On the dynamics of a linear and a nonlinear quantum oscillator with randomly changing harmonic frequency

Numerical experiments with a nonlinear (lambda x(4)) oscillator which has its harmonic frequency changing randomly with time reveal certain interesting features of its dynamics of quantum evolution. When lambda = 0, the level populations are seen to oscillate. But, as the nonlinear coupling is switched on (lambda > 0), a threshold is reached at lambda = lambda(c) when the evolution is seen to be characterized by an abrupt transition dominantly to the highest available state of the unperturbed (initial) oscillator. It is shown that this transition probability is maximized at a particular value of lambda. The time threshold for this transition decreases with increasing nonlinear coupling strength. The numerically obtained structures of the underlying quantum-phase spaces of the linear and nonlinear random oscillators are examined. Possible use of these results in a problem of chemical origin is explored. (C) 1997 John Wiley & Sons, Inc.