Exciton migration with end detectors: calculation of time-dependent luminescence

We present explicit plots of the time dependence of the detector luminescence intensity in surface quenching observations. They are obtained with the aid of numerical inversion methods applied to exact consequences of a master-equation theory of exciton migration. The existing disparity in reported values of the singlet diffusion constant in aromatic hydro-carbon crystals is one of the main issues addressed. It is shown how the theory can be used to extract the exciton diffusion constant without prior knowledge of the (detector) trapping rates, by combining information obtained from steady-state (yield) and time-resolved experiments.     

Transport Properties of Random Walks on Scale-Free/Regular-Lattice Hybrid Networks

We study numerically the mean access times for random walks on hybrid disordered structures formed by embedding scale-free networks into regular lattices, considering different transition rates for steps across lattice bonds (F) and across network shortcuts (f). For fast shortcuts (f/F≫1) and low shortcut densities, traversal time data collapse onto a universal curve, while a crossover behavior that can be related to the percolation threshold of the scale-free network component is identified at higher shortcut densities, in analogy to similar observations reported recently in Newman-Watts small-world networks. Furthermore, we observe that random walk traversal times are larger for networks with a higher degree of inhomogeneity in their shortcut distribution, and we discuss access time distributions as functions of the initial and final node degrees. These findings are relevant, in particular, when considering the optimization of existing information networks by the addition of a small number of fast shortcut connections.     

Classical Motion in Force Fields with Short Range Correlations

We study the long time motion of fast particles moving through time-dependent random force fields with correlations that decay rapidly in space, but not necessarily in time. The time dependence of the averaged kinetic energy 〈p ²(t)〉/2 and mean-squared displacement 〈q ²(t)〉 is shown to exhibit a large degree of universality; it depends only on whether the force is, or is not, a gradient vector field. When it is, 〈p ²(t)〉～t ^2/5 independently of the details of the potential and of the space dimension. The stochastically accelerated particle motion is then superballistic in one dimension, with 〈q ²(t)〉～t ^12/5, and ballistic in higher dimensions, with 〈q ²(t)〉～t ². These predictions are supported by numerical results in one and two dimensions. For force fields not obtained from a potential field, the power laws are different: 〈p ²(t)〉～t ^2/3 and 〈q ²(t)〉～t ^8/3 in all dimensions d≥1.     

Variational formula for the relaxation time in the Boltzmann equation

The relaxation time approximation (RTA) is commonly employed in nonequilibrium statistical mechanics to approximate solutions to the Boltzmann equation in terms of an exponential relaxation to equilibrium. Despite its common use, the RTA suffers from the drawback that relaxation times commonly employed are independent of initial conditions. We derive a variational principle for solutions to the Boltzmann equation, which allows us to extend the standard RTA using relaxation times that depend on the initial distribution. Tests of the approach on a calculation of the mobility for a one-dimensional (1D) tight-binding band indicate that our analysis typically provides a better approximation than the standard RTA.     

Motion and capture in the presence of cooperative trap interactions II: Exact calculations for perfect absorbers in one dimension

Exact calculations are presented for the survival fraction and other capturerelated observables in a problem involving migration on a one-dimensional lattice containing perfectly absorbing traps whose placement within the crystal is determined by explicit interactions among the trap molecules. These interactions, which are treated exactly in a lattice-gas model, may be attractive, in which case they lead to trap cluster formation and a reduction of the trapping efficiency, or they may be repulsive thus leading to increased separation of the trap molecules and an enhancement of the trapping process.Supported in part by the National Science Foundation under Grant Nos. DMR-8111434 and INT-8210098.     

Multi-megawatt superradiant emissions from coumarin-doped sol-gel derived silica

Fluorescence and lasing properties of coumarindoped silica samples prepared by sol-gel process were investigated. Superradiant emissions at peak power as high as 7MW were measured at around 535 nm when the silica samples were excited by a XeF laser. The energy of the superradiant pulse was 89 mJ, corresponding to a conversion efficiency of 36.6%.     

Motion and capture of quasiparticles in solids in the presence of cooperative trap interactions

The motion and capture of quasiparticles in periodic lattices are investigated with the help of a calculation which is exact in a one-dimensional system, and whose special feature is that it treats cooperative interactions among traps. These interactions are analyzed through lattice gas arguments. The motion is studied with the help of generalized master equations which allow for an arbitrary degree of transport coherence. The analysis, although of particular relevance to the dynamics of Frenkel excitons in molecular solids, is of general applicability.