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Periodic Dirac operator with dislocation. / Korotyaev, Evgeny; Mokeev, Dmitrii.

In: Journal of Differential Equations, Vol. 296, 25.09.2021, p. 369-411.

Research output: Contribution to journal › Article › peer-review

Harvard

Korotyaev, E & Mokeev, D 2021, 'Periodic Dirac operator with dislocation', Journal of Differential Equations, vol. 296, pp. 369-411. https://doi.org/10.1016/j.jde.2021.06.006

APA

Korotyaev, E., & Mokeev, D. (2021). Periodic Dirac operator with dislocation. Journal of Differential Equations, 296, 369-411. https://doi.org/10.1016/j.jde.2021.06.006

Vancouver

Korotyaev E, Mokeev D. Periodic Dirac operator with dislocation. Journal of Differential Equations. 2021 Sep 25;296:369-411. https://doi.org/10.1016/j.jde.2021.06.006

Author

Korotyaev, Evgeny ; Mokeev, Dmitrii. / Periodic Dirac operator with dislocation. In: Journal of Differential Equations. 2021 ; Vol. 296. pp. 369-411.

BibTeX

@article{04848aa3226e42179fced0fdf3add2a4,
title = "Periodic Dirac operator with dislocation",
abstract = "We consider Dirac operators with dislocation potentials on the line. The dislocation potential is a periodic potential for x<0 and the same potential but shifted by t∈R for x>0. Its spectrum has an absolutely continuous part (the union of bands separated by gaps) plus at most two eigenvalues in each gap. Its resolvent admits a meromorphic continuation onto a two-sheeted Riemann surface. We prove that it has only two simple poles on each open gap: eigenvalues or resonances. These poles are called states and there are no other poles. We prove: 1) states are continuous functions of t, and we obtain their local asymptotics; 2) for each t states in the gap are distinct; 3) states can be monotone or non-monotone functions of t; 4) we construct examples of operators with different types of states in gaps.",
keywords = "Dirac operator, Dislocation, Periodic potential, Resonances, SCHRODINGER OPERATOR, INVERSE PROBLEM, SCATTERING-THEORY",
author = "Evgeny Korotyaev and Dmitrii Mokeev",
note = "Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",
year = "2021",
month = sep,
day = "25",
doi = "10.1016/j.jde.2021.06.006",
language = "English",
volume = "296",
pages = "369--411",
journal = "Journal of Differential Equations",
issn = "0022-0396",
publisher = "Elsevier",

}

RIS

TY - JOUR

T1 - Periodic Dirac operator with dislocation

AU - Korotyaev, Evgeny

AU - Mokeev, Dmitrii

N1 - Publisher Copyright: © 2021 Elsevier Inc.

PY - 2021/9/25

Y1 - 2021/9/25

N2 - We consider Dirac operators with dislocation potentials on the line. The dislocation potential is a periodic potential for x<0 and the same potential but shifted by t∈R for x>0. Its spectrum has an absolutely continuous part (the union of bands separated by gaps) plus at most two eigenvalues in each gap. Its resolvent admits a meromorphic continuation onto a two-sheeted Riemann surface. We prove that it has only two simple poles on each open gap: eigenvalues or resonances. These poles are called states and there are no other poles. We prove: 1) states are continuous functions of t, and we obtain their local asymptotics; 2) for each t states in the gap are distinct; 3) states can be monotone or non-monotone functions of t; 4) we construct examples of operators with different types of states in gaps.

AB - We consider Dirac operators with dislocation potentials on the line. The dislocation potential is a periodic potential for x<0 and the same potential but shifted by t∈R for x>0. Its spectrum has an absolutely continuous part (the union of bands separated by gaps) plus at most two eigenvalues in each gap. Its resolvent admits a meromorphic continuation onto a two-sheeted Riemann surface. We prove that it has only two simple poles on each open gap: eigenvalues or resonances. These poles are called states and there are no other poles. We prove: 1) states are continuous functions of t, and we obtain their local asymptotics; 2) for each t states in the gap are distinct; 3) states can be monotone or non-monotone functions of t; 4) we construct examples of operators with different types of states in gaps.

KW - Dirac operator

KW - Dislocation

KW - Periodic potential

KW - Resonances

KW - SCHRODINGER OPERATOR

KW - INVERSE PROBLEM

KW - SCATTERING-THEORY

UR - http://www.scopus.com/inward/record.url?scp=85107759835&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2021.06.006

DO - 10.1016/j.jde.2021.06.006

M3 - Article

AN - SCOPUS:85107759835

VL - 296

SP - 369

EP - 411

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

ER -

ID: 86154239