Questions tagged [density-of-states]

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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 ...
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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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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 ...
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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 $A$ ...
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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 ...
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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(...
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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) =...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 \...
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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}...
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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 ...
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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, ...
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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 ...
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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 ...
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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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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(...
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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{...
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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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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 $n$-...
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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)\...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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 ...
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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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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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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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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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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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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} ...
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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: $$D(\epsilon) = \frac{1}{2\pi}\int_{0}^{\infty}\delta(\epsilon-\epsilon_k)dk \times2$$ $$\...
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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\...
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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 ...
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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?
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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 ...
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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 ...
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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 ...
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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 ...
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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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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 ...
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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 ...
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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\...