Questions tagged [density-of-states]

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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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11 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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54 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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21 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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52 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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18 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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35 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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22 views

Density of states in 1D semiconductor

I'm given the dispersion relation for the energy band of my semiconductor: $E(k)=\alpha+\beta\cos(ka)$ where $a, \alpha, \beta$ are know parameters and I must obtain the density of states from that. ...
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28 views

Momentum in breit wigner cross section

The Breit Wigner cross section derived in my lecture notes is $\sigma = \frac{g\pi}{p_i^2}\frac{\Gamma_{Z\rightarrow i}\Gamma_{Z \rightarrow f}}{(E-E_0)^2+\frac{\Gamma^2}{4}}$ where $g$ is the spin ...
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1answer
19 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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61 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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43 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)=(\...
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45 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 ...
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27 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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56 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" ...
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1answer
96 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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35 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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115 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 ...
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2answers
35 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
49 views

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
25 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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55 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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10 views

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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113 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
226 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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98 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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36 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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1answer
121 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{\...
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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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507 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 $\varepsilon=\frac{\hbar^2k^2}{2m}$:$$ D(\varepsilon)=\frac{L^2m}{2\pi\hbar}\,.$$ ...
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214 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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33 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 &...
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172 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\...
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392 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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1answer
132 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_\...
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316 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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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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1answer
131 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 ...
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1answer
354 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
177 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 ...
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1answer
92 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
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1answer
179 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 ...
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622 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{...
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1answer
812 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 ...
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1answer
266 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?
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1answer
61 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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1answer
332 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 ...
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1answer
547 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 ...