Watanabe, Takuya; Zerzeri, Maher Landau-Zener formula in a “non-adiabatic” regime for avoided crossings. (English) Zbl 1465.81020 Anal. Math. Phys. 11, No. 2, Paper No. 82, 47 p. (2021). MSC: 81Q05 34E20 34M60 81Q20 41A60 PDF BibTeX XML Cite \textit{T. Watanabe} and \textit{M. Zerzeri}, Anal. Math. Phys. 11, No. 2, Paper No. 82, 47 p. (2021; Zbl 1465.81020) Full Text: DOI arXiv OpenURL
Fialkovsky, Ignat; Perel, Maria Mode transformation for a Schrödinger type equation: avoided and unavoidable level crossings. (English) Zbl 1461.81031 J. Math. Phys. 61, No. 4, 043506, 30 p. (2020). Reviewer: Vatsal Dwivedi (Köln) MSC: 81Q05 81Q15 81Q37 35C20 34E20 PDF BibTeX XML Cite \textit{I. Fialkovsky} and \textit{M. Perel}, J. Math. Phys. 61, No. 4, 043506, 30 p. (2020; Zbl 1461.81031) Full Text: arXiv OpenURL
Simon, Barry Tosio Kato’s work on non-relativistic quantum mechanics. II. (English) Zbl 1472.81094 Bull. Math. Sci. 9, No. 1, Article ID 1950005, 105 p. (2019). Reviewer: Heinz Siedentop (München) MSC: 81Q10 81U05 47A55 35Q40 46N50 81Q15 PDF BibTeX XML Cite \textit{B. Simon}, Bull. Math. Sci. 9, No. 1, Article ID 1950005, 105 p. (2019; Zbl 1472.81094) Full Text: DOI arXiv OpenURL
Watson, Alexander; Weinstein, Michael I. Wavepackets in inhomogeneous periodic media: propagation through a one-dimensional band crossing. (English) Zbl 1400.81103 Commun. Math. Phys. 363, No. 2, 655-698 (2018). MSC: 81Q05 81Q35 81Q20 34L40 82D25 PDF BibTeX XML Cite \textit{A. Watson} and \textit{M. I. Weinstein}, Commun. Math. Phys. 363, No. 2, 655--698 (2018; Zbl 1400.81103) Full Text: DOI arXiv OpenURL
Lu, Jianfeng; Zhou, Zhennan Frozen Gaussian approximation with surface hopping for mixed quantum-classical dynamics: a mathematical justification of fewest switches surface hopping algorithms. (English) Zbl 1478.65007 Math. Comput. 87, No. 313, 2189-2232 (2018). Reviewer: T. C. Mohan (Chennai) MSC: 65C05 65M70 35Q55 81Q20 81Q05 PDF BibTeX XML Cite \textit{J. Lu} and \textit{Z. Zhou}, Math. Comput. 87, No. 313, 2189--2232 (2018; Zbl 1478.65007) Full Text: DOI arXiv OpenURL
Simon, Barry Tosio Kato’s work on non-relativistic quantum mechanics. I. (English) Zbl 1416.81063 Bull. Math. Sci. 8, No. 1, 121-232 (2018). Reviewer: Heinz Siedentop (München) MSC: 81Q10 81U05 47A55 35Q40 46N50 81Q15 01A70 PDF BibTeX XML Cite \textit{B. Simon}, Bull. Math. Sci. 8, No. 1, 121--232 (2018; Zbl 1416.81063) Full Text: DOI OpenURL
Faraj, Ali; Jin, Shi The Landau-Zener transition and the surface hopping method for the 2D Dirac equation for graphene. (English) Zbl 07413976 Commun. Comput. Phys. 21, No. 2, 313-357 (2017). MSC: 35Q41 37M05 65M70 65Z05 81-08 81Q20 81V99 PDF BibTeX XML Cite \textit{A. Faraj} and \textit{S. Jin}, Commun. Comput. Phys. 21, No. 2, 313--357 (2017; Zbl 07413976) Full Text: DOI arXiv OpenURL
Hari, Lysianne Propagation of semiclassical wave packets through avoided eigenvalue crossings in nonlinear Schrödinger equations. (English) Zbl 1342.35336 J. Inst. Math. Jussieu 15, No. 2, 319-365 (2016). Reviewer: Boris A. Malomed (Tel Aviv) MSC: 35Q55 35Q40 PDF BibTeX XML Cite \textit{L. Hari}, J. Inst. Math. Jussieu 15, No. 2, 319--365 (2016; Zbl 1342.35336) Full Text: DOI OpenURL
Jecko, Thierry On the mathematical treatment of the Born-Oppenheimer approximation. (English) Zbl 1298.81092 J. Math. Phys. 55, No. 5, 053504, 26 p. (2014). Reviewer: T. C. Mohan (Chennai) MSC: 81Q20 81V55 81U05 PDF BibTeX XML Cite \textit{T. Jecko}, J. Math. Phys. 55, No. 5, 053504, 26 p. (2014; Zbl 1298.81092) Full Text: DOI arXiv OpenURL
Carles, Rémi; Fermanian-Kammerer, Clotilde A nonlinear Landau-Zener formula. (English) Zbl 1275.81029 J. Stat. Phys. 152, No. 4, 619-656 (2013). MSC: 81Q05 34A34 82B26 81U05 81Q15 35Q55 PDF BibTeX XML Cite \textit{R. Carles} and \textit{C. Fermanian-Kammerer}, J. Stat. Phys. 152, No. 4, 619--656 (2013; Zbl 1275.81029) Full Text: DOI arXiv OpenURL
