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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F13%3A00395959" target="_blank" >RIV/61389005:_____/13:00395959 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1016/j.aop.2013.05.016" target="_blank" >http://dx.doi.org/10.1016/j.aop.2013.05.016</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.aop.2013.05.016" target="_blank" >10.1016/j.aop.2013.05.016</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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 nea

Název v anglickém jazyce

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

Popis výsledku anglicky

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 nea

Druh

J_x - Nezařazeno - Článek v odborném periodiku (Jimp, Jsc a Jost)

CEP obor

BE - Teoretická fyzika

OECD FORD obor

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Projekt

<a href="/cs/project/GAP203%2F11%2F1433" target="_blank" >GAP203/11/1433: Kryptohermitovské pojetí kvantové teorie a jejích aplikací</a><br>

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2013

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Annals of Physics

ISSN

0003-4916

e-ISSN

—

Svazek periodika

336

Číslo periodika v rámci svazku

SEP

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

14

Strana od-do

98-111

Kód UT WoS článku

000322847400006

EID výsledku v databázi Scopus

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