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

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 Kt 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 (ktun0v) (in the limit of zero rate of relaxation of the harmonic force constant) is obtained by extrapolation of ktunv(1τ) to 1τ = 0. The ktun0v 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.