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_Andreas
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In dispersion relation diagrams, where omega is plotted against k, omega is sometimes nonzero at k=0. How is this possible? I thought a wave had to have a nonzero wavenumber
Dispersion relation diagrams are graphical representations of the relationship between the frequency and wavevector of a wave in a given medium. They are commonly used in physics and engineering to study the propagation of waves, such as light or sound, through a material.
Phonons are quantized lattice vibrations in a solid material, and their dispersion relation diagrams show the relationship between their frequency and wavevector. These diagrams provide valuable information about the properties of the material, such as its elastic and thermal properties, and can also help in understanding how phonons contribute to thermal conductivity and heat capacity.
An acoustic phonon is a type of phonon that involves the collective motion of atoms in a solid, while an optical phonon involves the interaction between phonons and photons. Acoustic phonons are typically low frequency and have a linear dispersion relation, while optical phonons have a higher frequency and exhibit anharmonic behavior in their dispersion relation.
A dispersion relation diagram typically shows the frequency of a wave on the y-axis and the wavevector (or momentum) on the x-axis. The slope of the curve represents the speed of the wave, and the curvature of the curve provides information about the anharmonic behavior of the material. The points where the curve intersects the x-axis (zero frequency) are known as the Brillouin zone boundaries, which define the boundaries of the first Brillouin zone.
Yes, dispersion relation diagrams can be used to study various types of waves, such as electromagnetic waves, gravitational waves, and even quantum mechanical waves. They are a useful tool for understanding the behavior of waves in different media and can provide valuable insights into the properties of the material being studied.