Questions tagged [density-of-states]
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questions
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Degeneracy in linear tetrahedron method
In the linear tetrahedron method for the calculation of density of states, how does one circumnavigate the infinity error that would arise if two or more k-vertices of the tetrahedron have the same ...
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1answer
46 views
Motivation behind definition of density of state
The definition of density of state per unit volume stated in Girvin and Yang's Modern Condensed Matter Physics is $$\rho(E)=\int \frac{d^3k'}{(2\pi)^3} \delta(E-E')$$
I would like to gain more ...
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1answer
27 views
Is the number of spin states necessary in the density of states function?
I'm studying how to calculate the density of states in the final configuration in order to apply Fermi golden rule.
For free EM field the following expression is the starting point:
$$d^3n=\frac V {(2\...
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11 views
Density of States of electrons with tight binding and a Zeeman term in the Hamiltonian
Should density of states for electrons always be symmetric?
The Hamiltonian I am considering is:
$$
H= \Sigma_{<i,j>,\sigma} -t(C^{\dagger}_{i\sigma}C_{j\sigma}+ C^{\dagger}_{j\sigma}C_{i\sigma})...
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Show that the effective carrier density for electrons is $2\left(\frac{{m_c}^*k_BT}{2\pi\hbar^2}\right)^{3/2}$ [closed]
The 3-dimensional free electron density of states (DOS) including spin degeneracy is:
$$g(E)=\frac{1}{2\pi^2}\left(\frac{2m_e}{\hbar^2}\right)^{3/2}\sqrt{E}$$ where $m_e$ is the electron mass, and $E$ ...
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42 views
Density of States
For getting the density of states formula for photons, we simply multiply the density of states for atoms by 2 (due to two spins of photons).
I am getting the 2D density of states formula as :-
g(p)dp ...
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2answers
68 views
Generalisation of the density states of phonons
Is it possible to generalize de density of states for phonons $\left( \left(\frac{L}{2\pi} \right )^3 \int \frac{dS_\omega}{v_g}\right)$ to a density of states which is also applicable to Bloch ...
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45 views
Density of states: Debye phonons vs free electons
In the Debeye approximation the density of states goes with phonon-energy^2, while the density of states for free electrons goes with sqrt(energy of the electrons), why is that?
(I use Introduction ...
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42 views
Density of States (DOS) to energy graph
I am trying to find the amount of electrons in a conduction band in Si (Silicon), all I've got is a graph similar to this one:
I've tried to integrate like this:
$$ N = \int_{1}^{\infty} \frac{1}{1+\...
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27 views
2 different density of states for Graphene and Bismuth Selenide
I will solve the problem below by $1)$ working in reciprocal (wavenumber space) and in $2)$ energy space ($\epsilon$). But first some contextual background:
Graphene is a single sheet of carbon ...
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87 views
Phonon density of states
How can I easily calculate phonon density of states from phonon dispersion? I want to compare DOS of graphene and Si from phonon dispersion. Is there a better alternative to Debye DOS = $\frac{w^2}{2\...
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1answer
28 views
$dE$ stands in my way to know the density of states in bulk crystal, how to get rid of it?
In a book about semiconductors, I found the following formula for the density of states:
$$D(E)dE=\frac{(2m)^{3/2}E^{1/2}}{2\pi^2\hbar^2}dE. \tag{1}$$
In that book, the important lesson from this ...
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30 views
Density of states for free electron in one-dimension
I am trying to find the density of states of a free electron in one-dimension.
I know that the result is given by $D(\epsilon) = 2 \frac{dn}{d\epsilon}$. However, I am unsure where this factor of 2 ...
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66 views
Inaccuracies of an energy level's degeneracy
I know that the inaccuracy is negligible but I'm trying to understand how it can be considered negligible in more detail.
The formula for the discrete energy levels in a box with equal dimensions $L$ ...
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90 views
Physical explanation of temperature dependence of chemical potential
I have recently started my first course on statistical mechanics and have been learning about the Fermion gas.
I was calculating the temperature dependence of chemical potential for an electron gas ...
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11 views
Can you add the density of states of two mono-atomic gases?
Say I have a system of 2 gases with $N_1$ and $N_2$ particles, each with respective masses $m_1$ and $m_2$. Would I be able to find the density of states for this system of two mixed gases $p(E)$ by ...
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What is the difference between the joint density of states and the density of state?
