J. Phys. Soc. Jpn. 54 (1985) pp. 2037-2046  |Next Article|  |Table of Contents|
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Stochastic Theory for Nonadiabatic Level Crossing with Fluctuating Off-Diagonal Coupling

Yosuke Kayanuma

(Received November 22, 1984)

A simple stochastic model is presented describing the nonadiabatic transitions in the level crossing with fluctuating off-diagonal coupling, in which the fluctuation is assumed to obey the Markoffian Gaussian process. The probability P that the transition occurs from one diabatic state to another is calculated exactly in the two limiting situations: In the slow fluctuation limit, P is given by P=1-{1+(4πJ²/\hbar|v|)}^-1/2, where J is the averaged amplitude of the off-diagonal term and v is the velocity of the change of the energy difference between the crossing levels. In the rapid fluctuation limit, P is given by P={1-exp (-4πJ²/\hbar|v|)}/2. The intermediate case is studied numerically by the Wiener-Hermite expansion method. Generally, P approaches not 1 but 1/2 in the limit of slow passage, namely, v→0. ©1985 The Physical Society of Japan

URL: http://jpsj.ipap.jp/link?JPSJ/54/2037/
DOI: 10.1143/JPSJ.54.2037

References | Citing Articles (19)

1. Y. Kayanuma: J. Phys. Soc. Jpn. 53 (1984) 108[IPAP]; and J. Phys. Soc. Jpn. 53 (1984) 118[IPAP]. Referred as I and II, respectively, in the present paper.
2. L. D. Landau: Phys. Z. Sovietunion 1 (1932) 88.
3. C. Zener: Proc. R. Soc. London A137 (1932) 696.
4. See, for example, A. M. Stoneham: Rep. Prog. Phys. 44 (1981) 79[IoP STACKS].
5. Y. Kayanuma: J. Phys. Soc. Jpn. 51 (1982) 3536[IPAP].
6. Y. Mori, R. Hattori and H. Ohkura: J. Phys. Soc. Jpn. 51 (1982) 2713[IPAP].
7. A. Abragam: The Principles of Nuclear Magnetism (Oxford Univ. Press, Oxford, England, 1961).
8. M. M. T. Loy: Phys. Rev. Lett. 32 (1974) 814[APS].
9. S. Nakanishi, T. Endo, T. Muramoto and T. Hashi: Opt. Commun. 38 (1981) 419[Elsevier].