Geodesic
Asymptotic behavior of the solutions of nonstationary Dirac equation with the potential slowly depending on time
Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 49, Tome 483 (2019), pp. 189-198 Cet article a éte moissonné depuis la source Math-Net.Ru

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The asymptotic behavior of the solutions of the Cauchy problem for the non-stationary Dirac equation with a time-dependent potential is studied. The construction of asymptotic solutions is based on the spectral decomposition of the solution at a given time. The adiabatic theorem of scattering theory is not used. 
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     author = {V. V. Sukhanov},
     title = {Asymptotic behavior of the solutions of nonstationary {Dirac} equation with the potential slowly depending on time},
     journal = {Zapiski Nauchnykh Seminarov POMI},
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V. V. Sukhanov. Asymptotic behavior of the solutions of nonstationary Dirac equation with the potential slowly depending on time. Zapiski Nauchnykh Seminarov POMI, Mathematical problems in the theory of wave propagation. Part 49, Tome 483 (2019), pp. 189-198. http://geodesic.mathdoc.fr/item/ZNSL_2019_483_a11/

[1] J. D. Dollard, “Adiabatic switching in the Shroedinger theory of scattering”, J. Math. Phys., 7 (1966), 802–810 | DOI | MR

[2] G. Nenciu, “On the adiabatic limit for Dirac particles in external fields”, Com. Math. Phys., 76 (1980), 117–128 | DOI | MR | Zbl

[3] A. Martinez, Sh. Nakamura, “Adiabatic limit and scattering”, C. R. Acad. Sci. Paris ser I Math., 318:12, 1153–1158 | MR | Zbl

[4] L. A. Takhtadzhan, L. D. Faddeev, Gamiltonov podkhod v teorii solitonov, Nauka, M., 1986 | MR