Isotopic mass as discrete control variable in chaotic processes. The case of molecular vibrations

The dynamics of CO₂ and HCN molecules are studied with isotopic mass as a control variable thereby introducing a discrete control variable in chaos theory. An interesting variation of threshold energy for chaos is obtained with computation of Poincaré sections and Lyapunov exponent. On extending the mass range beyond these two molecules, highly non-monotonic behaviour (with various maxima and minima) for the threshold energy is found. The quantal correspondence is explored with NNLSD, Dyson-Mehta statistics and correlation coefficients. A correlation between symmetry (brought about with the isotopic mass variation) and the transition from Poisson distribution to Wigner-Dyson distribution is found for the CO₂ molecule.