Star exponentials and Wigner functions for time-dependent harmonic oscillators
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866917948573089792 |
|---|---|
| author | Berra-Montiel, Jasel Contreras-Bear, Daniel Molgado, Alberto Sanchez-Cordova, Mar |
| author_facet | Berra-Montiel, Jasel Contreras-Bear, Daniel Molgado, Alberto Sanchez-Cordova, Mar |
| contents | In this paper, we address the Wigner distribution and the star exponential function for a time-dependent harmonic oscillator for which the mass and the frequency terms are considered explicitly depending on time. To such an end, we explore the connection between the star exponential, naturally emerging within the context of deformation quantization, and the propagators constructed through the path integral formalism. In particular, the Fourier-Dirichlet expansion of the star exponential implies a distinctive quantization of the Lewis-Riesenfeld invariant. Further, by introducing a judicious time variable, we recovered a time-dependent phase function associated with the Lewis-Riesenfeld construction of the standard Schrödinger picture. In particular, we applied our results to the cases of the Caldirola-Kanai and the time-dependent frequency harmonic oscillators, recovering relevant results previously reported in the literature. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_06384 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Star exponentials and Wigner functions for time-dependent harmonic oscillators Berra-Montiel, Jasel Contreras-Bear, Daniel Molgado, Alberto Sanchez-Cordova, Mar Quantum Physics Mathematical Physics 53D55, 81S30, 46F10, 70S05 In this paper, we address the Wigner distribution and the star exponential function for a time-dependent harmonic oscillator for which the mass and the frequency terms are considered explicitly depending on time. To such an end, we explore the connection between the star exponential, naturally emerging within the context of deformation quantization, and the propagators constructed through the path integral formalism. In particular, the Fourier-Dirichlet expansion of the star exponential implies a distinctive quantization of the Lewis-Riesenfeld invariant. Further, by introducing a judicious time variable, we recovered a time-dependent phase function associated with the Lewis-Riesenfeld construction of the standard Schrödinger picture. In particular, we applied our results to the cases of the Caldirola-Kanai and the time-dependent frequency harmonic oscillators, recovering relevant results previously reported in the literature. |
| title | Star exponentials and Wigner functions for time-dependent harmonic oscillators |
| topic | Quantum Physics Mathematical Physics 53D55, 81S30, 46F10, 70S05 |
| url | https://arxiv.org/abs/2503.06384 |