Questions tagged [density-of-states]
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168
questions
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8 views
DOS of swave superconductor for nonzero chemical potential and existence of Andreev bound state
I keep getting something, which I thought was wrong, but now I am thinking maybe not. The issue I am dealing with has to do with the DOS and a nonzero $\mu$.
To begin let's note that the peak found in ...
0
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0answers
6 views
Isothermal Gruneisen parameter for Germanium?
If phonon density of states peak shifts are purely quasiharmonic, we have $\omega$(V(T)).
If phonon density of states peak shifts shifts are purely anharmonic, we have $\omega$(T).
Does anyone know if ...
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votes
1answer
14 views
Recent review on high density equation of state?
Can anyone suggest a recent review on the equation of state of the matter at high (nuclear and above) densities?
I would like this review to contain both astrophysical applications, mainly for neutron ...
1
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0answers
29 views
Double and triple sum into integral with density of states
I asked this on mathematical forum section.
I'm triying to expand the results of certain calculation, where the author has the following kind of sums:
$$
\sum_{j} A(\omega_j) n(\omega_j),
$$
where $A$ ...
-3
votes
1answer
28 views
Normalization of phonon density of states
Analogous to electronic structure calculations, we can solve for dispersion band structure of phonons for lattices using harmonic lattice approx. And we can find the so-called phonon density of states ...
1
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3answers
157 views
Canonical ensemble: what if the phase space density is not known?
In canonical ensemble, the probability is defined as
\begin{equation}
P(E)=\frac{g(E)\exp(-E/T)}{Z},
\end{equation}
and the partition function is defined as
\begin{equation}
Z(T)=\int_0^{\infty}dE\,g(...
0
votes
1answer
22 views
Constructing the density of states of multiple independent harmonic oscillators
I have a system of $N$ uncoupled 1D quantum harmonic oscillators, each with its own frequency $\omega_i$. The density of states for a single quantum harmonic oscillator shall be defined as
$$
\rho(E) =...
5
votes
1answer
159 views
Density of states and boundary conditions: how the density of states is physical if it depends on box size
This question is closely related to this one: Why is the density of states required conceptually? Should it be seen as a mathematical trick related to Fourier series?
But it was suggested that I ask ...
2
votes
1answer
27 views
Why is it valid to always use the particle in a box model in density of states calculations?
Suppose we would like to calculate the density of states of some 3-D system given the dispersion relation $\omega = f(k)$. In every such example I have come across (for instance, with phonon ...
5
votes
4answers
253 views
Why is the density of states required conceptually? Should it be seen as a mathematical trick related to Fourier series?
[edit]: My misunderstanding is more precisely asked here: Density of states and boundary conditions: how the density of states is physical if it depends on box size :it was suggested to open a new ...
1
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0answers
32 views
How to compute density of states for very large numbers of atoms?
I have a code to compute density of states of an Hamiltonian $H$. I'd like to compute it for a very large number of atoms (Currently I'm performing simulations with 1000 atoms, with polarization the ...
1
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1answer
37 views
Problem understanding what densities of states represent
I understand that the one particle partition function for a particle in a box can be written as: $$Z_1 = \sum_{k_x} \sum_{k_y} \sum_{k_z} (2s+1) e^{- \beta \epsilon( \vec k) } $$
My first question is ...
0
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2answers
57 views
Why don't we consider the negative values of $k_x, k_y$ and $k_z$ when we compute the density of states of a 3D infinit square well?
I watched some derivations of the density of states in a square box of length L with potential $V=0$ for the points inside the box and $V=\infty$ outside the box.
Using separation of variable one can ...
1
vote
0answers
36 views
How to do Wang-Landau sampling when the energy configurations are unknown?
My question is about estimating the density of states for boolean formula. Where the problem is that given a boolean formula $F$, with $n$ variables the energy is a function $E:\{0,1\}^{n}\rightarrow \...
1
vote
3answers
51 views
Density of quantum states allowed
For a 3D particle in a box, the density of states (or the number of allowed states with a wave vector whose magnitude lies between $k$ and $k + dk$ is) is given by: $$g(k) dk = \frac{V k^2 dk}{2 \pi^2}...
2
votes
1answer
74 views
Density of states of one classical harmonic oscillator
I have to determine the density of states of one tridimensional harmonic oscillator. I have to prove that the expression is the following $D(E) = aE^2$, a is a constant.
I know this is a 6-dimensional ...
0
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0answers
38 views
Ideal gas partition function
I am studying how to calculate the density of states and the partition function of $N$ non-interacting particles. My question is why the integral of the momentum, in the density of states calculation, ...
3
votes
1answer
149 views
Longitudinal conductivity from density of states (DOS)
It is well-known that using the so-called Streda formula, the transversal conductivity $\sigma_{xy}$ and thus the Hall conductivity in a two-dimensional material is given as the derivative of the ...
0
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1answer
38 views
The range of velocity in Maxwell Velocity Distribution [closed]
If we see the formula for velocity distributions in x,y, and z-direction their range of velocity goes from -infinity to +infinity but when we take the whole velocity distribution, the range goes from ...
0
votes
1answer
78 views
Density of states in a 1D infinite potential well [closed]
The question I have is how would I go about finding the density of states $\frac{dn}{dE}$ of an electron in a 1D infinite potential well with a width of $a$?
I'm only just starting my quantum physics ...
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0answers
27 views
Density function in microcanonical ensemble
From the Gibbs canonical ensemble, we have the density of states:
$$
\rho(\mathbf{q}, \mathbf{p})=Z^{-1} \mathrm{e}^{-\beta H(\mathbf{q}, \mathbf{p})}
$$
With $Z(T,V,N)$ the partition function:
$$
Z(...
0
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0answers
67 views
Density of states, Solid state physics
Im reading about Somerfeld's model, and under the assumptions of periodic boundary conditions for a particle in a box, the density of states in my book defined to be $$ g\left(\varepsilon\right)=\frac{...
0
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0answers
40 views
Density states of Cooper pairs
In superconductivity we can treat the electrons of a Cooper pair as a boson and electrons can occupy the same energy level. But for temperatures above $0$ K and below $T_c$ not all electrons will be ...
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0answers
108 views
Density of state of a 2D harmonic oscillator
I tried to find the DOS of a 2D harmonic oscillator using $2$ different methods but the results aren't the same.
The energy spectrum is: $$E_n=\hbar\omega(n+1)\tag{1}$$
and the degeneracy of the $n$-...
0
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0answers
378 views
If we put a spin-1 particle inside the 3D potential well, What will be the density of states for the system?
What will the density of states be if the particle inside the 3d potential well is a spin 1 particle?
$$\psi(x,y,z)_{n_x,n_y,n_z}= \left(\frac{2}{L}\right)^{3/2} \sin\left(\frac{n_x\pi x}{L}\right)\...
1
vote
3answers
64 views
Superposition of eigenstates in statistical mechanics
Consider the simplest case in quantum statistical mechanics, where we find the density of states in the case of a cuboidal 3 dimensional box. In the derivation we take only those states which are ...
1
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0answers
19 views
Why are electromagnetic field modes considered a continuum of states (e.g. in the Fermi Golden Rule calculation)?
When we consider a state transition e.g. from 2p to 1s in the hydrogen atom, the energy gets emitted in the form of a photon.
As an assumption underlying the Golden Rule application, we expect an ...
1
vote
2answers
74 views
Why can we approximate arbitrary volumes $V$ with cubic boxes of volume $L^3=V$ in quantum mechanics?
I've been studying quantum mechanics for two years now and it seems that in every textbook authors like to work with a box of size $L^3$ rather than an arbitrary volume $V$. Now the reason why seems ...
1
vote
1answer
49 views
Hit rate of molecules on a wall
Reviewing my final from last semester to prep for comps:
Question:
A piston of mass M can move freely in a tube with cross-section area A filled with ideal monoatomic gas with molecular mass m ≪ M and ...
0
votes
1answer
39 views
State density in one dimension
For a phonon we took in our lectures the state density for a 3D crystal and in order to find the number of states with an energy value between $[0,E)$ we did the division between the volume of the ...
2
votes
1answer
51 views
Is the density of states Lorentz invariant?
This is something that has been confusing me. A system can have a multitude of quantum states, and the energy of each will change depending on the frame of reference. However, the number of states ...
1
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0answers
61 views
Best way to calculate local density of states of tight binding model
I am currently trying to analyze a system using a tight binding model. I have a quite complicated unit cell with more than nearest neighbor hopping, that is repeating in one dimension. I have a matrix ...
0
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0answers
24 views
Dyson equation in terms of retarded Green function
Dyson equation, schematically written as $ G_0^{-1}-G^{-1}=\Sigma,$ holds for the causal Green function, which is the object used to formulate perturbation theory. However, working in a lattice model, ...
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0answers
34 views
Limits of integration on density of states in semiconductor
The density of electron states in a 3D semiconductor is given by $\rho(E)=\frac{1}{2\pi^2}\left(\frac{2 m^*}{\hbar^2}\right)^{3/2}\sqrt{E}$, derived commonly as shown here. I'm trying to understand ...
