Landau-Zener problem for energies close to potential crossing points
We examine a previously overlooked aspect of the well-known Landau-Zener (LZ) problem, namely, the behavior in the intermediate, i.e., close to a crossing point, energy region, when all four LZ states are coupled and should be taken into account. We calculate the 4×4 connection matrix in this intermediate energy region, possessing the same block structure as the known connection matrices for the tunneling and in the over-barrier regions of the energy and continuously matching those in the corresponding energy regions. Applications of the results may concern various systems of physics, chemistry, or biology, ranging from molecular magnets and glasses to Bose condensed atomic gases.
PACS numbers05.45.−a 31.50.Gh 72.10.−d
Unable to display preview. Download preview PDF.
- 1.L. D. Landau and E. M. Lifshitz, Course of Theoretical Physics, Vol. 3: Quantum Mechanics: Non-Relativistic Theory, 2nd ed. (Nauka, Moscow, 1963; Pergamon, New York, 1965).Google Scholar
- 2.C. Zhu, Y. Teranishi, and H. Nakamura, Adv. Chem. Phys. 117, 127 (2001).Google Scholar
- 5.S. Coleman, Aspects of Symmetry (Cambridge Univ. Press, Cambridge, 1985).Google Scholar
- 6.V. A. Benderskii, D. E. Makarov, and C. A. Wight, Chemical Dynamics at Low Temperatures (Wiley-Interscience, New York, 1994).Google Scholar
- 7.A. Erdelyi, W. Magnus, F. Oberhettinger, and F. G. Tricomi, Higher Transcendental Functions (McGraw-Hill, New York, 1953; Nauka, Moscow, 1965), Vols. 1–3.Google Scholar
- 9.V. A. Benderskii, E. V. Vetoshkin, and E. I. Kats, Phys. Rev. A 69, 062508 (2004).Google Scholar
- 13.J. Heading, An Introduction to Phase-Integral Methods (Wiley-Interscience, London, 1962; Mir, Moscow, 1965).Google Scholar
- 15.F. W. J. Olver, Asymptotics and Special Functions (Academic, New York, 1974; Nauka, Moscow, 1990).Google Scholar