Quantum star-graph analogues of PT-symmetric square wells
Result description
We recall the solvable PT-symmetric quantum square well on an interval of x E (?L, L) := G ?2? (with an a-dependent non-Hermiticity given by Robin boundary conditions) and generalize it. In essence, we just replace the support interval G ?2? (reinterpreted as an equilateral two-pointed star graph with Kirchhoff matching at the vertex x = 0) with a qpointed equilateral star graph G ?q? endowed with the simplest complex-rotation-symmetric external a-dependent Robin boundary conditions. The remarkably compact form of the secular determinant is then deduced. Its analysis reveals that (i) at any integer q = 2, 3, , there exists the same q-independent and infinite subfamily of the real energies, and (ii) at any special q = 2, 6, 10, , there exists another, additional, q-dependent infinite subfamily of the real energies. In the spirit of the recently proposed dynamical construction of the Hilbert space of a quantum system, the physical bound-state interpretation of these eigenvalues is finall
Keywords
non-Hermitian interactionsexactly solvable modelsquantum graphsequilateral q-pointed starRobin boundary condition
The result's identifiers
Result code in IS VaVaI
Result on the web
DOI - Digital Object Identifier
Alternative languages
Result language
angličtina
Original language name
Quantum star-graph analogues of PT-symmetric square wells
Original language description
We recall the solvable PT-symmetric quantum square well on an interval of x E (?L, L) := G ?2? (with an a-dependent non-Hermiticity given by Robin boundary conditions) and generalize it. In essence, we just replace the support interval G ?2? (reinterpreted as an equilateral two-pointed star graph with Kirchhoff matching at the vertex x = 0) with a qpointed equilateral star graph G ?q? endowed with the simplest complex-rotation-symmetric external a-dependent Robin boundary conditions. The remarkably compact form of the secular determinant is then deduced. Its analysis reveals that (i) at any integer q = 2, 3, , there exists the same q-independent and infinite subfamily of the real energies, and (ii) at any special q = 2, 6, 10, , there exists another, additional, q-dependent infinite subfamily of the real energies. In the spirit of the recently proposed dynamical construction of the Hilbert space of a quantum system, the physical bound-state interpretation of these eigenvalues is finall
Czech name
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Czech description
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Classification
Type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
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Result continuities
Project
GAP203/11/1433: The concept of cryptohermiticity in Quantum Theory and its applications
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Canadian Journal of Physics
ISSN
0008-4204
e-ISSN
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Volume of the periodical
90
Issue of the periodical within the volume
12
Country of publishing house
CA - CANADA
Number of pages
7
Pages from-to
1287-1293
UT code for WoS article
000312158000011
EID of the result in the Scopus database
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Basic information
Result type
Jx - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP
BE - Theoretical physics
Year of implementation
2012