Journal of Low Temperature Physics

, Volume 185, Issue 5–6, pp 495–501 | Cite as

Spatial-Dispersion Eigenvalues for Permittivity Operator of Conductors and Superconductors in a Microwave Field

  • M. A. Dresvyannikov
  • A. P. Chernyaev
  • A. L. Karuzskii
  • Yu. A. Mityagin
  • A. V. Perestoronin
  • N. A. Volchkov


An operator of the permittivity can completely describe alone a microwave response of conductors with the spatial dispersion. A wave problem is formulated to search the eigenvalues of the permittivity operator, similar to the problem of the wave propagation in hollow waveguides and resonators, but non-self conjugated. Dispersion relations and general solutions are obtained. A significant role of the spatial-type force resonances is considered. Due to the self-consistency of a kinetics problem, the spatial-type force resonances are added to and usually dominate over the influence of boundary conditions. The obtained resonances include particular solutions corresponding to the surface impedances for the anomalous skin effect, for superconductors, as well as four novel solutions. The general frequency dependence of the surface impedance is derived for all solutions except that for a superconductor.


Microwave Spatial dispersion Metal Superconductor Force resonance 



This research was supported by Grants of RFBR (15-02-09055, 14-02-00658), of Ministry of Education (16.513.11.3079), by Programmes of RAS (24, IV.12 and III.7).


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • M. A. Dresvyannikov
    • 1
  • A. P. Chernyaev
    • 2
  • A. L. Karuzskii
    • 1
  • Yu. A. Mityagin
    • 1
  • A. V. Perestoronin
    • 1
  • N. A. Volchkov
    • 1
  1. 1.P. N. Lebedev Physical Institute of RASMoscowRussia
  2. 2.Moscow Institute of Physics and TechnologyDolgoprudnyRussia

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