Discrete-coordinate crypto-Hermitian quantum system controlled by time-dependent Robin boundary conditions

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F24%3A00584744" target="_blank" >RIV/61389005:_____/24:00584744 - isvavai.cz</a>

Alternative codes found

RIV/62690094:18470/24:50021409

Result on the web

<a href="https://doi.org/10.1088/1402-4896/ad298b" target="_blank" >https://doi.org/10.1088/1402-4896/ad298b</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1402-4896/ad298b" target="_blank" >10.1088/1402-4896/ad298b</a>

Result language

angličtina

Original language name

Discrete-coordinate crypto-Hermitian quantum system controlled by time-dependent Robin boundary conditions

Original language description

A family of exactly solvable quantum square wells with discrete coordinates and with certain non-stationary Hermiticity-violating Robin boundary conditions is proposed and studied. Manifest non-Hermiticity of the model in conventional Hilbert space Hfriendly is required to coexist with the unitarity of system in another, ad hoc Hilbert space Hphysical . Thus, quantum mechanics in its non-Hermitian interaction picture (NIP) representation is to be used. We must construct the time-dependent states (say, psi(t)) as well as the time-dependent observables (say, Lambda(t)). Their evolution in time is generated by the operators denoted, here, by the respective symbols G(t) (a Schrodinger-equation generator) and sigma(t) (a Heisenberg-equation generator, a.k.a. quantum Coriolis force). The unitarity of evolution in Hphysical is then guaranteed by the reality of spectrum of the energy observable alias Hamiltonian H(t) = G(t) + sigma(t). The applicability of these ideas is illustrated via an N by N matrix model. At N = 2, closed formulae are presented not only for the measurable instantaneous energy spectrum but also for all of the eligible time-dependent physical inner-product metrics Theta(N=2)(t), for the related Dyson maps omega(N=2)(t), for the Coriolis force sigma(N=2)(t) as well as, in the very ultimate step of the construction, for the truly nontrivial Schrodinger-equation generator G (N=2)(t).

Czech name

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Czech description

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Type

J_imp - 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

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2024

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Physica Scripta

ISSN

0031-8949

e-ISSN

1402-4896

Volume of the periodical

99

Issue of the periodical within the volume

3

Country of publishing house

GB - UNITED KINGDOM

Number of pages

11

Pages from-to

035250

UT code for WoS article

001174878000001

EID of the result in the Scopus database

2-s2.0-85186264941