Emergent percolation length and localization in random elastic networks

We study, theoretically and numerically, a minimal model for phonons in a disordered system. For sufficient disorder, the vibrational modes of this classical system can become Anderson localized, yet this problem has received significantly less attention than its electronic counterpart. We find rich behavior in the localization properties of the phonons as a function of the density, frequency and the spatial dimension. We use a percolation analysis to argue for a Debye spectrum at low frequencies for dimensions higher than one, and for a localization/delocalization transition (at a critical frequency) above two dimensions. We show that in contrast to the behavior in electronic systems, the transition exists for arbitrarily large disorder, albeit with an exponentially small critical frequency. The structure of the modes reflects a divergent percolation length that arises from the disorder in the springs without being explicitly present in the definition of our model. Within the percolation approach we calculate the speed-of-sound of the delocalized modes (phonons), which we corroborate with numerics. We find the critical frequency of the localization transition at a given density, and find good agreement of these predictions with numerical results using a recursive Green function method adapted for this problem. The connection of our results to recent experiments on amorphous solids are discussed.Comment: accepted to PR

Sparse random matrices and vibrational spectra of amorphous solids

A random matrix approach is used to analyze the vibrational properties of amorphous solids. We investigated a dynamical matrix M=AA^T with non-negative eigenvalues. The matrix A is an arbitrary real NxN sparse random matrix with n independent non-zero elements in each row. The average values =0 and dispersion =V^2 for all non-zero elements. The density of vibrational states g(w) of the matrix M for N,n >> 1 is given by the Wigner quarter circle law with radius independent of N. We argue that for n^2 << N this model can be used to describe the interaction of atoms in amorphous solids. The level statistics of matrix M is well described by the Wigner surmise and corresponds to repulsion of eigenfrequencies. The participation ratio for the major part of vibrational modes in three dimensional system is about 0.2 - 0.3 and independent of N. Together with term repulsion it indicates clearly to the delocalization of vibrational excitations. We show that these vibrations spread in space by means of diffusion. In this respect they are similar to diffusons introduced by Allen, Feldman, et al., Phil. Mag. B 79, 1715 (1999) in amorphous silicon. Our results are in a qualitative and sometimes in a quantitative agreement with molecular dynamic simulations of real and model glasses.Comment: 24 pages, 7 figure

Semiclassical and quantum polarons in crystaline acetanilide

Crystalline acetanilide is a an organic solid with peptide bond structure similar to that of proteins. Two states appear in the amide I spectral region having drastically different properties: one is strongly temperature dependent and disappears at high temperatures while the other is stable at all temperatures. Experimental and theoretical work over the past twenty five years has assigned the former to a selftrapped state while the latter to an extended free exciton state. In this article we review the experimental and theoretical developments on acetanilide paying particular attention to issues that are still pending. Although the interpretation of the states is experimentally sound, we find that specific theoretical comprehension is still lacking. Among the issues that that appear not well understood is the effective dimensionality of the selftrapped polaron and free exciton states.Comment: 28 pages 13 figure

Coherent exciton-vibrational dynamics and energy transfer in conjugated organics

Coherence, signifying concurrent electron-vibrational dynamics in complex natural and man-made systems, is currently a subject of intense study. Understanding this phenomenon is important when designing carrier transport in optoelectronic materials. Here, excited state dynamics simulations reveal a ubiquitous pattern in the evolution of photoexcitations for a broad range of molecular systems. Symmetries of the wavefunctions define a specific form of the non-adiabatic coupling that drives quantum transitions between excited states, leading to a collective asymmetric vibrational excitation coupled to the electronic system. This promotes periodic oscillatory evolution of the wavefunctions, preserving specific phase and amplitude relations across the ensemble of trajectories. The simple model proposed here explains the appearance of coherent exciton-vibrational dynamics due to non-adiabatic transitions, which is universal across multiple molecular systems. The observed relationships between electronic wavefunctions and the resulting functionalities allows us to understand, and potentially manipulate, excited state dynamics and energy transfer in molecular materials.Fil: Nelson, Tammie R.. Los Alamos National Laboratory; Estados UnidosFil: Ondarse Alvarez, Dianelys. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes; ArgentinaFil: Oldani, Andres Nicolas. Universidad Nacional de Quilmes; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Rodríguez Hernández, Beatriz. Universidad Nacional de Quilmes; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Alfonso Hernandez, Laura. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes; ArgentinaFil: Galindo, Johan F.. Universidad Nacional de Colombia; ColombiaFil: Kleiman, Valeria D.. University of Florida; Estados UnidosFil: Fernández Alberti, Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes; ArgentinaFil: Roitberg, Adrián. University of Florida; Estados UnidosFil: Tretiak, Sergei. Los Alamos National Laboratory; Estados Unido

Photoinduced Intra- and Intermolecular Energy Transfer in Chlorophyll a Dimer

Applying nonadiabatic excited-state molecular dynamics, we investigate excitation energy transfer and exciton localization dynamics in a chlorophyll a (Chla) dimer system at the interface of two monomers of light-harvesting complex II trimer. After its optical excitation at the red edge of the Soret (B) band, the Chla dimer experiences an ultrafast intra- and intermolecular nonradiative relaxation process to the lowest band (Qy). The energy relaxation is found to run faster in the Chla dimer than in the Chla monomer. Once the molecular system reaches the lowest Qy band composed of two lowest excited states S1 and S2, the concluding relaxation step involves the S2 → S1 population transfer, resulting in a relatively slower relaxation rate. The strength of thermal fluctuations exceeds intraband electronic coupling between the states belonging to a certain band (B, Qx, and Qy), producing localized states on individual chromophores. Therefore, time evolution of spatial electronic localization during internal conversion reveals transient trapping on one of the Chla monomers participating in the events of intermonomeric energy exchange. In the phase space domains where electronic states are strongly coupled, these states become nearly degenerate promoting Frenkel-exciton-like delocalization and interchromophore energy transfer. As energy relaxation occurs, redistribution of the transition density on two Chla monomers leads to nearly equal distribution of the exciton among the molecules. For a single Chla, our analysis of excitonic dynamics reveals wave function amplitude transfer from nitrogen and outer carbon atoms to inner carbon atoms during nonradiative relaxation.Fil: Zheng, Fulu. Nanyang Technological University; SingapurFil: Fernández Alberti, Sebastián. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Quilmes; ArgentinaFil: Tretiak, Sergei. Los Alamos National Laboratory; Estados UnidosFil: Zhao, Yang. Nanyang Technological University; Singapu

Real-time observation of intramolecular proton transfer in the electronic ground state of chloromalonaldehyde: An ab initio study of time-resolved photoelectron spectra

The authors report on studies of time-resolved photoelectron spectra of intramolecular proton transfer in the ground state of chloromalonaldehyde, employing ab initio photoionization matrix elements and effective potential surfaces of reduced dimensionality, wherein the couplings of proton motion to the other molecular vibrational modes are embedded by averaging over classical trajectories. In the simulations, population is transferred from the vibrational ground state to vibrationally hot wave packets by pumping to an excited electronic state and dumping with a time-delayed pulse. These pump-dump-probe simulations demonstrate that the time-resolved photoelectron spectra track proton transfer in the electronic ground state well and, furthermore, that the geometry dependence of the matrix elements enhances the tracking compared with signals obtained with the Condon approximation. Photoelectron kinetic energy distributions arising from wave packets localized in different basins are also distinguishable and could be understood, as expected, on the basis of the strength of the optical couplings in different regions of the ground state potential surface and the Franck-Condon overlaps of the ground state wave packets with the vibrational eigenstates of the ion potential surface