Questions tagged [density-of-states]
251 questions
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The definition of Density of States
The density of states (DOS) is generally defined as $$D(E)=\frac{d\Omega(E)}{dE},$$ where $\Omega(E)$ is the number of states in a volume $V$. But why DOS can also be defined using delta function, as
$$D(E)~=~\sum\limits_{n} \int…
Timothy
- 2,539
12
votes
1 answer
Density of states in irregularly-shaped volumes
A very common result is that the density of momentum states in a cubic volume is $\displaystyle\frac{V}{(2\pi\hbar)^3}$ in momentum space. How does this result extend to arbitrary volumes? Are there any nice examples of volumes that are endowed with…
Aakash Lakshmanan
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11
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How to compute the density of state from the Green function?
I'd like to plot the density of state (DOS) for a specific system, say an s-wave BCS superconductor, the Green function of which is
$$G\left(p,\omega\right)=\dfrac{\omega+\xi}{\omega^{2}-\xi^{2}-\Delta^{2}}$$
as given e.g. in Abrikosov, Gor'kov and…
FraSchelle
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4 answers
Fermi's Golden Rule and Density of States
I know Fermi's Golden Rule in the form
$$\Gamma_{fi} ~=~ \sum_{f}\frac{2\pi}{\hbar}\delta (E_f - E_i)|M_{fi}|^2,$$
where $\Gamma_{fi}$ is the probability transition rate, $M_{fi}$ are the transition matrix elements.
I'm struggling to do a derivation…
Edward Hughes
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7
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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 a function called the Density of States. I am…
Time4Tea
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7
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What methods exist to calculate the density of states in the continuum of a molecule?
Say I have an arbitrary molecule in the Born-Oppenheimer approximation, and furthermore say that I can approximate the molecule as having only one active electron. What methods exist to calculate the density of states as a function of the energy of…
Dan
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6
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On the statistical meaning of density of states (DOS)
According to the so-called law of the unconscious statistician:
The expected value $\langle \cdot \rangle$ of a measurable function of ${\displaystyle X}$, ${\displaystyle g(X)}$, given that $X$ has a probability density function ${\displaystyle…
ric.san
- 1,694
6
votes
1 answer
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 this question separately.
My question is about the…
StarBucK
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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 we simple use the DOS?
edit: Let's consider we…
cerv21
- 255
6
votes
4 answers
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 chosen].
What I did is summing over $k$-points…
hbaromega
- 307
6
votes
2 answers
Rigorous definition of density of states for continuous spectrum
For operators with pure point spectra it is clear how to count number of states corresponding to a given eigenvalue - one can just calculate the dimension of eigenspaces. I am wondering how to do it for continuous spectra. What I usually saw in my…
Blazej
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6
votes
3 answers
Quantum versus classical computation of the density of states
If I consider for instance N non interacting particles in a box, I can compute the energy spectrum quantum mechanically, and thus the number of (quantum) microstates corresponding to a total energy between $E_0$ and $E_0 + \delta E$. In the limit of…
Jip
- 138
5
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Justification and interpretation of Fermi Golden Rule (second order) in Resonance Energy Transfer (RET)
I hope someone can give me some new insight to understand this.
Fermi's golden rule is wildly used to calculate the rate for RET. I have some difficulties in understanding its justification and connected to this its explicit application.
Fermi's…
JCF
- 79
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5
votes
4 answers
Average value of energy in statistical mechanics
I haven't taken any classes in Statistical Mechanics, but in studying Structure of Matter I found some ideas I'm not very familiar with, related with the average value of energy ($E$). Given a $p(E)$ probability density, the average energy…
Feynmate
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5
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Relation between critical temperature and density of states
The BCS theory predicts that the critical temperature of the superconducting transition is given by
$$
T_c \approx \theta \exp \left (- \frac{1}{U D(\epsilon_F)} \right )
$$
where $\theta$ is the Debye temperature, $U$ is the coupling constant of…
grjj3
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