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0answers
22 views
How to prove the flat region for density of states $D(\epsilon)$ in tight binding electron model in 3D
The density of states for tight binding electron, $D(\epsilon)$, with respect to $\epsilon$(electron energy) followed an inverse cosine, a flat region ,and inverse cosine function in 3D.
It was easy ...
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0answers
42 views
Find the density of states in X points of Silicon
The problem statement is given verbatim
In Si, the dispersion relation at the [001] X points is: $$E=\frac{\hbar^2}{2}\left(\frac{k_x^2+k_y^2}{m_t}+\frac{(k_z-G)^2}{m_l}\right)$$ where G is the ...
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0answers
26 views
Effective density of states $N_c$ at different temperature for $\rm Si$
For Silicon at room temperature, Nc = 2.8x10^19 per unit volume. For 300K, m*/m = 1.81 for Silicon. Now Nc is proportional to 1.5th power of both temperature and m* (effective mass). So, at any other ...
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0answers
25 views
DOS for anisotropic 2D electron gas dispersion
If we start with the simple 2D isotropic-parabolic dispersion,
\begin{align}
E\left(\textbf{p}\right) & \approx\tilde{\varepsilon}_{0}+\alpha p_{y}^{2}+\alpha p_{x}^{2},
\label{1}
\end{align}
...
1
vote
1answer
29 views
Density of States of 1D (ideal) Fermi Gas discrepency - Missing factor?
I wanted to find the density of states of a 1D ideal, noninteracting Fermi gas. My workings are below:
$$D(\epsilon) = \frac{1}{2\pi}\int_{0}^{\infty}\delta(\epsilon-\epsilon_k)dk \times2$$
$$\...
1
vote
1answer
134 views
The density of states for free electron in conduction band
In Introduction to Solid State Physics, eighth edition, by Kittel, page 141, eqs. (20,21), the density of states for electron in conduction in three dimensions is
$$D(\epsilon)\equiv \frac{dN}{d\...
1
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0answers
133 views
Why is the local density of states related to the retarded Green function?
Consider a Hamiltonian $H$ acting on the single-particle Hilbert space $\mathscr{H}$ representing lattice sites, i.e., $|r\rangle$ forms an orthonormal basis of $\mathscr{H}$ where $r$ ranges over ...
-3
votes
2answers
52 views
Density of states in deferent dimension
Why the density of states in 2D is constant?
Or in 3D why DOS is related to E^1/2 and in 1D and 0D how we can explain the relations physically?
3
votes
1answer
108 views
What is known about the density of states of the Anderson model?
This question was posted a week ago on MathOverflow without an answer:
https://mathoverflow.net/questions/369156/what-is-known-about-the-density-of-states-for-the-anderson-model
The Anderson Model is ...
-4
votes
1answer
49 views
What happens to weight when ice melts? [closed]
A block of ice is weighed in a container. Then, it is left out to melt. Would the weight of the water be greater, less than, or equal to the ice?
I know that it has something to do with density and ...
0
votes
1answer
77 views
Density of states for free electron confined to a volume
I'm confused on the difference in results I'm seeing for the density of states for a free electron (for example, a conduction electron in a metal). For one textbook (Kittel), I'm seeing that the ...
-1
votes
1answer
67 views
How to calculate the number of distinct energy levels below a certain energy level? [closed]
The energy levels of a infinite square well is given by :
$$\epsilon=\frac{h^2}{8ml^2}(n_x^2+n_y^2+n_z^2)=\frac{h^2}{8ml^2}r^2$$
The number of energy levels below a certain energy level for large ...
0
votes
1answer
60 views
Density of states - interpreting graph
I am trying to correctly wrap my head around the density of states concept, wonder if anyone can help....
When looking at the classical graph that is used to describe this concept, we have density of ...
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0answers
15 views
Degeneracy in linear tetrahedron method
In the linear tetrahedron method for the calculation of density of states, how does one circumnavigate the infinity error that would arise if two or more k-vertices of the tetrahedron have the same ...
0
votes
1answer
97 views
Motivation behind definition of density of state
The definition of density of state per unit volume stated in Girvin and Yang's Modern Condensed Matter Physics is $$\rho(E)=\int \frac{d^3k'}{(2\pi)^3} \delta(E-E')$$
I would like to gain more ...
-1
votes
1answer
32 views
Is the number of spin states necessary in the density of states function?
I'm studying how to calculate the density of states in the final configuration in order to apply Fermi golden rule.
For free EM field the following expression is the starting point:
$$d^3n=\frac V {(2\...
