Small frequency approximation of (causal) dissipative pressure waves

Details Small frequency approximation of (causal) dissipative pressure waves Small frequency approximation of (causal) dissipative pressure waves

2012-01-27

arxiv.org/abs/1201.5776v2

Physics

Mathematical Physics

The replacement corrects a misprint in eq. (2). The phase factor e^{i \omega |\x|/c} was missing

Scientific paper

In this paper we discuss the problem of small frequency approximation of the causal dissipative pressure wave model proposed in \cite{KoScBo:11}. We show that for appropriate situations the Green function $G^c$ of the causal wave model can be approximated by a noncausal Green function $G_M^{pl}$ that has frequencies only in the small frequency range $[-M,M]$ ($M\leq 1/\tau_0$, $\tau_0$ relaxation time) and obeys a power law. For such cases, the noncausal wave $G^{pl}_M$ contains partial waves propagating arbitrarily fast but the sum of the noncausal waves is small in the $L^2-$sense.

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