Spectral geometry in a rotating frame: Properties of the ground state

0525005 - ÚJF 2021 RIV US eng J - Journal Article
Barseghyan, Diana - Exner, Pavel
Spectral geometry in a rotating frame: Properties of the ground state.
Journal of Mathematical Analysis and Applications. Roč. 489, č. 1 (2020), č. článku 124130. ISSN 0022-247X. E-ISSN 1096-0813
R&D Projects: GA ČR GA17-01706S
Institutional support: RVO:61389005
Keywords : rotating quantum system * Dirichlet condition * ground state eigenvalue * optimalization * comparison to a rotating disk
OECD category: Applied mathematics
Impact factor: 1.583, year: 2020
Method of publishing: Limited access
https://doi.org/10.1016/j.jmaa.2020.124130

We investigate spectral properties of the operator describing a quantum particle confined to a planar domain Omega rotating around a fixed point with an angular velocity omega and demonstrate several properties of its principal eigenvalue lambda(omega)(1). We show that as a function of rotation center position it attains a unique maximum and has no other extrema provided the said position is unrestricted. Furthermore, we show that as a function omega, the eigenvalue attains a maximum at omega = 0, unique unless Omega has a full rotational symmetry. Finally, we present an upper bound to the difference lambda(omega)(1),Omega-lambda(omega)(1,B) where the last named eigenvalue corresponds to a disk of the same area as Omega.
Permanent Link: http://hdl.handle.net/11104/0309208