caa a22 4500 467892148 CHVBK 20180406152752.0 cr unu---uuuuu 170328e20060501xx s 000 0 eng 10.1007/s10955-006-9113-z doi (NATIONALLICENCE)springer-10.1007/s10955-006-9113-z Camus Brice Ruhr-Universität Bochum, Fakultät für Mathematik, Universitätsstr. 150, D-44780, Bochum, Germany aut Spectral Fluctuations of Schrödinger Operators Generated by Critical Points of the Potential [Elektronische Daten] [Brice Camus] Starting from the spectrum of Schrödinger operators on $${\mathbb R}^n$$ , we propose a method to detect critical points of the potential. We argue semi-classically on the basis of a mathematically rigorous version of Gutzwiller's trace formula which expresses spectral statistics in term of classical orbits. A critical point of the potential with zero momentum is an equilibrium of the flow and generates certain singularities in the spectrum. Via sharp spectral estimates, this fluctuation indicates the presence of a critical point and allows to reconstruct partially the local shape of the potential. Some generalizations of this approach are also proposed. Springer Science+Business Media, Inc., 2006 Semi-classical analysis nationallicence Schrödinger operators nationallicence equilibriums in classical mechanics nationallicence Journal of Statistical Physics Springer US; http://www.springer-ny.com 123/4(2006-05-01), 811-829 0022-4715 123:4<811 2006 123 10955 https://doi.org/10.1007/s10955-006-9113-z text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-006-9113-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Camus Brice Ruhr-Universität Bochum, Fakultät für Mathematik, Universitätsstr. 150, D-44780, Bochum, Germany aut NATIONALLICENCE 773 0- Journal of Statistical Physics Springer US; http://www.springer-ny.com 123/4(2006-05-01), 811-829 0022-4715 123:4<811 2006 123 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer