2002/09/30 by Kurt Broderix, Hajo Leschke, Peter Müller · 1 citation
Mathematics · Physics and Astronomy · #Quantum chaos and dynamical systems #Spectral Theory in Mathematical Physics #Theoretical and Computational Physics #math-ph #math.FA #math.MP #msc:47B25 #msc:47B34 #msc:47D08
paper · pdf · doi:10.1016/j.jfa.2004.01.009
published as Journal of Functional Analysis 212 (2004) 287-323 · 41 pages. Final version. Dedicated to Volker Enss on the occasion of his 60th birthday
openalex publication_date 2004/05/13 · arxiv created 2004/07/05 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
By suitably extending a Feynman-Kac formula of Simon [Canadian Math. Soc. Conf. Proc, 28 (2000), 317-321], we study one-parameter semigroups generated by (the negative of) rather general Schroedinger operators, which may be unbounded from below and include a magnetic vector potential. In particular, a common domain of essential self-adjointness for such a semigroup is specified. Moreover, each member of the semigroup is proven to be a maximal Carleman operator with a continuous integral kernel given by a Brownian-bridge expectation. The results are used to show that the spectral projections of the generating Schroedinger operator also act as Carleman operators with continuous integral kernels. Applications to Schroedinger operators with rather general random scalar potentials include a rigorous justification of an integral-kernel representation of their integrated density of states - a relation frequently used in the physics literature on disordered solids.