Abstract
This article is to give an account of stochastic approach to the energy-level statistics for those quantum systems with varying degree of nonintegrability; those lying between the regular limit adapted for the Poisson statistics and the chaotic limit for the Gaussian ensemble of random matrices. It is a modification of Dyson’s Brownian Motion theory for the above purpose by incorporating the original idea into the recent dynamical proposal of Yukawa. The interpolation formula for the nearest-neighbor spacing distribution we propose is discussed in the light of its application to the diamagnetic Kepler problem.
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© 1988 Plenum Press, New York
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Hasegawa, H. (1988). Stochastic Formulation of Energy Level Statistics: Application to the Hydrogen Atom in a Magnetic Field. In: Taylor, K.T., Nayfeh, M.H., Clark, C.W. (eds) Atomic Spectra and Collisions in External Fields. Physics of Atoms and Molecules. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-1061-7_24
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DOI: https://doi.org/10.1007/978-1-4613-1061-7_24
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