Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2024
|
| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2405.01187 |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866907888803381248 |
|---|---|
| author | Ruby V, Chithiika M, Lakshmanan |
| author_facet | Ruby V, Chithiika M, Lakshmanan |
| contents | Liénard-type nonlinear oscillators with linear and nonlinear damping terms exhibit diverse dynamical behavior in both the classical and quantum regimes. In this paper, we consider examples of various one-dimensional Liénard type-I and type-II oscillators. The associated Euler-Lagrange equations are divided into groups based on the characteristics of the damping and forcing terms. The Liénard type-I oscillators often display localized solutions, isochronous and non-isochronous oscillations and are also precisely solvable in quantum mechanics in general, where the ordering parameters play an important role. These include Mathews-Lakshmanan and Higgs oscillators. However, the classical solutions of some of the nonlinear oscillators are expressed in terms of elliptic functions and have been found to be quasi-exactly solvable in the quantum region. The three-dimensional generalizations of these classical systems add more degrees of freedom, which show complex dynamics. Their quantum equivalents are also explored in this article. The isotonic generalizations of the non-isochronous nonlinear oscillators have also been solved both classically and quantum mechanically to advance the studies. The modified Emden equation categorized as Liénard type-II exhibits isochronous oscillations at the classical level. This property makes it a valuable tool for studying the underlying nonlinear dynamics. The study on the quantum counterpart of the system provides a deeper understanding of the behavior in the quantum realm as a typical PT-symmetric system. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_01187 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Liénard Type Nonlinear Oscillators and Quantum Solvability Ruby V, Chithiika M, Lakshmanan Quantum Physics Exactly Solvable and Integrable Systems Liénard-type nonlinear oscillators with linear and nonlinear damping terms exhibit diverse dynamical behavior in both the classical and quantum regimes. In this paper, we consider examples of various one-dimensional Liénard type-I and type-II oscillators. The associated Euler-Lagrange equations are divided into groups based on the characteristics of the damping and forcing terms. The Liénard type-I oscillators often display localized solutions, isochronous and non-isochronous oscillations and are also precisely solvable in quantum mechanics in general, where the ordering parameters play an important role. These include Mathews-Lakshmanan and Higgs oscillators. However, the classical solutions of some of the nonlinear oscillators are expressed in terms of elliptic functions and have been found to be quasi-exactly solvable in the quantum region. The three-dimensional generalizations of these classical systems add more degrees of freedom, which show complex dynamics. Their quantum equivalents are also explored in this article. The isotonic generalizations of the non-isochronous nonlinear oscillators have also been solved both classically and quantum mechanically to advance the studies. The modified Emden equation categorized as Liénard type-II exhibits isochronous oscillations at the classical level. This property makes it a valuable tool for studying the underlying nonlinear dynamics. The study on the quantum counterpart of the system provides a deeper understanding of the behavior in the quantum realm as a typical PT-symmetric system. |
| title | Liénard Type Nonlinear Oscillators and Quantum Solvability |
| topic | Quantum Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2405.01187 |