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VOLUME 113 (2021) | ISSUE 2 | PAGE 132
Resonant excitation of oscillator with randomly shifted levels
The problem of resonant excitation of a harmonic oscillator whose energy levels are slightly shifted is solved. It is shown that, in this case, there exists a threshold magnitude of the exciting resonance field, below which the excitation is localized on lower levels, and above which the oscillator is indefinitely excited so that it is necessary to take into account dissipative processes. A method similar to that developed for the oscillator is applied to examine the localization of electrons in a wire with cross-section varying along its length. It is shown, in particular, that there is no localization if this variation is superlinear.