Unitary unfoldings of a Bose-Hubbard exceptional point with and without particle number conservation

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F62690094%3A18470%2F20%3A50017331" target="_blank" >RIV/62690094:18470/20:50017331 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/61389005:_____/20:00534289

Výsledek na webu

<a href="https://royalsocietypublishing.org/doi/10.1098/rspa.2020.0292" target="_blank" >https://royalsocietypublishing.org/doi/10.1098/rspa.2020.0292</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1098/rspa.2020.0292" target="_blank" >10.1098/rspa.2020.0292</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Unitary unfoldings of a Bose-Hubbard exceptional point with and without particle number conservation

Popis výsledku v původním jazyce

The conventional non-Hermitian but PT-symmetric three-parametric Bose-Hubbard Hamiltonian H(gamma, v, c) represents a quantum system of N bosons, unitary only for parameters gamma, v and c in a domain D. Its boundary partial derivative D contains an exceptional point of order K (EPK; K=N+1) at c=0 and gamma=v, but even at the smallest non-vanishing parameter c not equal 0 the spectrum of H(v, v, c) ceases to be real, i.e. the system ceases to be observable. In this paper, the question is inverted: all of the stable, unitary and observable Bose-Hubbard quantum systems are sought which would lie close to the phenomenologically most interesting EPK-related dynamical regime. Two different families of such systems are found. Both of them are characterized by the perturbed Hamiltonians H(lambda)=H(v,v,0)+lambda V for which the unitarity and stability of the system is guaranteed. In the first family the number N of bosons is assumed conserved while in the second family such an assumption is relaxed. Attention is paid mainly to an anisotropy of the physical Hilbert space near the EPK extreme. We show that it is reflected by a specific, operationally realizable structure of perturbations lambda V which can be considered small.

Název v anglickém jazyce

Unitary unfoldings of a Bose-Hubbard exceptional point with and without particle number conservation

Popis výsledku anglicky

The conventional non-Hermitian but PT-symmetric three-parametric Bose-Hubbard Hamiltonian H(gamma, v, c) represents a quantum system of N bosons, unitary only for parameters gamma, v and c in a domain D. Its boundary partial derivative D contains an exceptional point of order K (EPK; K=N+1) at c=0 and gamma=v, but even at the smallest non-vanishing parameter c not equal 0 the spectrum of H(v, v, c) ceases to be real, i.e. the system ceases to be observable. In this paper, the question is inverted: all of the stable, unitary and observable Bose-Hubbard quantum systems are sought which would lie close to the phenomenologically most interesting EPK-related dynamical regime. Two different families of such systems are found. Both of them are characterized by the perturbed Hamiltonians H(lambda)=H(v,v,0)+lambda V for which the unitarity and stability of the system is guaranteed. In the first family the number N of bosons is assumed conserved while in the second family such an assumption is relaxed. Attention is paid mainly to an anisotropy of the physical Hilbert space near the EPK extreme. We show that it is reflected by a specific, operationally realizable structure of perturbations lambda V which can be considered small.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10303 - Particles and field physics

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2020

Kód důvěrnosti údajů

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

Název periodika

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

ISSN

1364-5021

e-ISSN

—

Svazek periodika

476

Číslo periodika v rámci svazku

2242

Stát vydavatele periodika

GB - Spojené království Velké Británie a Severního Irska

Počet stran výsledku

19

Strana od-do

"Article Number: 20200292"

Kód UT WoS článku

000581913500001

EID výsledku v databázi Scopus

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