Questions tagged [density-of-states]
The density-of-states tag has no usage guidance.
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1answer
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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 $$D(E)=\frac{L^3}{\pi^2\hbar^3}(2m_e^2E)^{1/2},$...
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0answers
35 views
Density of state $g(e)$ Bose-Einstein Condensation system [closed]
Consider Bose-Einstein condensation of a hypothetical system consisting of N boson particles.
The energy of single-particle states is e= eo n^2, where eo is the energy of the ground state and n = 1, ...
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1answer
53 views
Whats the function of density of states equation?
There was a question in Statistical Mechanics 3rd ed by RK Pathria and PD Beale, section 3.8, asking to show that the harmonic oscillator obeys the equipartition theorem. It was well proven. But at ...
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0answers
20 views
Calculate phonon density of states
I need to calculate phonon density of states for a cuprate superconductor. I know there is a general formula for the calculation of phonon density of states by Einstein models like this
$$D(\omega)=(\...
3
votes
0answers
42 views
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 $$C_v\sim ...
1
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0answers
23 views
Distribution of photons emitted by atoms
I am currently revising quantum gases, and a small but confusing thought experiment has been bugging me for a while.
I understand the bookwork stuff on photons and how a photon gas in a blackbody ...
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0answers
32 views
Weighted histogram analysis method (WHAM) equations
I am struggling in deriving the WHAM equations. Among others, I follow this paper by Kumar et al. In the appendix, in eq. 24 they write the density of states as a weighted sum over the "measured" ...
2
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1answer
57 views
Why phonon density of state depends on velocity autocorrelation?
We know that if we take the Fourier Transformation of velocity autocorrelation function, we will get the phonon density of state. But why phonon density of state depends on this? What is the physical ...
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33 views
What is the density of states $SiO_2$?
We build the model by the finite element method. In our model here is silicon dioxide (SiO2). To carry out calculations, it is necessary to know the density of states and the effective mass.
Question:...
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0answers
49 views
Density of states for a tight binding model
So we have been given a dispersion relation of the form:
$$
E=6-2(\cos k_xa+\cos k_ya)
$$
and asked to calculate the density of states.
The equation for the density of states is (eq 2.48 from here ...
0
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2answers
33 views
Is the DOS (density of states) wrong for degenerated case?
The density of states (DOS) is defined as $$\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,$$ ...
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1answer
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Problem with finding the density of states of an $N$-body system
I am having problems solving a particular problem in my Statistical Mechanics course.
We have a system that is composed of $N$ non-interacting particles each of mass $m$.
The particles are bound to ...
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1answer
17 views
Is this equation for the density of states of an elastic isotropic material an approximation?
The density of states of phonons can be calculated with
$$
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 ...
0
votes
2answers
52 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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0answers
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Physical interpretation of Total and element resolved density of states
[
What can be the physical interpretation of Total and partial(element resolved) density of states as given in picture. Here redline is representing the fermi level. How we can relate it to the ...
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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
94 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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0answers
46 views
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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0answers
61 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 < \...
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0answers
30 views
Fourier transform involving Bessel functions
I need help finding the Fourier transform of the function
$$
\rho(\vec{r}) = \alpha \delta_{\vec{r},0} \left(\lambda\lambda' J_1
(\beta |\vec{r}|)Y_1(\beta |\vec{r}|) - \pi^2 J_0
(\beta |\vec{r}|)Y_0(...
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0answers
36 views
Density of states after scattering
I need some help with a probably simple question because I'm not sure whether my approach is correct.
Let the free Green's function of a system on a discrete lattice described by a massless Dirac ...
2
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1answer
103 views
Liouville's Theorem For Spacetime
Liouville's theorem states that the density of phase space governs the continuity equation.
$$\frac{\partial\rho}{\partial t}+\sum_{i=1}^n\Big(\frac{\partial(\rho\dot{q_i})}{\partial q_i}+\frac{\...