I think I understood the density of states, but I didn't understand the joint DOS. What is the main difference? What is the exact definition of the joint DOS?
When do we use the joint DOS and when do ...
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75 views
Van Hove singularity (calculating the logarithm)
I am trying for hours to understand this calculation, I hope someone can help me with it. In the paper of Van Hove himself (https://journals.aps.org/pr/abstract/10.1103/PhysRev.89.1189) he derived the ...
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1answer
40 views
Periodicity of density of states with decreasing dimension
In my lecture notes, there is the following graphic:
With the 3D "bulk" configuration, there is clearly a $1/2$ power law, which I am able to explain by myself just by deriving the density of states ...
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1answer
128 views
Where does the Density of States come from?
There is an existing question here, which asks about the propagator for a free particle and the difference in its form when expressed as an integral over $p$ or over $E$. The accepted answer points to ...
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1answer
51 views
Number density of phonons in superfluid
I'm reading Superfluidity and Superconductivity by Tilley & Tilley. In section 2.4, the argument is made that the normal component of superfluid helium consists of phonons and rotons. The ...
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1answer
50 views
Density of States for a quantum well: Derivation?
Consider a quantum well, where we have:
$E_{k_x,k_y,n_z}=\frac{\hslash^2k_x^2}{2m}+\frac{\hslash^2k_y^2}{2m}+f(n_z)$
with $k_x$ and $k_y$ having widths of $\frac{2\pi}{L}$ and $n_z$ varing in ...
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What are the meaning of the $s$, $p$, $d$ orbital contributions in partial density of states?
Lets say I have pDOS of Na, K or Al. Integrating total DOS for the last energy interval until Fermi level gives number of valence electrons for corresponding metal. That's also okay. My question is, ...
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1answer
210 views
Density of states in irregularly-shaped volumes
A very common result is that the density of momentum states in a cubic volume is $\displaystyle\frac{V}{(2\pi\hbar)^3}$ in momentum space. How does this result extend to arbitrary volumes? Are there ...
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41 views
Where does the superconducting density of states come from?
I'm going through Tinkham (2nd edition) and in section 3.7.1 he makes a claim which seems quite weird:
$N_n(\xi)$ is the Normal density of states (normal mode), so how would it be that the density of ...
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1answer
70 views
Find the density of states of a bouncing ball
Imagine a ball falling from a maximum height of $h$ and colliding with the ground at $z=0$. The ball only moves in the z-axis and the collisions are elastic. My job is to show that the density of ...
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1answer
48 views
Derivation of density of states (free electrons)
I am reading Condensed matter physics from M.Marder.
This is the derivation for the density of states for free electrons.
$\begin{aligned} D(\mathcal{E}) &=\int[d \vec{k}] \delta\left(\mathcal{E}...
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22 views
Validity of formula for density of states for free electron gas
I believe the formula for density of states given by $\frac{\hbar^2}{2m}{(\frac{3\pi^2N}{V})}^{\frac{2}{3}}$ is a good approximation to actual count only when $E_f$ is much larger than energies given ...
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41 views
Calculating density of state from a certain dispersion relation analytically
This used to be a really frustrating question when I was taking the solid state physics. It is still a knotty one for me now. I wish to figure it out completely.
If one reads the definitions or ...
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19 views
What is a pseudo wave and how to calculate it?
In a description of the density of states in
https://wiki.fysik.dtu.dk/gpaw/documentation/pdos/pdos.html
I find the term pseudo (partial) wave (in the section Molecular Orbital PDOS). What is it and ...
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2answers
127 views
Density Of states derivation
In the aspect of density of state derivation or simply assuming the frequency of a solid as a continuous distribution we have to come up with an equation expressing the density of states. Its derived ...
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32 views
Density of states LL in graphene [closed]
I am using the Kernel Polynomial Method to determine the spectral density of a 2DEG system that has been sujected to a perpendicular magnetic field B.
I wish to determine
(a) What the amplitudes of ...
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94 views
1D density of states help
I am given a 1D band whose energy is $$E(k)=E_0-t\cos(ak)$$
Then I have to compute the DOS relative to that band. Here is my calculation: $$g(E)=\dfrac{1}{L}\dfrac{dN}{dk}\dfrac{dk}{dE}$$ where $\...
