Generalized Bose-Hubbard Hamiltonians exhibiting a complete non-Hermitian degeneracy
Result description
The method of construction of the tridiagonal and symmetric complex-matrix Hamiltonians H-(N)(z) exhibiting an exceptional point (EP) degeneracy of the Nth (i.e., maximal) order at a preselected parameter z = z((EPN)) = 1 is proposed and tested. In general, the implementation of the method requires the use of computer-assisted symbolic manipulations, especially at the larger matrix dimensions N. The well known PT-symmetric N-by-N-matrix Bose-Hubbard Hamiltonians as well as their recent N <= 5 non-Bose-Hubbard alternatives are obtained as special solutions. Several other N >= 6 non-Bose-Hubbard models H-(N)(z) exhibiting the maximal EPN degeneracy are also constructed and analyzed in detail. In particular, their z-dependent, real or complex spectra of energies are displayed and discussed near as well as far from z((EPN)).
Keywords
non-Hermitian quantum dynamicsmultilevel degeneracieshigher-order exceptional points
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
Generalized Bose-Hubbard Hamiltonians exhibiting a complete non-Hermitian degeneracy
Original language description
The method of construction of the tridiagonal and symmetric complex-matrix Hamiltonians H-(N)(z) exhibiting an exceptional point (EP) degeneracy of the Nth (i.e., maximal) order at a preselected parameter z = z((EPN)) = 1 is proposed and tested. In general, the implementation of the method requires the use of computer-assisted symbolic manipulations, especially at the larger matrix dimensions N. The well known PT-symmetric N-by-N-matrix Bose-Hubbard Hamiltonians as well as their recent N <= 5 non-Bose-Hubbard alternatives are obtained as special solutions. Several other N >= 6 non-Bose-Hubbard models H-(N)(z) exhibiting the maximal EPN degeneracy are also constructed and analyzed in detail. In particular, their z-dependent, real or complex spectra of energies are displayed and discussed near as well as far from z((EPN)).
Czech name
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Czech description
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Classification
Type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Result continuities
Project
GA16-22945S: Quantum Wheeler-DeWitt equation and its unitary evolution interpretation
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2019
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Annals of Physics
ISSN
0003-4916
e-ISSN
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Volume of the periodical
405
Issue of the periodical within the volume
6
Country of publishing house
US - UNITED STATES
Number of pages
15
Pages from-to
325-339
UT code for WoS article
000469902700021
EID of the result in the Scopus database
2-s2.0-85064438464
Result type
Jimp - Article in a specialist periodical, which is included in the Web of Science database
OECD FORD
Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)
Year of implementation
2019