Quantum Lamb model
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2025
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866911040417038336 |
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| author | Clougherty, Dennis P. Dinh, Nam H. |
| author_facet | Clougherty, Dennis P. Dinh, Nam H. |
| contents | H. Lamb considered the classical dynamics of a vibrating particle embedded in an elastic medium before the development of quantum theory. Lamb was interested in how the back-action of the elastic waves generated can damp the vibrations of the particle. We propose a quantum version of Lamb's model. We show that this model is exactly solvable by using a multimode Bogoliubov transformation. We find that the exact system ground state is a multimode squeezed vacuum state, and we obtain the exact Bogoliubov frequencies by numerically solving a nonlinear integral equation. A closed-form expression for the damping rate of the particle is obtained, and it agrees with the result obtained by perturbation theory. The model provides a solvable example of the damped quantum harmonic oscillator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00562 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Quantum Lamb model Clougherty, Dennis P. Dinh, Nam H. Quantum Physics Mesoscale and Nanoscale Physics H. Lamb considered the classical dynamics of a vibrating particle embedded in an elastic medium before the development of quantum theory. Lamb was interested in how the back-action of the elastic waves generated can damp the vibrations of the particle. We propose a quantum version of Lamb's model. We show that this model is exactly solvable by using a multimode Bogoliubov transformation. We find that the exact system ground state is a multimode squeezed vacuum state, and we obtain the exact Bogoliubov frequencies by numerically solving a nonlinear integral equation. A closed-form expression for the damping rate of the particle is obtained, and it agrees with the result obtained by perturbation theory. The model provides a solvable example of the damped quantum harmonic oscillator. |
| title | Quantum Lamb model |
| topic | Quantum Physics Mesoscale and Nanoscale Physics |
| url | https://arxiv.org/abs/2503.00562 |