On the tunneling dynamics of a cubic oscillator with a time-dependent harmonic frequency

Abstract

The dynamics of a 1-d cubic oscillator having a time-dependent harmonic force constant is studied numerically by invoking the time-dependent Fourier grid Hamiltonian method. The temporal variation in K t causes the tunneling rate constant to decrease or increase, depending upon the nature of the time-dependence of K. For the exponentially increasing or decreasing force constant, the intrinsic tunneling rate constant ( k tun 0 v ) (in the limit of zero rate of relaxation of the harmonic force constant) is obtained by extrapolation of k tun v( 1 τ ) to 1 τ = 0 . The k tun 0 v computed this way compares well with those obtained from the complex scaled Fourier grid Hamiltonian method. The effects of changing the form of the time-dependence of K are analysed and the possibility of mapping real systems onto the present model is explored.