Summary
The theory has been used, which expresses the response to the external field through the set of three functionsF m , introduced in an earlier work (1). These functions satisfy a system of coupled linear integral equations which has been derived from a version of the Bethe-Salpeter equation. The approximations in kernels are considered, which are applicable for description of the high-frequency and low-frequency sound propagation. Finally, forωτ≪1, the single integral equation of the linearized Boltzmann type is derived and the kernel of this equation is found to be identical with the Boltzmann one.
Riassunto
Si ricorre alla teoria, introdotta in un lavoro precedente (1), che esprime la risposta al campo esterno per mezzo del gruppo di tre funzioniF m . Queste funzioni soddisfano un sistema di equazioni integrali lineari accoppiate che è stato dedotto da una versione dell’equazione di Bethe-Salpeter. Si studiano le approssimazioni nei noccioli, che sono applicabili alla descrizione della propagazione del suono di alta e bassa frequenza. Infine, perωτ ≪1, si deduce la singola equazione integrale del tipo di Boltzmann linearizzato e si trova che il nocciolo di questa equazione è identico a quello di Boltzmann.
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Literatur
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The kernels of these equations are essentially the same as the functions ℱ (1) mn used byEliashberg (2) in a similar context.
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Compare a similar situation for the Boltzmann electron gas, ref. (7), Sect.20.
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This work was started when the author was still at the Institute « J. Stefan », Ljubljana. This refers especially to the Sections 1 and 2.
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Pičman, L. Two-particle Green’s function and the derivation of the Boltzmann equation — II. Nuovo Cim 35, 66–84 (1965). https://doi.org/10.1007/BF02734825
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DOI: https://doi.org/10.1007/BF02734825