Path integral representation for schrödinger operators with bernstein functions of the laplacian

Fumio Hiroshima, Takashi Ichinose, József Lrinczi

研究成果: ジャーナルへの寄稿記事

22 引用 (Scopus)

抄録

Path integral representations for generalized Schrödinger operators obtained under a class of Bernstein functions of the Laplacian are established. The one-to-one correspondence of Bernstein functions with Lévy subordinators is used, thereby the role of Brownian motion entering the standard FeynmanKac formula is taken here by subordinate Brownian motion. As specific examples, fractional and relativistic Schrödinger operators with magnetic field and spin are covered. Results on self-adjointness of these operators are obtained under conditions allowing for singular magnetic fields and singular external potentials as well as arbitrary integer and half-integer spin values. This approach also allows to propose a notion of generalized Kato class for which an L p-L q bound of the associated generalized Schrödinger semigroup is shown. As a consequence, diamagnetic and energy comparison inequalities are also derived.

元の言語英語
記事番号1250013
ジャーナルReviews in Mathematical Physics
24
発行部数6
DOI
出版物ステータス出版済み - 7 1 2012

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Bernstein Function
Curvilinear integral
Integral Representation
operators
integers
Brownian motion
Operator
Magnetic Field
Kato Class
Feynman-Kac Formula
Self-adjointness
Subordinator
Integer
One to one correspondence
magnetic fields
Fractional
Semigroup
Arbitrary
Energy
energy

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

これを引用

Path integral representation for schrödinger operators with bernstein functions of the laplacian. / Hiroshima, Fumio; Ichinose, Takashi; Lrinczi, József.

:: Reviews in Mathematical Physics, 巻 24, 番号 6, 1250013, 01.07.2012.

研究成果: ジャーナルへの寄稿記事

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