Abstract
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.
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References
M. V. Kuzelev and A. A. Rukhadze, Izv. Vyssh. Uchebn. Zaved. 22, 1223 (1979) [Radiophys. Quantum Electron. 22, 846 (1979)].
Yu. S. Barash and V. L. Ginzburg, Usp. Fiz. Nauk 118, 523 (1976) [Sov. Phys. Usp. 19, 263 (1976)].
M. A. Mikaelyan, Usp. Fiz. Nauk 168, 1331 (1998) [Phys. Usp. 41, 1219 (1998)].
M. A. Mikaelyan, Kratkie Soobshcheniya po Fizike FIAN, No. 8, 61 (1992) [Bulletin of the Lebedev Physics Institute, No. 8, 19 (1992)].
V. L. Ginzburg, Zh. Eksp. Teor. Fiz. 15, 739 (1945).
V. L. Ginzburg, Zh. Eksp. Teor. Fiz. 19, 36 (1949).
C. Itzykson and J. B. Zuber, Quantum Field Theory (McGraw-Hill, New York, 1980; Mir, Moscow, 1984).
J. A. Stratton, Electromagnetism Theory (McGraw-Hill, New York, 1941; GITTL, Moscow, 1948).
J. D. Jackson, Classical Electrodynamics (John Wiley, New York, 1962; Mir, Moscow, 1965).
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Original Russian Text © M.A. Mikaelyan, 2017, published in Kratkie Soobshcheniya po Fizike, 2017, Vol. 44, No. 3, pp. 46–57.
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Mikaelyan, M.A. On the energy transport velocity in a dissipative medium. Bull. Lebedev Phys. Inst. 44, 81–88 (2017). https://doi.org/10.3103/S1068335617030071
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DOI: https://doi.org/10.3103/S1068335617030071