Bound states in waveguides with complex Robin boundary conditions
Result description
We consider the Laplacian in a tubular neighbourhood of a hyperplane subjected to non-self-adjoint PT-symmetric Robin boundary conditions. Its spectrum is found to be purely essential and real for constant boundary conditions. The influence of the perturbation in the boundary conditions on the threshold of the essential spectrum is studied using the Birman-Schwinger principle. Our aim is to derive a sufficient condition for existence, uniqueness and reality of discrete eigenvalues. We show that discrete spectrum exists when the perturbation acts in the mean against the unperturbed boundary conditions and we are able to obtain the first term in its asymptotic expansion in the weak coupling regime.
Keywords
non-self-adjointnesswaveguideRobin boundary conditionsspectral analysisessential spectrumweak couplingBirman-Schwinger principlereality of the spectrum
The result's identifiers
Result code in IS VaVaI
Alternative codes found
RIV/68407700:21340/16:00239846
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Bound states in waveguides with complex Robin boundary conditions
Original language description
We consider the Laplacian in a tubular neighbourhood of a hyperplane subjected to non-self-adjoint PT-symmetric Robin boundary conditions. Its spectrum is found to be purely essential and real for constant boundary conditions. The influence of the perturbation in the boundary conditions on the threshold of the essential spectrum is studied using the Birman-Schwinger principle. Our aim is to derive a sufficient condition for existence, uniqueness and reality of discrete eigenvalues. We show that discrete spectrum exists when the perturbation acts in the mean against the unperturbed boundary conditions and we are able to obtain the first term in its asymptotic expansion in the weak coupling regime.
Czech name
—
Czech description
—
Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
—
Result continuities
Project
GA14-06818S: Rigorous Methods in Quantum Dynamics: Geometry and Magnetic Fields
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2016
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Asymptotic Analysis
ISSN
0921-7134
e-ISSN
—
Volume of the periodical
96
Issue of the periodical within the volume
3-4
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
31
Pages from-to
251-281
UT code for WoS article
000371334700003
EID of the result in the Scopus database
2-s2.0-84958980236
Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BE - Theoretical physics
Year of implementation
2016