Quantum Lamb model

• URL: http://arxiv.org/abs/2503.00562v2
• Date: Tue, 25 Mar 2025 01:04:56 GMT
• Title: Quantum Lamb model
• Authors: Dennis P. Clougherty, Nam H. Dinh,
• Abstract summary: H. Lamb considered the classical dynamics of a vibrating particle embedded in an elastic medium before the development of quantum theory.<n>We show that this model is exactly solvable by using a multimode Bogoliubov transformation.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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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