A bound on group velocity for Bloch wave packets
Gr\'egoire Allaire, Mariapia Palombaro, Jeffrey Rauch
TL;DR
This paper proves that the group velocity of Bloch wave packets in periodic media cannot exceed the maximum speed of wave propagation in the original wave equation, providing a fundamental bound on wave packet dynamics.
Contribution
It establishes a theoretical bound on the group velocity of Bloch wave packets, linking it to the maximal wave speed in periodic media.
Findings
Group velocity is bounded by the maximal wave speed.
Provides a theoretical limit for wave packet propagation in periodic media.
Connects wave packet behavior to fundamental wave speed constraints.
Abstract
This short note is a sequel to our previous papers on the asymptotic behavior of Bloch wave packet solutions of the wave equation in periodic media. The purpose is to prove that the group velocity for these Bloch wave packets is bounded by the maximal speed of propagation for the original wave equation.
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