Noise-induced dynamic symmetry breaking and stochastic transitions in ABA molecules: II. Symmetric-antisymmetric normal mode switching

Graphical abstract: A typical trajectory in action-angle variables that shows antisymmetric-to-symmetric normal mode transitions in ABA molecules as a function of dimensionless time. The plot (a) represents the time-dependence of AB and BA bond phase difference: the stable oscillations around π/2 and 3π/2 indicate antisymmetric normal mode behavior, while the stable oscillations around π correspond to symmetric normal-mode behavior. Plot (b) shows the corresponding time-dependence of the local action variables J1 and J2: the complete energy exchange between J1 and J2 indicates the normal-mode behavior. - Abstract: The second paper of the series discusses the effect of thermal noise o the stretching vibraional dynamics of symmetric triatomic ABA molecules. In particular, noise-induced transitions between symmetric and antisymmetric normal-mode vibrations are discussed, in the context of symmetry breaking of vibrational dynamics. The statistics of symmetry breaking transitions and the average lifetimes of normal modes of different symmetries are derived analytically and compared with direct numerical simulations. The average lifetimes of symmetric and antisymmetric normal modes are found to be inversely proportional to bath friction strength and depend on the dimensionless parameter κ which is the combination of bath temperature, bond anharmonicity and bond-bond coupling strength. Antisymmetric normal mode depends weakly on κ and is always stable. Symmetric normal mode depends significantly on κ and becomes unstable at κ=1. Higher temperatures destabilize symmetric normal mode and therefore decrease the ratio of symmetric-to-antisymmetric normal mode populations contrary to intuitive expectation.