Quantum phase transitions mediated by clustered non-Hermitian degeneracies

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F21%3A00542746" target="_blank" >RIV/61389005:_____/21:00542746 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/62690094:18470/21:50018614

Výsledek na webu

<a href="https://doi.org/10.1103/PhysRevE.103.032120" target="_blank" >https://doi.org/10.1103/PhysRevE.103.032120</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1103/PhysRevE.103.032120" target="_blank" >10.1103/PhysRevE.103.032120</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Quantum phase transitions mediated by clustered non-Hermitian degeneracies

Popis výsledku v původním jazyce

The phenomenon of degeneracy of an N-plet of bound states is studied in the framework of the quasi-Hermitian (a.k.a. PT-symmetric) formulation of quantum theory of closed systems. For a general non-Hermitian Hamiltonian H = H(lambda) such a degeneracy may occur at a real Kato's exceptional point lambda((EPN)) of order N and of the geometric multiplicity alias clusterization index K. The corresponding unitary process of collapse (loss of observability) can be then interpreted as a generic quantum phase transition. The dedicated literature deals, predominantly, with the non-numerical benchmark models of the simplest processes where K = 1. In our present paper it is shown that in the 'anomalous' dynamical scenarios with 1 < K <= N/2 an analogous approach is applicable. A multiparametric anharmonic-oscillator-type exemplification of such systems is constructed as a set of real-matrix N by N Hamiltonians which are exactly solvable, maximally non-Hermitian, and labeled by specific ad hoc partitionings R(N) of N.

Název v anglickém jazyce

Quantum phase transitions mediated by clustered non-Hermitian degeneracies

Popis výsledku anglicky

The phenomenon of degeneracy of an N-plet of bound states is studied in the framework of the quasi-Hermitian (a.k.a. PT-symmetric) formulation of quantum theory of closed systems. For a general non-Hermitian Hamiltonian H = H(lambda) such a degeneracy may occur at a real Kato's exceptional point lambda((EPN)) of order N and of the geometric multiplicity alias clusterization index K. The corresponding unitary process of collapse (loss of observability) can be then interpreted as a generic quantum phase transition. The dedicated literature deals, predominantly, with the non-numerical benchmark models of the simplest processes where K = 1. In our present paper it is shown that in the 'anomalous' dynamical scenarios with 1 < K <= N/2 an analogous approach is applicable. A multiparametric anharmonic-oscillator-type exemplification of such systems is constructed as a set of real-matrix N by N Hamiltonians which are exactly solvable, maximally non-Hermitian, and labeled by specific ad hoc partitionings R(N) of N.

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

2021

Kód důvěrnosti údajů

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

Název periodika

Physical Review E

ISSN

2470-0045

e-ISSN

2470-0053

Svazek periodika

103

Číslo periodika v rámci svazku

3

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

13

Strana od-do

032120

Kód UT WoS článku

000650938800005

EID výsledku v databázi Scopus

2-s2.0-85102943972