Мақаланы E-mail арқылы жіберу On the Bifurcation of Thresholds of the Essential Spectrum with a Spectral Singularity
- Авторлар: Borisov D.I1,2,3, Zezyulin D.A4
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Мекемелер:
- Institute of Mathematics with Computing Centre, Subdivision of the Ufa Federal Research Centre, Russian Academy of Sciences, Ufa, 450008, Russia
- Akmulla Bashkir State Pedagogical University, Ufa, 450008, Russia
- Univerzita Hradec Králové, Hradec Králové III, 500 03, Czech Republic
- ITMO University, St. Petersburg, 197101, Russia
- Шығарылым: Том 59, № 2 (2023)
- Беттер: 270-274
- Бөлім: Articles
- URL: https://journal-vniispk.ru/0374-0641/article/view/144919
- DOI: https://doi.org/10.31857/S0374064123020127
- EDN: https://elibrary.ru/PVRLHB
- ID: 144919
Дәйексөз келтіру
Ашық рұқсат
Рұқсат берілді
Тек жазылушылар үшін
Аннотация
We consider the Schrödinger operator on the plane with bounded potential, where is a real potential, and are compactly supported complex potentials, and
is a small parameter, assuming that the lower part of the spectrum of the one-dimensional Schrödinger operator consists of a pair of isolated eigenvalues and the essential spectrum of the operator has a virtual level at its lower edge and a spectral singularity inside.
Additionally, we assume that there is a certain superposition of eigenvalues of the operator with the virtual level and spectral singularity of the operator; this leads to the emergence of a special threshold in the essential spectrum of the perturbed operator, with the perturbation leading to a bifurcation of this threshold into eigenvalues and resonances with multiplicity doubling. The bifurcation scenario described in this paper is qualitatively different from the previously known ones.
Авторлар туралы
D. Borisov
Institute of Mathematics with Computing Centre, Subdivision of the Ufa Federal Research Centre, Russian Academy of Sciences, Ufa, 450008, Russia; Akmulla Bashkir State Pedagogical University, Ufa, 450008, Russia; Univerzita Hradec Králové, Hradec Králové III, 500 03, Czech Republic
Email: borisovdi@yandex.ru
D. Zezyulin
ITMO University, St. Petersburg, 197101, Russia
Хат алмасуға жауапты Автор.
Email: d.zezyulin@gmail.com
Әдебиет тізімі
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