Unitarity corridors to exceptional points
Result description
Phenomenological quantum Hamiltonians H-(N)(lambda) = J((N)) + lambda V-(N) (lambda) representing a general real N-2-parametric perturbation of an exceptional-point-related unperturbed Jordan-block Hamiltonian J((N)) are considered. Tractable as non-Hermitian (in a preselected, unphysical Hilbert space) as well as, simultaneously, Hermitian (in another, 'physical' Hilbert space), these matrices may represent a unitary, closed quantum system if and only if the spectrum is real. At small A we show that the parameters are then confined to a 'stability corridor' S of the access to the extreme dynamical exceptional-point lambda -> 0 regime. The corridors are narrow and N-dependent: they are formed by multiscale perturbations which are small in physical Hilbert space, i.e., which are such that lambda V-j+k,j((N)) (lambda) = O (lambda((k+1)/2)) at k = 1, 2, ..., N - 1 and all j.
Keywords
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
Unitarity corridors to exceptional points
Original language description
Phenomenological quantum Hamiltonians H-(N)(lambda) = J((N)) + lambda V-(N) (lambda) representing a general real N-2-parametric perturbation of an exceptional-point-related unperturbed Jordan-block Hamiltonian J((N)) are considered. Tractable as non-Hermitian (in a preselected, unphysical Hilbert space) as well as, simultaneously, Hermitian (in another, 'physical' Hilbert space), these matrices may represent a unitary, closed quantum system if and only if the spectrum is real. At small A we show that the parameters are then confined to a 'stability corridor' S of the access to the extreme dynamical exceptional-point lambda -> 0 regime. The corridors are narrow and N-dependent: they are formed by multiscale perturbations which are small in physical Hilbert space, i.e., which are such that lambda V-j+k,j((N)) (lambda) = O (lambda((k+1)/2)) at k = 1, 2, ..., N - 1 and all j.
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
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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
Physical Review A
ISSN
2469-9926
e-ISSN
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Volume of the periodical
100
Issue of the periodical within the volume
3
Country of publishing house
US - UNITED STATES
Number of pages
9
Pages from-to
032124
UT code for WoS article
000488248700004
EID of the result in the Scopus database
2-s2.0-85072921563
Basic information
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