Quantum corrections to the classical model of the atom-field system

Author: Simon Chkhaidze
Co-authors: A. Ugulava, G. Mchedlishvili, L. Chotorlishvili
Keywords: Resonance in nonlinear oscillation, moderate nonlinearity, quantum pendulum
Annotation:

The nonlinear-oscillating system in action-angle variables is characterized by the dependence of frequency of oscillation on action. Periodic perturbation is capable of realizing in the system a stable nonlinear resonance at which the action adapts to the resonance condition, that is, “sticking” in the resonance frequency. For a particular physical problem there may be a case when action is the classical quantity, whereas its correction is the quantum quantity. Naturally, dynamics of action correction is described by the quantum equation of motion. In particular, in the moderate nonlinearity approximation, the description of quantum state is reduced to the solution of the Mathieu-Schr¨odinger equation. The state formed as a result of sticking in resonance is an eigenstate of the action correction operator that does not commute with the Hamiltonian. Expanding the eigenstate wave functions in Hamiltonian eigenfunctions, one can obtain a probability distribution of energy level population. Thus, an inverse level population for times lower than the relaxation time can be obtained

Lecture files:

Quantum corrections to the classical model of the atom-field system [en]
ატომი – ველი სისტემის კლასიკური მოდელის კვანტური შესწორება [ka]