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1answer
61 views
Density of states for fermions for temperatures other than absolute zero
Let's say I wanted to calculate the density of states for $\mathrm{2D}$ Fermions with an energy dispersion of $E_F=ck^6$ at $T=0$
The process would be quite mathematically simple. I'd take the ...
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37 views
Density of states, $\pi$ vs $2\pi$ [duplicate]
When calculating density of states for an electron, some arrive that k (the wavenumber) is $2\pi n x /L $ and some say it is $\pi n x /L$?
Where L is the dimension of the well
I’ve heard vague ...
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1answer
103 views
Confusion about average KE in free electron model via Density of States (DOS)
Assume a low temperature regime in which levels up to the Fermi Level, $E_F$, are populated.
I have evaluated the density of states in energy space as $$D(E)=\frac{L^3}{\pi^2\hbar^3}(2m_e^2E)^{1/2},$...
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1answer
70 views
Whats the function of density of states equation?
There was a question in Statistical Mechanics 3rd ed by RK Pathria and PD Beale, section 3.8, asking to show that the harmonic oscillator obeys the equipartition theorem. It was well proven. But at ...
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Why do the $C_v$ of gapless systems have a power law behaviour?
The functional dependence of the heat capacity $C_v$ of systems with gapless excitations (e.g., lattice with acoustic phonons, Heisenberg ferromagnet with spin waves etc) is like a power law $$C_v\sim ...
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Distribution of photons emitted by atoms
I am currently revising quantum gases, and a small but confusing thought experiment has been bugging me for a while.
I understand the bookwork stuff on photons and how a photon gas in a blackbody ...
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1answer
204 views
Why phonon density of state depends on velocity autocorrelation?
We know that if we take the Fourier Transformation of velocity autocorrelation function, we will get the phonon density of state. But why phonon density of state depends on this? What is the physical ...
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41 views
What is the density of states $SiO_2$?
We build the model by the finite element method. In our model here is silicon dioxide (SiO2). To carry out calculations, it is necessary to know the density of states and the effective mass.
Question:...
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Density of states for a tight binding model
So we have been given a dispersion relation of the form:
$$
E=6-2(\cos k_xa+\cos k_ya)
$$
and asked to calculate the density of states.
The equation for the density of states is (eq 2.48 from here ...
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2answers
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Is the DOS (density of states) wrong for degenerated case?
The density of states (DOS) is defined as $$\mathcal{N}\left(\lambda\right)=\sum_{n=1}^{M}\delta\left(\lambda-\lambda_{n}\right).$$ We can then get
$$\int d\lambda\mathcal{N}\left(\lambda\right)=M,$$ ...
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1answer
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Problem with finding the density of states of an $N$-body system
I am having problems solving a particular problem in my Statistical Mechanics course.
We have a system that is composed of $N$ non-interacting particles each of mass $m$.
The particles are bound to ...
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1answer
41 views
Is this equation for the density of states of an elastic isotropic material an approximation?
The density of states of phonons can be calculated with
$$
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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2answers
102 views
Deriving density of states in different dimensions in k space
The results for deriving the density of states in different dimensions is as follows:
3D: $g(k)dk = 1/(2\pi)^3 4 \pi k^2 dk$
2D: $g(k)dk = 1/(2\pi)^2 2 \pi k dk$
1D: $g(k)dk = 1/(2\pi) 2 dk$
I get ...
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251 views
Density of states of bosons in function of momentum with energy $\epsilon = cp$
I am working out an average number N of bosons of spin $S = 0$ connected to a two-dimensional domain with surface A. The gas is ultrarelativistic with a single particle energy $\epsilon = cp$.
The ...
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1answer
2k views
Getting the density of states for photons
I know that the density of states $g(\epsilon)d\epsilon$ is the number of states in the energy range $[\epsilon, \epsilon + d\epsilon]$.
I considered a system of non-interacting free photons in 3 ...
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When can we say $x$ and $p$ are “independent variable”, in order to find the Vlasov equation?
I have a question about "independent variable" in physics, and especially variable in Lagrangian or Density Function. I read several questions about it in this forum and although I have the feeling I ...
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184 views
Density of states as a function of dimension: what happens between 3D and 4D?
Consider a parabolic dispersion $\varepsilon_{\boldsymbol q} = \frac{\boldsymbol |q|^2}{2m}$.
The two-particle density of states $\rho_2(\boldsymbol k, \varepsilon)$ is zero for $\varepsilon < \...
