On the energy transport velocity in a dissipative medium

An exact definition of the group velocity v g is proposed for a wave process with arbitrary dispersion relation ω = ω ′( k ) + iω ″( k ). For the monochromatic approximation, a limit expression v g ( k ) is obtained. A condition under which v g ( k ) takes the form of the Kuzelev–Rukhadze expression...

Full description

Saved in:
Bibliographic Details
Published in:Bulletin of the Lebedev Physics Institute 2017-03, Vol.44 (3), p.81-88
Main Author: Mikaelyan, M. A.
Format: Article
Language:English
Subjects:
Dispersion
Dissipation
Energy transfer
Group velocity
Light speed
Oscillators
Physics
Physics and Astronomy
Velocity
Wave dispersion
Citations: Items that this one cites
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:An exact definition of the group velocity v g is proposed for a wave process with arbitrary dispersion relation ω = ω ′( k ) + iω ″( k ). For the monochromatic approximation, a limit expression v g ( k ) is obtained. A condition under which v g ( k ) takes the form of the Kuzelev–Rukhadze expression [1] dω ′( k )/ dk is found. In the general case, it appears that v g ( k ) is defined not only by the dispersion relation ω ( k ), but also by other elements of the initial problem. As applied to the dissipative medium, it is shown that v g ( k ) defines the field energy transfer velocity, and this velocity does not exceed thee light speed in vacuum. An expression for the energy transfer velocity is also obtained for the case where the dispersion relation is given in the form k = k ′( ω ) + ik ″( ω ) which corresponds to the boundary problem.
ISSN:1068-3356
1934-838X
DOI:10.3103/S1068335617030071