Quantum Lamb model
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 mod...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2025-07-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/9fxx-2x6n |
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| _version_ | 1849427920172351488 |
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| author | Dennis P. Clougherty Nam H. Dinh |
| author_facet | Dennis P. Clougherty Nam H. Dinh |
| author_sort | Dennis P. Clougherty |
| collection | DOAJ |
| description | 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 | Article |
| id | doaj-art-3185c910118d4e08b9941671e308ba4c |
| institution | Kabale University |
| issn | 2643-1564 |
| language | English |
| publishDate | 2025-07-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj-art-3185c910118d4e08b9941671e308ba4c2025-08-20T03:28:52ZengAmerican Physical SocietyPhysical Review Research2643-15642025-07-0173L03200410.1103/9fxx-2x6nQuantum Lamb modelDennis P. CloughertyNam H. DinhH. 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.http://doi.org/10.1103/9fxx-2x6n |
| spellingShingle | Dennis P. Clougherty Nam H. Dinh Quantum Lamb model Physical Review Research |
| title | Quantum Lamb model |
| title_full | Quantum Lamb model |
| title_fullStr | Quantum Lamb model |
| title_full_unstemmed | Quantum Lamb model |
| title_short | Quantum Lamb model |
| title_sort | quantum lamb model |
| url | http://doi.org/10.1103/9fxx-2x6n |
| work_keys_str_mv | AT dennispclougherty quantumlambmodel AT namhdinh quantumlambmodel |