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Title: Probabilistic representation and fall-off of bound states of relativistic Schrodinger operators with spin 1/2
Authors: Hiroshima, Fumio
Ichinose, Takashi
Lorinczi, Jozsef
Keywords: Relativistic Schrodinger operators
Bound states
Spatial decay
Feynman-Kac formulae
Poisson process
Subordinate Brownian motion
Martingales
Issue Date: 2013
Publisher: European Mathematical Society (© Kyoto University)
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
Abstract: 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.
Version: Accepted for publication
DOI: 10.4171/PRIMS/102
URI: https://dspace.lboro.ac.uk/2134/21512
Publisher Link: http://dx.doi.org/10.4171/PRIMS/102
ISSN: 0034-5318
Appears in Collections:Published Articles (Maths)

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