Abstract:
Scattering by a potential which decreases at large distances faster than |x|−1 is considered.
The spectrum of the S matrix at fixed energy is studied. The asymptotic behavior of the
eigenvalues at large values of the serial number is obtained. Similar expressions are
obtained when allowance is made for an electromagnetic field. The scheme is also applied
to the Dirac equation.
Citation:
M. Sh. Birman, D. R. Yafaev, “Asymptotic behavior of the limiting phase shifts in the case of scattering by a potential without spherical symmetry”, TMF, 51:1 (1982), 44–53; Theoret. and Math. Phys., 51:1 (1982), 344–350
\Bibitem{BirYaf82}
\by M.~Sh.~Birman, D.~R.~Yafaev
\paper Asymptotic behavior of the limiting phase shifts in the case of scattering by a potential without spherical symmetry
\jour TMF
\yr 1982
\vol 51
\issue 1
\pages 44--53
\mathnet{http://mi.mathnet.ru/tmf2389}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=672765}
\transl
\jour Theoret. and Math. Phys.
\yr 1982
\vol 51
\issue 1
\pages 344--350
\crossref{https://doi.org/10.1007/BF01029260}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1982PP79800005}
Linking options:
https://www.mathnet.ru/eng/tmf2389
https://www.mathnet.ru/eng/tmf/v51/i1/p44
This publication is cited in the following 11 articles:
Jesse Gell-Redman, Andrew Hassell, “The Distribution of Phase Shifts for Semiclassical Potentials with Polynomial Decay”, International Mathematics Research Notices, 2020:19 (2020), 6294
Jesse Gell-Redman, Andrew Hassell, Steve Zelditch, “Equidistribution of phase shifts in semiclassical potential scattering”, Journal of the London Mathematical Society, 91:1 (2015), 159
Kiril Datchev, Jesse Gell-Redman, Andrew Hassell, Peter Humphries, “Approximation and Equidistribution of Phase Shifts: Spherical Symmetry”, Commun. Math. Phys., 326:1 (2014), 209
M. Z. Solomyak, T. A. Suslina, D. R. Yafaev, “On the mathematical works of M. Sh. Birman”, St. Petersburg Math. J., 23:1 (2012), 1–38
N. Lerner, D. Yafaev, “Trace theorems for pseudo-differential operators”, J. Anal. Math., 74:1 (1998), 113
R G Newton, “A note on trace-class scattering amplitudes”, J. Phys. A: Math. Gen., 24:1 (1991), L49
S. Z. Levendorskii, “The method of approximate spectral projection”, Math. USSR-Izv., 27:3 (1986), 451–502
N.M. Bogoliubov, V.E. Korepin, A.G. Izergin, “Structure of the vacuum in the quantum sine-Gordon model”, Physics Letters B, 159:4-6 (1985), 345
N. M. Bogolyubov, A. G. Izergin, “Lattice sine-Gordon model with local Hamiltonian”, Theoret. and Math. Phys., 61:3 (1984), 1195–1204
F. A. Smirnov, “Quantum Gel'fand–Levitan–Marchenko equations for the sine-Gordon model”, Theoret. and Math. Phys., 60:3 (1984), 871–880
N. M. Bogolyubov, A. G. Izergin, “Lattice completely integrable regularization of the sine-Gordon model for small coupling constants”, Theoret. and Math. Phys., 59:2 (1984), 441–452
Citation in format AMSBIB
Contact us: