# New PDF release: Adiabatic Expansion in Case of Vanishing Increments

By Barus C.

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**Example text**

We note that e1 ( w) is negative at frequencies in the range wT < w < wL. This range of frequencies is determined by the effective plasma frequency of the optical phonons, (73) In this range of frequencies the wave vector q(w) is predominantly imaginary and the E waves do not propagate through the crystal. The magnitude of q(w) is given by q(w) = (2n/A 0 )('f}(w) + ix(w)) = (2n/A 0 )ij(w) (74) When e1 (w) = 'YJ(w) 2 is negative, x(w) is greater than 'f}(w), and in regions where e2 (w) = 2'f}(w)x(w) = 0, this means that 'f}(w) = 0.

Although the normal to the plane of the orbit in k space is parallel to H 0 , the normal to the plane of the orbit in real space is tilted away from the direction of the magnetic field. Consequently, an electron near the surface moves into and out of the "skin depth," o, of the metal. and momentum take the form hw = fiQ and hq = hQ. Since Q is always in the direction of q, this means that E waves and transverse A waves can only excite collective excitations which have a transverse component of the electric moment and that longitudinal A waves can only excite collective excitations having a longitudinal component of the electric moment.

One notes that there are two dielectric anomalies. These occur at the frequencies of the coupled plasmon-LO phonon modes discussed on p. 30. Ho =;t=. 0. Faraday Configuration The q = 0 dielectric constant of an electron plasma in a magnetic field for E waves propagating in the Faraday (q II H 0 ) configuration can be derived in a straightforward manner from the equations of motion of the electron in a magnetic field and the relation P(w) = x(w) E(w) = (E(w) - I) E(w )/4n. One obtains the following expression (1 7 ): 2 E(w)l,r = t: 0 (w)- Wpo w[w =f We+ (iwjr)] 2 = 'f}(w)z,r (78) 42 E.

### Adiabatic Expansion in Case of Vanishing Increments by Barus C.

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