Resonance excitation of a damped quantum anharmonic oscillator

Nikolai N Rozanov, В. А. Смирнов

Nikolai N Rozanov, В. А. Смирнов

Nikolai N Rozanov, В. А. Смирнов

Daphna G. Enzer

Daphna G. Enzer, G. Gabrielse

Driving a damped, anharmonic oscillator produces stable, steady-state excitations according to the familiar classical description. A quantum mechanical description, however, shows the surprising result that such excitations are intrinsically unstable, and can be much smaller than classical expectations. We illustrate by calculating the motion of one electron in a magnetic field. This physically realizable system is among the simplest of nonlinear systems, being anharmonic because of special relativity and being damped by the spontaneous emission of synchrotron radiation.

Subir Kumar Bose, U. B. Dubey, N. Varma

The present review is devoted to the study of certain aspects of anharmonic, time-dependent and damped oscillator(s) system using different theoretical techniques. A theoretical understanding of these systems is important for application in many problems in physics, mechanics and other fields. We discuss in detail the difficulties in the theoretical analysis of the problem. In particular we discuss here the regular, well-behaved perturbative solution, the large quantum number behaviour of anharmonic oscillator(s) using the technique of coherent states, exact solution of quantum anharmonic oscillators, the electromagnetic radiation emitted by a charged particle executing damped anharmonic oscillator motion using Krylov-Bogoliubov approximation method, use of invariants to obtain solution and coherent states of time-dependent oscillator(s), the derivation of perturbative frequencies of a damped coupled anharmonic oscillators system using suitable canonical transformation in the framework of Hamilton-Jacobi formalism and the quantisation and construction of coherent states of a damped oscillator using time-dependent operators.