nu_1=\hbar\nu_0\...
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25 views
Long-ranged Coulomb Interaction $\Rightarrow$ Longitudinal Plasmon Modes?
I am currently taking a lecture on quantum theory of condesed matter systems. In the lecture notes it is stated that
For long-ranged Coulomb interactions only longitudinal plasmon modes are ...
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43 views
Can we consider oscillation of air column in the wind instruments as phonons subject to Bose- Einstein statistics ?
A flute is a wind instrument, which could be modelled as a resonance cylinder open at both ends. Any cylinder resonates at multiple frequencies. A skilful player produces a standing wave in the flute ...
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1answer
204 views
Why the chemical potential of phonon gas in Einstein 's solid model is not zero
In Einstein’s model of solid, each atom in the solid is considered to be an independent three-dimensional quantum harmonic oscillator with characteristic frequency $ω$ that is constant. Each degree of ...
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51 views
Understanding what the Bose-Einstein distribution
I'm currently studying Kittel's Solid State Physics and in his chapter on Phonon heat capacity, we need to first calculate the total energy $U$. Phonons have energy $E_n = (n+1/2)\hbar\omega$ and he ...
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29 views
Understanding the technical bits of quantising elastic waves
I'm reading Kittel's Solid State book and I have a number of 'simple-ish' questions regarding phonons. He starts with the hamiltonian
$$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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81 views
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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1answer
91 views
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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119 views
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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38 views
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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1answer
59 views
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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2answers
88 views
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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51 views
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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Action of phonon creation/annihilation operator on negative momentum states
The phonon-phonon scattering amplitude through the cubic interaction for a one dimensional phonon system is proportional to:
$$
\tau\propto \langle n'|\color{red}{[a^\dagger(q)+a(-q)]}\color{blue}{[a^\...
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1answer
132 views
How many types of phonons are there, and what are their characteristics?
I've skimmed through Wikipedia's article, as well as as PSE question What is a phonon?, but I am still entirely left in confusion as to the types of phonons and their corresponding characteristics and ...
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93 views
Pauli principle for “Phonons”
I'm reading in Feynman's "Statistical Mechanics" Chap. 6.4 about a system of $M$ interacting particles, they may be bosons or fermions. Let the hamiltonian be
$$ H=\sum_i^{3M}p_i^2+\sum_{ij}^{3M}U_{...
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63 views
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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113 views
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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47 views
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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3answers
63 views
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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28 views
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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38 views
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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38 views
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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1answer
19 views
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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27 views
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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91 views
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 ...
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2answers
102 views
What does phonon mediated absorption of photon to excite electron from valence band to conduction band mean?
What does phonon mediated absorption from valence band to conduction band mean ?
Suppose we have an indirect band gap semiconductor. The excitation of an electron from valence band to conduction band ...
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49 views
electron phonon scaterring rate calculation
The scattering rate by emission of phonon is given by following formula;
$$\frac{1}{\tau_{emi}}\propto\int_0^{\omega_{max}}d\omega\ \omega^2[n_B(\omega)+1]\propto T \ for\ 1>>\beta\hbar\omega\ \...
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142 views
Are phonons eigenstates of the momentum operator?
In the case of electrons in a periodic potential it can be demonstrated that the eigenstates of the Hamiltonian containing the periodic potential are the Bloch functions:
$$\Psi_{n \mathbf{k}}(\mathbf{...
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Elastic scattering mechanism in solids: Mott versus Phonon
I read from many papers that phonon scattering is dominant for low energy electrons (<100 eV) and Mott scattering is dominant for high energy electrons.
1) As far as I understood, they are ...
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176 views
Why do electrons emit phonons instead of photons?
Why do electrons emit phonons when they "relax" into the minimum energy level of the conduction band after getting into it from the valence band by absorbing a photon with an energy higher than their ...
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1answer
127 views
Connection between the 'spin' and 'polarization' of relativistic and non-relativistic particles
Context 1 The spin $s$ of a relativistic particle of mass $m$ can be read off from the eigenvalue $s(s+1)$ of the operator $-
\frac{W_\mu W^\mu}{m^2}$ in the rest frame of the particle where $W^\mu=\...
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1answer
78 views
Obtaining the phonon Hamiltonian
I am currently following Ashcroft's Solid State Physics. In Appendix L, he proceeds to show how to derive the phonon Hamiltonian
$$
H=\sum\hbar\omega_s(k)(a_{ks}^{\dagger}a_{ks}+1/2)
$$
where
$$
...
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36 views
Interaction between lattice displacement waves with different polarization for harmonic crystals
I'm studying the classical theory of harmonic crystals and I don't understand a step in the derivation.
Let $\vec u_{s,\vec R}$ be the displacement from the equilibrium position of the basis atom $s$ ...
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1answer
411 views
Why does a phonon obey the Bose statistic?
Could somebody please explain why the phonon must be a Boson (strictly speaking, it must obey the Bose statistic) regardless what it is composed of? (As I have heard, the lattice vibration of both ...
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169 views
How can phonons possibly be assigned precise locations?
I was reading through this paper on thermal transport in crystals, and saw that a primary function of their interest was $n_{\mu}(\mathbf{x},t)$, which they state is the phonon excitation/occupation ...
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51 views
How to calculate the permitted resultant states of 3 quadrupole phonons ($\ell=2$)?
How do i get the permitted resultant states of 3 quadrupole phonons ($\ell=2$)?
I think im supposed to somehow tabulate the $m$ states.
Can anyone help?
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295 views
Is there a “Planck's constant” equivalent for phonons, sound particles
As per de Broglie's Law, every wave has a particle nature associated with it. I tried to find what sound particles are called, and I got that they are phonons.
Now, I am curious about what it's ...
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What's the meaning of chemical potential of photons or phonons?
The chemical potential of photons or phonons vanishes due to their particle number not conserved, I don't understand it very well. So can you expain what's the meaning of chemical potential of them ...
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40 views
For 1D linear chain. Why does the vibration of atom at na, u(0) is equal to it at Na, u(Na)
For 1D linear chain, a is the lattice constant, u is the displacement of every atom from the equilibrium. N is the total number of atom
the boundary condition is u(0)=u(Na)
but my question is why? ...
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1answer
83 views
Why does this indicate a phonon?
In the very cool LaTeX package svrsymbols, the authors associate a phonon with the following symbol:
Why is this iconography appropriate for a phonon?
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150 views
“Dynamically Stable” vs. “Elastically Stable”?
I am studying a group of materials using density functional theory. I am able to calculate elastic constants, phonon densities of states, and formation energies. The results imply that the materials ...
