Hybrid form of quantum theory with non-Hermitian Hamiltonians

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F23%3A00570944" target="_blank" >RIV/61389005:_____/23:00570944 - isvavai.cz</a>
Alternative codes found
RIV/62690094:18470/23:50020913
Result on the web
<a href="https://doi.org/10.1016/j.physleta.2022.128556" target="_blank" >https://doi.org/10.1016/j.physleta.2022.128556</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.physleta.2022.128556" target="_blank" >10.1016/j.physleta.2022.128556</a>

Result language
angličtina
Original language name
Hybrid form of quantum theory with non-Hermitian Hamiltonians
Original language description
In Schrodinger picture the unitarity of evolution is usually guaranteed by the Hermiticity of the Hamiltonian operator 1) = 1)dagger in a conventional Hilbert space Htextbook. After a Dyson-inspired operatortransformation (OT) non-unitary preconditioning S2 : 1) -> H the simplified Hamiltonian H is, in its manifestly unphysical Hilbert space Hauxiliary, non-Hermitian. Besides its natural OT-based physical interpretation it can also be 'Hermitized' (i.e., made compatible with the unitarity) via a metric-amendment (MA) change of the Hilbert space, Hauxiliary -> Hphysical. In our present letter we propose another, third, hybrid form (HF) of the Hermitization of H in which the change involves, simultaneously, both the Hamiltonian and the metric. Formally this means that the original Dyson map is assumed factorizable, S2 = S2MS2H. A key practical advantage of the new HF approach lies in the model-dependent adaptability of such a factorization. The flexibility and possible optimality of the balance between the MA-related (i.e., metric-amending) factor S2M and the OT-related (i.e., Hamiltonian-changing) factor S2H are explicitly illustrated via an elementary two-state quantum model.
Czech name
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Czech description
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Type
J<sub>imp</sub> - 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)

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2023
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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