From the point of view of perturbation theory, (perturbations of) near-resonant systems are plagued by small denominators. These do not affect (perturbations of) fully resonant systems; so it is in many ways convenient to approximate near resonant systems as fully resonant ones, which correspond to considering the "detuning" as a perturbation itself. This approach has proven very fruitful in Classical Mechanics, but it is also standard in (perturbations of) Quantum Mechanical systems. Actually, its origin may be traced back (at least) to the Rayleigh-Ritz method for computing eigenvalues and eigenvectors of perturbed matrix problems. We will discuss relations between these approaches, and consider some case study models in the different contexts.

Near-resonances and detuning in classical and quantum mechanics / G. Gaeta, G. Pucacco. - In: MATHEMATICS IN ENGINEERING. - ISSN 2640-3501. - 5:1(2022), pp. 1-44. [10.3934/mine.2023005]

Near-resonances and detuning in classical and quantum mechanics

G. Gaeta
Primo
;
2022

Abstract

From the point of view of perturbation theory, (perturbations of) near-resonant systems are plagued by small denominators. These do not affect (perturbations of) fully resonant systems; so it is in many ways convenient to approximate near resonant systems as fully resonant ones, which correspond to considering the "detuning" as a perturbation itself. This approach has proven very fruitful in Classical Mechanics, but it is also standard in (perturbations of) Quantum Mechanical systems. Actually, its origin may be traced back (at least) to the Rayleigh-Ritz method for computing eigenvalues and eigenvectors of perturbed matrix problems. We will discuss relations between these approaches, and consider some case study models in the different contexts.
perturbation theory; detuning; classical mechanics; quantum mechanics; resonance; near-resonance
Settore MAT/07 - Fisica Matematica
2022
Article (author)
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/903609
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