About: Quantum star-graph analogues of PT-symmetric square wells

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	We recall the solvable PT-symmetric quantum square well on an interval of x E (–L, L) := G ð2Þ (with an a-dependent non-Hermiticity given by Robin boundary conditions) and generalize it. In essence, we just replace the support interval G ð2Þ (reinterpreted as an equilateral two-pointed star graph with Kirchhoff matching at the vertex x = 0) with a qpointed equilateral star graph G ðqÞ 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 finally proposed. We recall the solvable PT-symmetric quantum square well on an interval of x E (–L, L) := G ð2Þ (with an a-dependent non-Hermiticity given by Robin boundary conditions) and generalize it. In essence, we just replace the support interval G ð2Þ (reinterpreted as an equilateral two-pointed star graph with Kirchhoff matching at the vertex x = 0) with a qpointed equilateral star graph G ðqÞ 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 finally proposed. (en)
Title	Quantum star-graph analogues of PT-symmetric square wells Quantum star-graph analogues of PT-symmetric square wells (en)
skos:prefLabel	Quantum star-graph analogues of PT-symmetric square wells Quantum star-graph analogues of PT-symmetric square wells (en)
skos:notation	RIV/61389005:_____/12:00388204!RIV13-AV0-61389005
http://linked.open...avai/predkladatel	Ústav jaderné fyziky AV ČR, v.v.i.
http://linked.open...avai/riv/aktivita	I P
http://linked.open...avai/riv/aktivity	I, P(GAP203/11/1433)
http://linked.open...iv/cisloPeriodika	12
http://linked.open...vai/riv/dodaniDat	2013
http://linked.open...aciTvurceVysledku	Znojil, Miloslav
http://linked.open.../riv/druhVysledku	J - Článek v odborném periodiku
http://linked.open...iv/duvernostUdaju	S - Úplné a pravdivé údaje nepodléhající ochraně podle zvláštních právních předpisů
http://linked.open...titaPredkladatele	Ústav jaderné fyziky AV ČR, v. v. i.
http://linked.open...dnocenehoVysledku	163836
http://linked.open...ai/riv/idVysledku	RIV/61389005:_____/12:00388204
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	non-Hermitian interactions; exactly solvable models; quantum graphs; equilateral q-pointed star; Robin boundary condition (en)
http://linked.open.../riv/klicoveSlovo	Robin boundary condition equilateral q-pointed star exactly solvable models non-Hermitian interactions quantum graphs
http://linked.open...odStatuVydavatele	CA - Kanada
http://linked.open...ontrolniKodProRIV	[8FAED90E1581]
http://linked.open...i/riv/nazevZdroje	Canadian Journal of Physics
http://linked.open...in/vavai/riv/obor	BE
http://linked.open...ichTvurcuVysledku	1 (xsd:int)
http://linked.open...cetTvurcuVysledku	1 (xsd:int)
http://linked.open...vavai/riv/projekt	The concept of cryptohermiticity in Quantum Theory and its applications
http://linked.open...UplatneniVysledku	2012
http://linked.open...v/svazekPeriodika	90
http://linked.open...iv/tvurceVysledku	Znojil, Miloslav
http://linked.open...ain/vavai/riv/wos	000312158000011
issn	0008-4204
number of pages	7 (xsd:int)
http://bibframe.org/vocab/doi	10.1139/P2012-107
is http://linked.open...avai/riv/vysledek of	Quantum star-graph analogues of PT-symmetric square wells

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