Questions tagged [dispersion]

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

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Connection between dispersion relation and symmetries of the Hamiltonian

I am having trouble understanding intuitively the connection between the dispersion relation and the symmetries of the Hamiltonian. For example, suppose we have a lattice and there are four sub-...
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Deriving dispersion relation of hyperbolic material

I am trying to derive the following form of the dispersion relation for hyperbolic material: From the literature, this dispersion relation is achieved by setting the determinant of the below matrix ...
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Are there Dirac equations for different energy-momentum dispersion relations?

When I was introduced to the Dirac equation they wrote a PDE such that plane waves satisfy $E^2 = P^2 + m^2$. They went on to show that other options (ie Klein–Gordon) don't have spin. Are there Dirac ...
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Can an optical medium be lossless and dispersive?

Occasionally, I come across the phrase "lossless dispersive linear optical medium". How can such a medium be possible mathematically? I mean the real and imaginary parts of the electric ...
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Local Maxima in a Dispersion Curve

Hello I programmed a dispersion curve and plotted the phase velocity. I am noticing that for one of my modes (the S2 mode) my phase velocity reaches a maxima and then decreases. Is this a physical ...
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Factor for observed redshift - light dispersion (chromatic aberration) caused by a gravitational lensing

This thought tortured me for a while now, and I can't find if this has been hypothesized/discussed before, and if so, is there a consensus: Can redshift be to at least some degree a result of a ...
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Mathematical definition of a wave [duplicate]

I am aware that, in general, a wave is a type of energy transfer (though I admit I don't know if there are more complicated types of waves for which this isn't true). But I want to understand how a ...
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Dispersion Relation for one dimensional monoatomic lattice in Kronig-Penny model and in Tight-Binding Approximation model

In the tight binding approximation model, we have the dispersion relation for a one-dimensional atomic lattice given as: $$E(k) = E_0 - \alpha - 2\beta \cos(ka)$$ Here, $\alpha$ and $\beta$ are ...
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What are the exact conditions for the constancy of the speed of a wave?

Do two mechanical transverse waves traveling in the same medium have the same speed whatever the source might be? If the answer to this question is yes, can I generalize and say "all waves of the ...
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How to obtain the high frequency dispersion relation for transverse waves in the Drude model?

Context I am studying electrodynamics using Zangwill [1]. I have a narrow question regarding a proposition found there in. In the section on the Drude model of conducting matter that applies to ...
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Why does the green light change to red in the prism? [duplicate]

I know that white light, upon entering another medium from air/ vacuum, disperses into its constituent colours. Essentially when travelling in the air, all of the constituent colours have the same ...
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Does refraction depend on the colour of light?

Consider passing red and yellow lights separately through the same interfaces and with the same angles of incidence. Light of which colour will be refracted more? This question was given to me. All I ...
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Discontinuities in the $u$ channel

if we consider a 2-to-2 scattering, we have normally an $s$ channel a $t$ channel and $u$ channel. In CMS frame $s$ is positive and $t$ and $u$ negative, by crossing symmetry there are kinematics ...
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I was studying the phenomena of the formation of a rainbow. In my book, the following diagram is given: So, the rays at the red end of the spectrum make a larger angle with the incident ray than the ...
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How the $-2t\cos(k)$ term appears in the dispersion of the $1D$ tight binding model?

I am trying to derive the tight binding dispersion relation with periodic boundary condition with $N$ lattice sites of the simplest Hamiltonian: \label{ham} \tag{1} H = -t\sum\...
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Complex values for the dispersion relation obtained through an $s$-band only tight binding model for diamond cubic crystal
Any given atom in a diamond cubic lattice (Like Si or Ge) has four nearest neighbours at at a distance $\sqrt{3}a/4$, being $a$ the lattice constant. The translation vectors to these neighbours can be ...