Relaxation channels of two-vibron bound states in α-helix proteins

Relaxation channels for two-vibron bound states in an anharmonic α-helix protein are studied. According to a recently established small polaron model [V. Pouthier, Phys. Rev. E 68, 021909 (2003)], it is shown that the relaxation originates in the interaction between the dressed anharmonic vibrons and the remaining phonons. This interaction is responsible for the occurrence of transitions between two-vibron eigenstates mediated by both phonon absorption and phonon emission. At biological temperature, the relaxation rate does not significantly depend on the nature of the two-vibron states involved in the process. The lifetime for both bound and free states is of the same order of magnitude and ranges between 0.1 and 1.0 ps for realistic parameter values. By contrast, the relaxation channels strongly depend on the nature of the two-vibron states which is a consequence of the breatherlike behavior of the two-vibron bound states.