Elgart, Alexander; Hagedorn, George A. A note on the switching adiabatic theorem. (English) Zbl 1283.81034 J. Math. Phys. 53, No. 10, 102202, 14 p. (2012). Reviewer: Gernot Schaller (Berlin) MSC: 81P68 35Q41 81Q05 68Q12 34E05 70H11 PDF BibTeX XML Cite \textit{A. Elgart} and \textit{G. A. Hagedorn}, J. Math. Phys. 53, No. 10, 102202, 14 p. (2012; Zbl 1283.81034) Full Text: DOI arXiv OpenURL
Watanabe, Takuya; Zerzeri, Maher Transition probability for multiple avoided crossings with a small gap through an exact WKB method and a microlocal approach. (English. French summary) Zbl 1257.81029 C. R., Math., Acad. Sci. Paris 350, No. 17-18, 841-844 (2012). MSC: 81Q20 70H11 PDF BibTeX XML Cite \textit{T. Watanabe} and \textit{M. Zerzeri}, C. R., Math., Acad. Sci. Paris 350, No. 17--18, 841--844 (2012; Zbl 1257.81029) Full Text: DOI OpenURL
Kucherenko, V. V. Semi-classical asymptotics of the vector Sturm-Liouville problem with parameters. (English) Zbl 1131.34021 Russ. J. Math. Phys. 14, No. 2, 174-187 (2007). Reviewer: Pavel Rehak (Brno) MSC: 34B24 81Q20 PDF BibTeX XML Cite \textit{V. V. Kucherenko}, Russ. J. Math. Phys. 14, No. 2, 174--187 (2007; Zbl 1131.34021) Full Text: DOI OpenURL
Hagedorn, George A.; Joye, Alain Time development of exponentially small non-adiabatic transitions. (English) Zbl 1059.81043 Commun. Math. Phys. 250, No. 2, 393-413 (2004). MSC: 81Q05 81Q70 81U99 PDF BibTeX XML Cite \textit{G. A. Hagedorn} and \textit{A. Joye}, Commun. Math. Phys. 250, No. 2, 393--413 (2004; Zbl 1059.81043) Full Text: DOI arXiv OpenURL
Fermanian Kammerer, Clotilde Wigner measures and molecular propagation through generic energy level crossings. (English) Zbl 1069.81548 Rev. Math. Phys. 15, No. 10, 1285-1317 (2003). MSC: 81S30 81Q20 PDF BibTeX XML Cite \textit{C. Fermanian Kammerer}, Rev. Math. Phys. 15, No. 10, 1285--1317 (2003; Zbl 1069.81548) Full Text: DOI OpenURL
Métivier, G.; Schochet, S. Averaging theorems for conservative systems and the weakly compressible Euler equations. (English) Zbl 1029.34035 J. Differ. Equations 187, No. 1, 106-183 (2003). Reviewer: P.Smith (Keele) MSC: 34C29 35Q05 76N99 PDF BibTeX XML Cite \textit{G. Métivier} and \textit{S. Schochet}, J. Differ. Equations 187, No. 1, 106--183 (2003; Zbl 1029.34035) Full Text: DOI OpenURL
Buslaev, Vladimir; Grigis, Alain Turning points for adiabatically perturbed periodic equations. (English) Zbl 0987.35013 J. Anal. Math. 84, 67-143 (2001). Reviewer: Ion Onciulescu (Iaşi) MSC: 35B10 PDF BibTeX XML Cite \textit{V. Buslaev} and \textit{A. Grigis}, J. Anal. Math. 84, 67--143 (2001; Zbl 0987.35013) Full Text: DOI OpenURL
Hagedorn, George A.; Joye, Alain Molecular propagation through small avoided crossings of electron energy levels. (English) Zbl 0965.81138 Rev. Math. Phys. 11, No. 1, 41-101 (1999). MSC: 81V55 81Q15 PDF BibTeX XML Cite \textit{G. A. Hagedorn} and \textit{A. Joye}, Rev. Math. Phys. 11, No. 1, 41--101 (1999; Zbl 0965.81138) Full Text: DOI OpenURL
Colin de Verdière, Yves; Lombardi, Maurice; Pollet, Joël The microlocal Landau-Zener formula. (English) Zbl 0986.81027 Ann. Inst. Henri Poincaré, Phys. Théor. 71, No. 1, 95-127 (1999). Reviewer: A.Parmeggiani (Bologna) MSC: 81Q20 81Q15 34C20 34E20 35Q40 35S30 PDF BibTeX XML Cite \textit{Y. Colin de Verdière} et al., Ann. Inst. Henri Poincaré, Phys. Théor. 71, No. 1, 95--127 (1999; Zbl 0986.81027) Full Text: Numdam EuDML OpenURL
Hagedorn, George A.; Joye, Alain Landau-Zener transitions through small electric eigenvalue gaps in the Born-Oppenheimer approximation. (English) Zbl 0915.35090 Ann. Inst. Henri Poincaré, Phys. Théor. 68, No. 1, 85-134 (1998). Reviewer: André Martinez (Bologna) MSC: 35Q40 81V55 PDF BibTeX XML Cite \textit{G. A. Hagedorn} and \textit{A. Joye}, Ann. Inst. Henri Poincaré, Phys. Théor. 68, No. 1, 85--134 (1998; Zbl 0915.35090) Full Text: Numdam EuDML OpenURL
Nenciu, G. Linear adiabatic theory. Exponential estimates. (English) Zbl 0768.34038 Commun. Math. Phys. 152, No. 3, 479-496 (1993). MSC: 34G10 81Q10 47A55 PDF BibTeX XML Cite \textit{G. Nenciu}, Commun. Math. Phys. 152, No. 3, 479--496 (1993; Zbl 0768.34038) Full Text: DOI OpenURL