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

Kód výsledku v 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>

Nalezeny alternativní kódy

RIV/62690094:18470/24:50021409

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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).

Název v anglickém jazyce

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

Popis výsledku anglicky

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).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10301 - Atomic, molecular and chemical physics (physics of atoms and molecules including collision, interaction with radiation, magnetic resonances, Mössbauer effect)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2024

Kód důvěrnosti údajů

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

Název periodika

Physica Scripta

ISSN

0031-8949

e-ISSN

1402-4896

Svazek periodika

99

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

11

Strana od-do

035250

Kód UT WoS článku

001174878000001

EID výsledku v databázi Scopus

2-s2.0-85186264941