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: Dennis P. Clougherty, Nam H. Dinh
Format: Article
Language:English
Published: American Physical Society 2025-07-01
Series:Physical Review Research
Online Access:http://doi.org/10.1103/9fxx-2x6n
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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.
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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
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