Equations of motion governing the dynamics of the exceptional points of parameterically dependent nonhermitian Hamiltonians

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389021%3A_____%2F23%3A00571732" target="_blank" >RIV/61389021:_____/23:00571732 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/00216208:11320/23:10475044

Výsledek na webu

<a href="https://iopscience.iop.org/article/10.1088/1751-8121/acc0ea" target="_blank" >https://iopscience.iop.org/article/10.1088/1751-8121/acc0ea</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1088/1751-8121/acc0ea" target="_blank" >10.1088/1751-8121/acc0ea</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Equations of motion governing the dynamics of the exceptional points of parameterically dependent nonhermitian Hamiltonians

Popis výsledku v původním jazyce

We study exceptional points (EPs) of a nonhermitian Hamiltonian circumflex expressionccent H(lambda, delta) whose parameters lambda is an element of C and (delta is an element of R. As the real control parameter (delta is varied, the kth EP (or kth cluster of simultaneously existing EPs) of circumflex expressionccent H(lambda, delta) moves in the complex plane of lambda along a continuous trajectory, lambda(k)(delta). Using an appropriate non-hermitian formalism (based upon the c-product and not upon the conventional Dirac product), we derive a self-contained set of equations of motion (EOM) for the trajectory lambda(k)(delta), while interpreting delta as the propagation time. Such EOM become of interest whenever one wishes to study the response of EPs to external perturbations or continuous parametric changes of the pertinent Hamiltonian. This is e.g. the case of EPs emanating from hermitian curve crossings/degeneracies (which turn into avoided crossings/neardegeneracies when the Hamiltonian parameters are continuously varied). The presented EOM for EPs have not only their theoretical merits, they possess also a substantial practical relevance. Namely, the just presented approach can be regarded even as an efficient numerical method, useful for generating EPs for a broad class of complex quantum systems encountered in atomic, nuclear and condensed matter physics. Performance of such a method is tested here numerically on a simple yet nontrivial toy model.

Název v anglickém jazyce

Equations of motion governing the dynamics of the exceptional points of parameterically dependent nonhermitian Hamiltonians

Popis výsledku anglicky

We study exceptional points (EPs) of a nonhermitian Hamiltonian circumflex expressionccent H(lambda, delta) whose parameters lambda is an element of C and (delta is an element of R. As the real control parameter (delta is varied, the kth EP (or kth cluster of simultaneously existing EPs) of circumflex expressionccent H(lambda, delta) moves in the complex plane of lambda along a continuous trajectory, lambda(k)(delta). Using an appropriate non-hermitian formalism (based upon the c-product and not upon the conventional Dirac product), we derive a self-contained set of equations of motion (EOM) for the trajectory lambda(k)(delta), while interpreting delta as the propagation time. Such EOM become of interest whenever one wishes to study the response of EPs to external perturbations or continuous parametric changes of the pertinent Hamiltonian. This is e.g. the case of EPs emanating from hermitian curve crossings/degeneracies (which turn into avoided crossings/neardegeneracies when the Hamiltonian parameters are continuously varied). The presented EOM for EPs have not only their theoretical merits, they possess also a substantial practical relevance. Namely, the just presented approach can be regarded even as an efficient numerical method, useful for generating EPs for a broad class of complex quantum systems encountered in atomic, nuclear and condensed matter physics. Performance of such a method is tested here numerically on a simple yet nontrivial toy model.

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

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Journal of Physics A-Mathematical and Theoretical

ISSN

1751-8113

e-ISSN

1751-8121

Svazek periodika

56

Číslo periodika v rámci svazku

14

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

27

Strana od-do

145201

Kód UT WoS článku

000948843000001

EID výsledku v databázi Scopus

2-s2.0-85150416276