On the metric operator for the imaginary cubic oscillator
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F12%3A00388200" target="_blank" >RIV/61389005:_____/12:00388200 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1103/PhysRevD.86.121702" target="_blank" >http://dx.doi.org/10.1103/PhysRevD.86.121702</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1103/PhysRevD.86.121702" target="_blank" >10.1103/PhysRevD.86.121702</a>
Alternative languages
Result language
angličtina
Original language name
On the metric operator for the imaginary cubic oscillator
Original language description
We show that the eigenvectors of the PT-symmetric imaginary cubic oscillator are complete, but do not form a Riesz basis. This results in the existence of a bounded metric operator having intrinsic singularity reflected in the inevitable unboundedness ofthe inverse. Moreover, the existence of nontrivial pseudospectrum is observed. In other words, there is no quantum-mechanical Hamiltonian associated with it via bounded and boundedly invertible similarity transformations. These results open new directions in physical interpretation of PT-symmetric models with intrinsically singular metric, since their properties are essentially different with respect to self-adjoint Hamiltonians, for instance, due to spectral instabilities.
Czech name
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Czech description
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Classification
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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Result continuities
Project
<a href="/en/project/GAP203%2F11%2F0701" target="_blank" >GAP203/11/0701: Guided Quantum Dynamics</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2012
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Physical Review D: Particles, Fields, Gravitation and Cosmology
ISSN
1550-7998
e-ISSN
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Volume of the periodical
86
Issue of the periodical within the volume
12
Country of publishing house
US - UNITED STATES
Number of pages
6
Pages from-to
"121702/1"-"121702/6"
UT code for WoS article
000311928000001
EID of the result in the Scopus database
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