Two-vibron bound states in a stochastic surrounding: Quantum breather diffusion

A kinetic equation is established for characterizing the quantum diffusion of two-vibron bound states in a molecular lattice coupled with a stochastic bath. It is shown that two trapped vibrons behave as a single particle whose coherent motion is controlled by the bound state band. The bath is responsible for the quantum decoherence of that particle and for its diffusion along the lattice. In addition, it yields a finite lifetime due to the irreversible decay of the trapped vibrons into the continuum of two-vibron free states. Diffusion, decoherence and lifetime are studied both numerically and analytically with special emphasis on the influence of intramolecular anharmonicity. It is shown that the anharmonicity prevents the diffusion of the vibron pair as a consequence of its breather-like behavior but enhances the pair lifetime. Consequently, the pair covers a finite length during its diffusion before its disappearance into the continuum of free states. The diffusion length does not depend on the anharmonicity and it is very small for low-dimensional molecular lattices.