Method of resurgent analysis in the atomic collision theory
Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 2, pp. 308-323 Cet article a éte moissonné depuis la source Math-Net.Ru

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A problem of atomic collisions is considered in the adiabatic approximation. It is shown that in this approximation transfer probabilities can be obtained by using resurgent analysis. A computation algorithm for finding the transfer probabilities as well as it's mathematical proof are presented. All considerations are performed by using a simple but representative example of the two-level Landau–Singer model.
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B. Yu. Sternin; V. E. Shatalov. Method of resurgent analysis in the atomic collision theory. Teoretičeskaâ i matematičeskaâ fizika, Tome 112 (1997) no. 2, pp. 308-323. http://geodesic.mathdoc.fr/item/TMF_1997_112_2_a7/

[1] E. A. Solovev, UFN, 157:3 (1989), 437–476 | DOI

[2] B. Sternin, V. Shatalov, Collision problem in Atomic Physics and Resurgent Analysis, Preprint No NI 94047, May, 1995, Isaac Newton Inst. for Math. Sci., Cambridge, 1995

[3] B. Sternin, V. Shatalov, Theory of Atomic Collisions and Resurgent Analysis, Preprint MPI/95-68, Max-Planck-Institut für Mathematik, Bonn, 1995 | MR

[4] M. Born, V. Fock, Z. Phys., 51 (1928), 165–180 | DOI | Zbl

[5] B. Sternin, V. Shatalov, Borel-Laplace Transform and Asymptotic Theory, CRC-Press, Boca Raton, Florida, USA, 1996 | MR | Zbl

[6] L. D. Landau, Phys. Z. der Sovjetunion, 1 (1932), 88–99

[7] C. Zener, Proc. R Soc. A, 137:833 (1932), 696–702 | DOI | Zbl

[8] B. Candelpergher, J. C. Nosmas, F. Pham, Approche de la Résurgence, Hermann éditeurs des sciences et des arts, Paris, 1993 | MR | Zbl

[9] B. Yu. Sternin, V. E. Shatalov, Matem. zam., 49:6 (1991), 107–118 | MR | Zbl

[10] B. Sternin, V. Shatalov, Differential Equations on Complex Manifolds, Kluwer Academic Publishers, Dordrecht, 1994 | MR | Zbl

[11] B. Sternin, V. Shatalov, Complex Rays Method and Resurgent Analysis, Preprint No NI 94046. May, 1995, Isaac Newton Inst. for Math. Sci., Cambridge, 1995

[12] B. Sternin, V. Shatalov, Does One Need Resurgent Equations for Exact Semi-Classical Asymptotics?, Preprint MPI/95-89, Max-Planck-Institut für Mathematik, Bonn, 1995

[13] E. Delabaere, “Introduction to the Écalle theory”, Computer Algebra and Differential Equations, London Mathematical Society, Lecture Note Series, 193, ed. E. Tournier, Cambridge University Press, Cambridge, 1994, 59–102 | MR

[14] L. D. Landau, E. M. Lifshits, Kvantovaya mekhanika (nerelyativistskaya teoriya), Nauka, M., 1989 | MR