By Bethe H., Schweber S.
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Example text
It follows at once that m is a good "quantum number": different values of m are completely decoupled. We can therefore classify the solutions as "longitudinal" (m = 0), "transverse" (m = 1), "quadrupolar" (m = 2), etc. 127). The collective modes thus correspond to a single m, but to a mixture of t's. This renders the actual solution of Eq. 127) rather difficult. Among the collective modes perhaps the most important is the longitudinal symmetric mode. I t is the only mode which involves fluctuations of the particle density, and thus represents the high frequency (w» v) counterpart of ordinary sound.
98) p ') ' Let us insert Eq. 97): we recover the expression of (jp v p) derived from Eq. 91). On comparing Eqs. pp' by Galilean invariance. In the case of an isotropic system, such as liquid 3He, jp and V p are both parallel to p; Eq. pp" We note that F I 8 must be larger than - 3; otherwise the system becomes unstable, since for a negative effective mass it is energetically favorable to excite quasiparticles across the Fermi surface. 6. LOCALIZED QUASIPARTICLE EXCITATIONS We consider now the Landau transport equation in the absence of an external field and collision terms.
The collective modes thus correspond to a single m, but to a mixture of t's. This renders the actual solution of Eq. 127) rather difficult. Among the collective modes perhaps the most important is the longitudinal symmetric mode. I t is the only mode which involves fluctuations of the particle density, and thus represents the high frequency (w» v) counterpart of ordinary sound. For that reason, it has been called by Landau zero sound. Another important mode is the longitudinal antisymmetric mode, which involves spin density fluctuations.