Scattering of particles bounded to an infinite planar curve

0538359 - ÚJF 2021 RIV SG eng J - Článek v odborném periodiku
Dittrich, Jaroslav
Scattering of particles bounded to an infinite planar curve.
Reviews in Mathematical Physics. Roč. 32, č. 10 (2020), č. článku 2050029. ISSN 0129-055X. E-ISSN 1793-6659
Grant CEP: GA ČR GA17-01706S
Institucionální podpora: RVO:61389005
Klíčová slova: curve supporting delta interaction * absolutely continuous spectrum * scattering * wave operator
Obor OECD: Pure mathematics
Impakt faktor: 1.361, rok: 2020
Způsob publikování: Omezený přístup
https://doi.org/10.1142/S0129055X20500294

Non-relativistic quantum particles bounded to a curve in 2 by attractive contact delta -interaction are considered. The interval between the energy of the transversal bound state and zero is shown to belong to the absolutely continuous spectrum, with possible embedded eigenvalues. The existence of the wave operators is proved for the mentioned energy interval using the Hamiltonians with the interaction supported by the straight lines as the free ones. Their completeness is not proved. The curve is assumed C3-smooth, non-intersecting, unbounded, asymptotically approaching two different half-lines (non-parallel or parallel but excluding the 'U-case'). Physically, the system can be considered as a model of long nanostructural channel.
Trvalý link: http://hdl.handle.net/11104/0316170