2
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0answers
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The formula for the average number of fermions $\langle N \rangle$
In the context of Fermi gases (or fluids in general), one would typically in the grand-canonical formalism use the formula
$\langle N \rangle = -\frac{\partial \psi}{\partial \mu}$, where $\psi$ is ...
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0answers
72 views
Density of States General Formula
So I have this formula regarding the density of states in 3D and 2D respectively are given by a function of the dispersion relation:
$N=\frac18 \frac{4\pi}{3}(V^{\frac13}\frac{k(\omega)}{\pi})^3$
$N=...
2
votes
2answers
271 views
How to calculate density of states for different gas models?
There are a couple examples I'm trying to understand, all in a box/square of length $L$:
For an ideal gas in 2-D with $\varepsilon=\frac{\hbar^2k^2}{2m}$:$$
D(\varepsilon)=\frac{L^2m}{2\pi\hbar}\,.$$
...
0
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1answer
140 views
Band structure and Density of states (DOS)
Can someone explain how these two plots are related?
How are the peaks in the right are associated with the left figure?
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0answers
32 views
Finding the chemical potential of a system
For a system of non interacting electrons at temperature T the density of states is given by
$$g(\epsilon)=\begin{cases}\sqrt{\epsilon-\epsilon_0} & \text{for }\epsilon > \epsilon_0 \\ 0 &...
3
votes
0answers
152 views
Density of states for a system of $N$ particles (both interacting and non-interacting case)
The density of states $\rho(\epsilon)$ for a single particle (with $g$ number of internal states such as spin) confined in a volume $V$ can be calculated as $$\rho(\epsilon)=\frac{4\pi gV}{h^3}p^2\...
0
votes
2answers
362 views
Calculating density of states for $N$ identical Fermions subject to a potential
Given a system with N identical Fermions, with spin $\frac{1}{2}$ and mass $m$, subject to the potential:
$V(\vec{r}) = \frac{1}{2}m\omega^{2}(x^{2}+y^{2}+z^{2})$
and the single particle energy ...
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0answers
101 views
Density of states from band structure
Let the density of states be given by
$$ g(\epsilon) = \int \frac{\mathop{d^3 q}}{4\pi^3} \delta(\epsilon - \epsilon(\vec{q})), $$
where $\epsilon(\vec{q}) = \frac{\hbar^2}{2m}q_\perp^2 + h_\pm(q_\...
0
votes
1answer
271 views
Calculating density of states given energy levels and degeneracy
In my statistical mechanics class, my professors did a problem in which he calculated the density of states, however I am having trouble justifying his approach. I did the problem beforehand in an ...
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0answers
43 views
Density of States and Quantum Jumps
The specific question that I'm working on is "If I have a particle in the bound state of a 1-D delta function potential at $t = - \infty$, and I apply a harmonic perturbation $V(x,t) = V_0xcos(\omega ...
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vote
1answer
109 views
Are there two kinds of boundary conditions for Density of States of electron in 1D/2D/3D bulk?
when I'm going through the online Density of States(DOS) deriving courses, I find that there seem to be 2 set of boundary condition which will lead to the same result.
Note: K is the one in p=(h/2π)K ...
1
vote
1answer
338 views
Density of states for free particle [closed]
I am asked to find the density of states for a free particle as a function of $|p|$, $\Delta|p|$ and $\Delta V$. I also have the expression for the number of states $\Delta\Omega(p) = g(p)\Delta p = \...
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1answer
162 views
Density of states of electrons
The problem is as follows:
Let the density of states of the electrons in some sample be assumed to be a constant D for $\epsilon > 0$ ($D=0$ for $\epsilon<0$) and the total number of electrons ...
0
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1answer
66 views
Calculate total number of electrons from density of states? [closed]
Can someone tell me how to calculate the total number of electrons from partial density of states (projected on each atom)?
