About: Solvable model of quantum phase transitions and the symbolic-manipulation-based study of its multiply degenerate exceptional points and of their unfolding

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About: Solvable model of quantum phase transitions and the symbolic-manipulation-based study of its multiply degenerate exceptional points and of their unfolding Goto Sponge NotDistinct Permalink

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rdf:type	skos:Concept http://linked.opendata.cz/ontology/domain/vavai/Vysledek
Description	It is known that the practical use of non-Hermitian (i.e., typically, PT-symmetric) phenomenological quantum Hamiltonians H not equal HI requires an efficient reconstruction of an ad hoc Hilbert-space metric Theta = Theta(H) which would render the time-evolution unitary. Once one considers just the N-dimensional matrix toy models H = H-(N), the matrix elements of Theta(H) may be defined via a coupled set of N-2 polynomial equations. Their solution is a typical task for computer-assisted symbolic manipulations. The feasibility of such a model-completion construction is illustrated here via a discrete square well model H = p(2) + V endowed with a k-parametric close-to-the-boundary interaction V. The model is shown to possess (possibly, multiply degenerate) exceptional points marking the phase transitions which are attributable, due to the exact solvability of the model at any N < infinity, to the loss of the regularity of the metric. In the parameter-dependence of the energy spectrum near these singularities one encounters a broad variety of alternative, topologically non-equivalent scenarios. It is known that the practical use of non-Hermitian (i.e., typically, PT-symmetric) phenomenological quantum Hamiltonians H not equal HI requires an efficient reconstruction of an ad hoc Hilbert-space metric Theta = Theta(H) which would render the time-evolution unitary. Once one considers just the N-dimensional matrix toy models H = H-(N), the matrix elements of Theta(H) may be defined via a coupled set of N-2 polynomial equations. Their solution is a typical task for computer-assisted symbolic manipulations. The feasibility of such a model-completion construction is illustrated here via a discrete square well model H = p(2) + V endowed with a k-parametric close-to-the-boundary interaction V. The model is shown to possess (possibly, multiply degenerate) exceptional points marking the phase transitions which are attributable, due to the exact solvability of the model at any N < infinity, to the loss of the regularity of the metric. In the parameter-dependence of the energy spectrum near these singularities one encounters a broad variety of alternative, topologically non-equivalent scenarios. (en)
Title	Solvable model of quantum phase transitions and the symbolic-manipulation-based study of its multiply degenerate exceptional points and of their unfolding Solvable model of quantum phase transitions and the symbolic-manipulation-based study of its multiply degenerate exceptional points and of their unfolding (en)
skos:prefLabel	Solvable model of quantum phase transitions and the symbolic-manipulation-based study of its multiply degenerate exceptional points and of their unfolding Solvable model of quantum phase transitions and the symbolic-manipulation-based study of its multiply degenerate exceptional points and of their unfolding (en)
skos:notation	RIV/61389005:_____/13:00395959!RIV14-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	SEP
http://linked.open...vai/riv/dodaniDat	2014
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	106277
http://linked.open...ai/riv/idVysledku	RIV/61389005:_____/13:00395959
http://linked.open...riv/jazykVysledku	eng - angličtina
http://linked.open.../riv/klicovaSlova	Non-Hermitian quantum Hamiltonian; exceptional point; phase transition; exactly solvable model (en)
http://linked.open.../riv/klicoveSlovo	phase transition Non-Hermitian quantum Hamiltonian exactly solvable model exceptional point
http://linked.open...odStatuVydavatele	US - Spojené státy americké
http://linked.open...ontrolniKodProRIV	[160B5DA6AEF6]
http://linked.open...i/riv/nazevZdroje	Annals 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	2013
http://linked.open...v/svazekPeriodika	336
http://linked.open...iv/tvurceVysledku	Znojil, Miloslav
http://linked.open...ain/vavai/riv/wos	000322847400006
issn	0003-4916
number of pages	14 (xsd:int)
http://bibframe.org/vocab/doi	10.1016/j.aop.2013.05.016

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