From quantum ladder climbing to classical autoresonance

A classic autoresonance phenomenon as an alternative to quantum ladder climbing is discussed. Excitation of a classical, nonlinear system to high energies is achieved in the autoresonance phenomenon by using a weak, chirped frequency forcing. The conditions for transition from quantum to classical regimes were elaborated and the similarities and differences between the two approaches were discussed. It was observed that if the conditions for classicality were met, it was possible to use a more transparent classical theory instead of the quantum-mechanical formulation.