Thanks
0
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1answer
159 views
Phonon Density of State
Suppose there is a material such as graphane which has two atoms, Carbon and Hydrogen (I mean that it has two or more atoms). How can I calculate phonon Density of State (DoS) for such system? Can I ...
-2
votes
2answers
565 views
Probability density in Quantum mechanics and mass of particle
Is there any relationship between the probability density in QM given by \begin{equation}
P\left(t\right) = \int\limits_{V} \psi^{*}(\mathbf{x},t)\psi(\mathbf{x},t)\mathrm{d}^{3}\mathbf{x}
\end{...
0
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1answer
673 views
Physical interpretation of density of states
The following pictures shows some typical examples of density of states:
and for superconductor:
Here is my interpretation:
Energy level zero represents Fermi energy level. Positive energy ...
0
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1answer
232 views
Is there a relation between density of states (DOS) and carrier mobility in semiconductors?
By changing DOS, mobility how to change?
What is the relationship between DOS and mobility, if there is?
1
vote
1answer
58 views
Clarification on how to calculate the density of states
I'm a little confused on how this works. The question asks to calculate the density of states $$\nu(E) = \int_0^{\infty}dp\,\delta(E-E_p)$$ where $$E_p = \frac{p^2}{2m}$$
This should be simple right? ...
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0answers
299 views
Effective mass for density of states calculation and for conductivity calculation
In silicon, for the effective mass for density of states calculation, electron mass (1.08) is more than hole mass (0.81). Whereas, the effective mass for conductivity calculation, hole mass (0.386) is ...
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1answer
2k views
The fermi gas model of a nucleus
In my nuclear physics lecture we learned about the "fermi gas modell" of a nucleus with which I have some problems. First the potential for the nucleons is shown in the picture below and it makes ...
3
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1answer
498 views
Getting tight binding density of states more accurately
I calculated numerically the density of states (DoS) for the 3-D tightbinding dispersion $\epsilon(k_x,k_y,k_z)=-2t\,(\cos k_x + \cos k_y + \cos k_z)$ and obtained the following plot [$t=1$ has been ...
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1answer
168 views
density of states of bogoliubov quasiparticles
For a simple fermionic system the formula for calculating the density of states(DOS) is $N(E) = \sum_{n}\delta(E-E_{n})$ where $\{E_{n}\}$ is the set of eigenvalues obtained after diagonalizing the ...
3
votes
1answer
113 views
What does it mean to divide by the degeneracy of the state in this textbook excerpt?
This section of Griffiths Introduction to Quantum Mechanics deals with Boltzmann, Fermi-Dirac, and Bose-Einstein distributions. I don't understand this line (highlighted in yellow):
Let's talk only ...
2
votes
1answer
1k views
Photon density of states: Polarization/Helicity degree of freedom?
Sakurai's "Advanced Quantum Mechanics" states in Eq. (2.116) that the density of states of a single photon with $\vec k$ vector pointing into the solid angle $d\Omega$ is given by
\begin{equation}
\...
2
votes
1answer
645 views
Density of phonon states from dispersion relation
I have a dispersion relation
$$
\omega(
\textbf{q}
)
=
\omega_0
\sqrt{
\sum_{j=1}^{D}
\sin^2{\frac{q_ja}{2}}.
}
$$
Where D is the dimension D=1,2,3. And my excersise is to calculate (numericaly on a ...
3
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0answers
75 views
Passing from a discrete summation to a continous integal
I'm having trouble understanding the math behind a step in an explanation of BCS theory.
At one point the superconductor gap $\Delta$ is defined as
\begin{equation}
1 = V \sum_q \frac{1}{\xi_q^2+\...
0
votes
1answer
206 views
Number of states $\Omega(E)$ derivation (Reif problem 2.4)
Problem 2.4 from Reif's "Fundamentals of Statistical and Thermal Physics":
Consider an isolated system consisting of a large number $N$ of virtually non-interacting localized (not translating) ...
