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

Result code in 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>
Result on the web
<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>

Result language
angličtina
Original language name
Solvable model of quantum phase transitions and the symbolic-manipulation-based study of its multiply degenerate exceptional points and of their unfolding
Original language 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 nea
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BE - Theoretical physics
OECD FORD branch
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Project
<a href="/en/project/GAP203%2F11%2F1433" target="_blank" >GAP203/11/1433: The concept of cryptohermiticity in Quantum Theory and its applications</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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