Exciton-phonon dynamics on complex networks: Comparison between a perturbative approach and exact calculations

Quantum graph wave external triggering: Energy transfer and damping

The propagation of wave trains resulting from a local external trigger inside a network described by a metric graph is analyzed using quantum graph theory. The external trigger is a finite-time perturbation imposed at one vertex of the graph, leading to a consecutive wave train into the network, supposedly at rest before the applied external perturbation. A complete analytical solution for the induced wave train is found having a specific spectrum as well as mode's amplitudes. Furthermore the precise condition by which the external trigger can transfer a maximal energy to any specific natural mode of the quantum graph is derived. Finally, the wave damping associated with boundary-layer dissipation is computed within a multiple time-scale asymptotic analysis. Exponential damping rates are explicitly found related to their corresponding mode's eigenvalue. Each mode energy is then obtained, as well as their exponential damping rate. The relevance of these results to the physics of waves within networks are discussed.

Linear and non-linear infrared response of one-dimensional vibrational Holstein polarons in the anti-adiabatic limit: Optical and acoustical phonon models

The theory of linear and non-linear infrared response of vibrational Holstein polarons in one-dimensional lattices is presented in order to identify the spectral signatures of self-trapping phenomena. Using a canonical transformation, the optical response is computed from the small polaron point of view which is valid in the anti-adiabatic limit. Two types of phonon baths are considered: optical phonons and acoustical phonons, and simple expressions are derived for the infrared response. It is shown that for the case of optical phonons, the linear response can directly probe the polaron density of states. The model is used to interpret the experimental spectrum of crystalline acetanilide in the C=O range. For the case of acoustical phonons, it is shown that two bound states can be observed in the two-dimensional infrared spectrum at low temperature. At high temperature, analysis of the time-dependence of the two-dimensional infrared spectrum indicates that bath mediated correlations slow down spectral diffusion. The model is used to interpret the experimental linear-spectroscopy of model α-helix and β-sheet polypeptides. This work shows that the Davydov Hamiltonian cannot explain the observations in the NH stretching range.