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The Classical and Quantum Lamb Model
Dinh, Nam H.
Dinh, Nam H.
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In 1900, Horace Lamb considered the classical dynamics of a vibrating particle embedded in an elastic medium. Lamb described how the back action of the elastic waves generated damps the vibrations of the particle. This process is of renewed interest in the quantum regime. The quantum theory of such dissipative systems finds relevance to a variety of mesoscopic and nanoscopic mechanical systems currently under intense experimental study. The Lamb model is revisited here using a Lagrangian framework. The coupling between the vibrating particle and the elastic medium arises from enforcing a holonomic constraint with a Lagrange multiplier. The classical equations of motion, obtained from the Lagrangian, are subsequently solved exactly using integral transform methods. The model is then quantized, and the acoustic power radiated is calculated using time-dependent perturbation theory. These results are valid in the regime of light damping.
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2024-01-01
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