Schrodinger operators with a switching effect

0539673 - ÚJF 2021 RIV DE eng C - Konferenční příspěvek (zahraniční konf.)
Exner, Pavel
Schrodinger operators with a switching effect.
Industrial and Applied Mathematics. Berlin: Springer, 2020, s. 13-31. ISBN 978-981-15-0927-8. ISSN 2364-6837.
[14th Biennial Conference of Indian Society of Industrial and Applied Mathematics. Amristar (IN), 02.02.2018-04.02.2018]
Grant CEP: GA ČR GA17-01706S
Institucionální podpora: RVO:61389005
Klíčová slova: Schrodinger operators * model * spectral change
Obor OECD: Pure mathematics

This paper summarizes the contents of a plenary talk given at the 14th Biennial Conference of Indian SIAM in Amritsar in February 2018. We discuss here
the effect of an abrupt spectral change for some classes of Schrodinger operators depending on the value of the coupling constant, from below bounded and partly
or fully discrete, to the continuous one covering the whole real axis. A prototypeof such a behavior can be found in Smilansky-Solomyak model devised to illustrate
that an an irreversible behavior is possible even if the heat bath to which the systemsis coupled has a finite number of degrees of freedom and analyze several modifications of this model, with regular potentials or a magnetic field, as well as another system in which p-x p-y potential is amended by a negative radially symmetric term.Finally, we also discuss resonance effects in such models.
Trvalý link: http://hdl.handle.net/11104/0317386