A Reappraisal of Lagrangians with Non-Quadratic Velocity Dependence and Branched Hamiltonians

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61389005%3A_____%2F24%3A00588316" target="_blank" >RIV/61389005:_____/24:00588316 - isvavai.cz</a>

Nalezeny alternativní kódy

RIV/62690094:18470/24:50021892

Výsledek na webu

<a href="https://doi.org/10.3390/sym16070860" target="_blank" >https://doi.org/10.3390/sym16070860</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3390/sym16070860" target="_blank" >10.3390/sym16070860</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A Reappraisal of Lagrangians with Non-Quadratic Velocity Dependence and Branched Hamiltonians

Popis výsledku v původním jazyce

Time and again, non-conventional forms of Lagrangians with non-quadratic velocity dependence have received attention in the literature. For one thing, such Lagrangians have deep connections with several aspects of nonlinear dynamics including specifically the types of the Liénard class, for another, very often, the problem of their quantization opens up multiple branches of the corresponding Hamiltonians, ending up with the presence of singularities in the associated eigenfunctions. In this article, we furnish a brief review of the classical theory of such Lagrangians and the associated branched Hamiltonians, starting with the example of Liénard-type systems. We then take up other cases where the Lagrangians depend on velocity with powers greater than two while still having a tractable mathematical structure, while also describing the associated branched Hamiltonians for such systems. For various examples, we emphasize the emergence of the notion of momentum-dependent mass in the theory of branched Hamiltonians.

Název v anglickém jazyce

A Reappraisal of Lagrangians with Non-Quadratic Velocity Dependence and Branched Hamiltonians

Popis výsledku anglicky

Time and again, non-conventional forms of Lagrangians with non-quadratic velocity dependence have received attention in the literature. For one thing, such Lagrangians have deep connections with several aspects of nonlinear dynamics including specifically the types of the Liénard class, for another, very often, the problem of their quantization opens up multiple branches of the corresponding Hamiltonians, ending up with the presence of singularities in the associated eigenfunctions. In this article, we furnish a brief review of the classical theory of such Lagrangians and the associated branched Hamiltonians, starting with the example of Liénard-type systems. We then take up other cases where the Lagrangians depend on velocity with powers greater than two while still having a tractable mathematical structure, while also describing the associated branched Hamiltonians for such systems. For various examples, we emphasize the emergence of the notion of momentum-dependent mass in the theory of branched Hamiltonians.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

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

Symmetry-Basel

ISSN

2073-8994

e-ISSN

2073-8994

Svazek periodika

16

Číslo periodika v rámci svazku

7

Stát vydavatele periodika

CH - Švýcarská konfederace

Počet stran výsledku

16

Strana od-do

860

Kód UT WoS článku

001277631800001

EID výsledku v databázi Scopus

2-s2.0-85199896324