Stochastic formulation of energy-level statistics

authored by: H. Hasegawa, H. J. Mikeska, H. Frahm
Abstract: It is shown that the joint distribution of energy eigenvalues for systems with a varying degree of nonintegrability which has been obtained dynamically by T. Yukawa [Phys. Rev. Lett. 54, 1883 (1985)] can also be deduced by putting his equations of motion in the form of stochastic differential equations. We obtain an interpolation formula for the nearest-neighbor-spacing distribution as a smooth one-parameter family of density functions P(S), 0<. This distribution retains a nonanalytic nature near 0; when =0 it agrees with the Poissonian distribution but whenever 0 it is proportional to S for small S, as predicted by M. Robnik [J. Phys. A 20, L495 (1987)]. A considerable improvement on the agreement between the energy-level histogram in a real system (hydrogen in a magnetic field) and theoretical formulas which have been studied by Wintgen and Friedrich [Phys. Rev. A 35, 1464 (1987)] is demonstrated.
Organisation(s): Institute of Theoretical Physics
External Organisation(s): Kyoto University
Type: Article
Journal: Physical Review A
Volume: 38
Pages: 395-399
No. of pages: 5
ISSN: 1050-2947
Publication date: 01.01.1988
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Atomic and Molecular Physics, and Optics
Electronic version(s): https://doi.org/10.1103/PhysRevA.38.395 (Access: Unknown)
https://doi.org/10.15488/5096 (Access: Open)

BibTeX

@article{09f79edbf2fa49de8092ee5196cb3c88,
title = "Stochastic formulation of energy-level statistics",
abstract = "It is shown that the joint distribution of energy eigenvalues for systems with a varying degree of nonintegrability which has been obtained dynamically by T. Yukawa [Phys. Rev. Lett. 54, 1883 (1985)] can also be deduced by putting his equations of motion in the form of stochastic differential equations. We obtain an interpolation formula for the nearest-neighbor-spacing distribution as a smooth one-parameter family of density functions P(S), 0<. This distribution retains a nonanalytic nature near 0; when =0 it agrees with the Poissonian distribution but whenever 0 it is proportional to S for small S, as predicted by M. Robnik [J. Phys. A 20, L495 (1987)]. A considerable improvement on the agreement between the energy-level histogram in a real system (hydrogen in a magnetic field) and theoretical formulas which have been studied by Wintgen and Friedrich [Phys. Rev. A 35, 1464 (1987)] is demonstrated.",
author = "H. Hasegawa and Mikeska, {H. J.} and H. Frahm",
note = "Funding information: This work was supported by National Institutes of Health Grants P01HL129941 (toK. E. B.),R01AI143599(toK. E. B.),R21AI114965(toK. E. B.),R01HL142672(to J. F. G.), R00HL128787 (to S. J. P.), K99HL141638 (to D. O. D.), T32DK007770 (to L. C. V.), T32CA009056 (to A. E. J.), P30DK063491 (to J. F. G.), R01HL111362 (to J. E. V. E.), and R01HL132075 (to J. E. V. E.) and American Heart Association (AHA) Grants 17GRNT33661206 (to K. E. B.), 16SDG30130015 (to J. F. G.), and 19CDA34760010 (to Z. K.). The authors declare that they have no conflicts of interest with the contents of this article. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.",
year = "1988",
month = jan,
day = "1",
doi = "10.1103/PhysRevA.38.395",
language = "English",
volume = "38",
pages = "395--399",
journal = "Physical Review A",
issn = "1050-2947",
publisher = "American Physical Society",
number = "1",
}