2024-03-28T20:18:46Zhttps://gredos.usal.es/oai/requestoai:gredos.usal.es:10366/1331522022-02-07T15:43:21Zcom_10366_116214com_10366_4512com_10366_3823col_10366_116215
Soliton defects in one-gap periodic system and exotic supersymmetry
Arancibia, Adrián
Correa, Francisco
Jakubský, Vít
Mateos Guilarte, Juan María
Plyushchay, Mikhail S.
MATHEMATICS
High Energy Physics
Physics
Mathematical Physics
Exactly Solvable and Integrable Systems
Quantum Physics
[EN] By applying Darboux-Crum transformations to the quantum one-gap Lam ́e system, we introduce an arbitrary countable number of bound states into forbidden bands. The perturbed potentials are reflectionless and contain two types of soliton defects in the periodic background. The bound states with finite number of nodes are supported in the lower forbidden band by the periodicity defects of the potential well type, while the pulse type bound states in the gap have infinite number of nodes and are trapped by defects of the compression modulations nature.We investigate the exotic nonlinear N= 4 supersymmetric structure in such paired Schrödinger systems, which extends an ordinary N= 2 supersymmetry and involves two bosonic generators
composed from Lax-Novikov integrals of the subsystems. One of the bosonic integrals has a nature of a central charge, and allows us to liaise the obtained systems with the stationary equations of the Korteweg-de Vries and modified Korteweg-de Vrieshierarchies. This exotic supersymmetry opens the way for the construction of self-consistent condensates based on the Bogoliubov-de Gennes equations and associated with them new solutions to the Gross-Neveu model. They correspond to the kink or kink-antikink defects of the crystalline background independence on whether the exotic supersymmetry is unbroken or spontaneously broken.
2017-05-19
2017-05-19
2014
info:eu-repo/semantics/article
http://hdl.handle.net/10366/133152
10.1103/PhysRevD.90.125041
eng
http://dx.doi.org/10.1103/PhysRevD.90.125041
http://creativecommons.org/licenses/by-nc-nd/4.0/
info:eu-repo/semantics/openAccess
Attribution-NonCommercial-NoDerivs 4.0 International