Dispersion refers to the frequency dependence of the properties of a wave.

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Equations of motion of displacement field

We have an action: $$S[\boldsymbol{u}] = \frac{1}{2} \int dt \int d^3x \left\{ \mu (\frac{\partial u_{i}}{\partial t})^{2} - \nu (u_{ii})^{2} - \rho(u_{ij})^{2}\right\} $$ Where $u_{ij} = ...
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Dispersion-less media

As far as I know, vacuum is the only dispersion free medium for electromagnetic waves. This makes me wonder if there are any other dispersion free media for these waves? (Experimentally established or ...
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PDE from dispersion relation?

Suppose I have knowledge of a system's dispersion relation $f(\omega,k)$. Is it possible to recover the underlying PDE describing the system? Can I simply use the replacement $k=-i\nabla$, ...
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What is the difference between Lehmann-Kallen and Dispersion relation?

I know that the Lehmann-Kallen (LK) form of an operator concerns just that, an operator. But the LK is very similar in form to dispersion relations found in analytic S-matrix theory.
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Dispersion relation for TE and TM waves in general anisotropic medium

I want to calculate the dispersion relation (the relation between $\bf k$ and permittivity and permeability tensors and $\omega$) for a TE and a TM wave with wave vector $\mathbf k=k_x\mathbf {\hat ...
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What phenomenon is responsible for the evolution pattern of waves created by waterfalls?

I have been fascinated lately by the pattern of the waves created by a waterfall in my town. Specifically, the pattern shows a gradual decrease in the density of the waves as they travel away from ...
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dispersion relation in presence of a potential

Let there be a particle in a step potential: if its energy $E$ is higher than the step $V_0$, then it will have the momentum $\sqrt{2m(E-V_0)}$ and no more $\sqrt{2mE}$. (See ...
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Mass frequency problem

For Dispersion relation , according to Gaussian profile, the author in the equation 3 wrote as $\omega= \left(k^2+\omega_{mass}^2\right)^{1/2}$ My question is what is mass frequency and how it arose ...
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antiferromagnetic spin wave

I have a hamiltonian that is derived from a spin wave energy dispersion calculation for a nearest neighbor interacting cubic antiferromagnet. After a Holstein-Primakoff transformation and making a ...