Abstract:
The waveguide with a rectangular cross section of size and orientation slowly changing along the waveguide's length is considered. Methods of the canonical perturbation theory to describe the ray dynamics in the waveguide are used. As the size and orientation of cross section slowly changes along the ray trajectory, certain resonance conditions can be satisfied. The phenomena of scattering on a resonance and capture into a resonance is studied. These phenomena lead to destruction of adiabatic invariance in the system.
Citation:
A. P. Itin, A. I. Neishtadt, A. A. Vasil'ev, “Resonant phenomena in slowly irregular rectangular waveguides”, Representation theory, dynamical systems. Part VIII, Special issue, Zap. Nauchn. Sem. POMI, 300, POMI, St. Petersburg, 2003, 173–179; J. Math. Sci. (N. Y.), 128:2 (2005), 2778–2781
\Bibitem{ItiNeiVas03}
\by A.~P.~Itin, A.~I.~Neishtadt, A.~A.~Vasil'ev
\paper Resonant phenomena in slowly irregular rectangular waveguides
\inbook Representation theory, dynamical systems. Part~VIII
\bookinfo Special issue
\serial Zap. Nauchn. Sem. POMI
\yr 2003
\vol 300
\pages 173--179
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl1006}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1993035}
\zmath{https://zbmath.org/?q=an:1117.78321}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2005
\vol 128
\issue 2
\pages 2778--2781
\crossref{https://doi.org/10.1007/s10958-005-0230-z}
Linking options:
https://www.mathnet.ru/eng/znsl1006
https://www.mathnet.ru/eng/znsl/v300/p173
This publication is cited in the following 4 articles:
A. P. Itin, A. I. Neishtadt, “Fermi acceleration in time-dependent rectangular billiards due to multiple passages through resonances”, Chaos: An Interdisciplinary Journal of Nonlinear Science, 22:2 (2012)
Itin A.P., Watanabe S., Konotop V.V., “Nonlinear dynamical instabilities of a condensate system in an atom-molecule dark state”, Physical Review A, 77:4 (2008), 043610
Itin A.P., Watanabe S., “Universality in nonadiabatic behavior of classical actions in nonlinear models of Bose–Einstein condensates”, Physical Review E, 76:2, Part 2 (2007), 026218
Neishtadt A.I., Vasifiev A.A., “Destruction of adiabatic invariance at resonances in slow-fast Hamiltonian systems”, Nuclear Instruments & Methods in Physics Research Section A-Accelerators Spectrometers Detectors and Associated Equipment, 561:2 (2006), 158–165
Citation in format AMSBIB
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