Physics – Mathematical Physics
Scientific paper
2002-09-12
Journal of Functional Analysis 212 (2004) 287-323
Physics
Mathematical Physics
41 pages. Final version. Dedicated to Volker Enss on the occasion of his 60th birthday
Scientific paper
10.1016/j.jfa.2004.01.009
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.
Broderix Kurt
Leschke Hajo
Müller Peter
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