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Probabilistic representation and fall-off of bound states of relativistic Schrodinger operators with spin 1/2

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journal contribution
posted on 2016-06-07, 13:55 authored by Fumio Hiroshima, Takashi Ichinose, Jozsef Lorinczi
A Feynman-Kac type formula of relativistic Schrodinger operators with unbounded vector potential and spin 1/2 is given in terms of a three-component process consisting of Brownian motion, a Poisson process and a subordinator. This formula is obtained for unbounded magnetic fields and magnetic fields with zeros. From this formula an energy comparison inequality is derived. Spatial decay of bound states is established separately for growing and decaying potentials by using martingale methods.

History

School

  • Science

Department

  • Mathematical Sciences

Published in

PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES

Volume

49

Issue

1

Pages

189 - 214 (26)

Citation

HIROSHIMA, F., ICHINOSE, T. and LORINCZI, J., 2013. Probabilistic representation and fall-off of bound states of relativistic Schrodinger operators with spin 1/2. Publications of the Research Institute for Mathematical Sciences, 49 (1), pp.189-214

Publisher

European Mathematical Society (© Kyoto University)

Version

  • AM (Accepted Manuscript)

Publisher statement

This work is made available according to the conditions of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0) licence. Full details of this licence are available at: https://creativecommons.org/licenses/by-nc-nd/4.0/

Publication date

2013

ISSN

0034-5318

eISSN

1663-4926

Language

  • en