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.     

Generalized master equations for continuous-time random walks

An equivalence is established between generalized master equations and continuous-time random walks by means of an explicit relationship between(t), which is the pausing time distribution in the theory of continuous-time random walks, and(t), which represents the memory in the kernel of a generalized master equation. The result of Bedeaux, Lakatos-Lindenburg, and Shuler concerning the equivalence of the Markovian master equation and a continuous-time random walk with an exponential distribution for(t) is recovered immediately. Some explicit examples of(t) and(t) are also presented, including one which leads to the equation of telegraphy.This study was partially supported by ARPA and monitored by ONR Contract No. (N00014-17-C-0308).For continuity, the reader is directed to the article entitled Random Walks on Lattices. IV. Continuous Time Walks and Influence of Absorbing Boundaries, by E. W. Montroll and H. Scher, which will appear in Volume 9, Number 2, of this journal, and which should precede the following article. Regrettably, the two articles were inadvertently switched during processing.     

Theory of depolarization of fluorescence in molecular pairs

Depolarization of fluorescence as a result of energy transfer is studied phenomenologically for a model pair of electronically coupled molecules. The usual rate equations are replaced by the Stochastic Liouville Equations and new radiative terms are included. An expression for the fluorescence polarization for all strengths of electronic coupling between the molecules is obtained. The inclusion of off-diagonal density matrix elements is essential for resolving a paradox arising in the Förster theory of depolarization. The calculation points the way toward using a previously untapped source of information on coherence in complex systems.     

A model calculation for vibrational propagation in a chain of nonlinear oscillators II: Effects of optical dispersion and of initial conditions

We extend our previous analysis of vibrational propagation in a chain of nonlinear oscillators to obtain explicit expressions for oscillator displacements and mean-squaredisplacements of the vibrational excitation for optical dispersion and study the effects of the interplay of initial conditions with nonlinearity.     

Comments on the effect of disorder on transport with intermediate degree of coherence: Calculation of the mean square displacement

We use the generalized master equation with a simple exponential memory but with disorder in its spatial dependence to analyze the combined effect of coherence and randomness on the transport of quasiparticles. We calculate the mean-square-displacement and find that it retains well-known properties in the presence of randomness.Supported by NSF grant no. DMR-7919539     

Thermal stability of nonlinear structures: A Gibbs analysis of the semiclassical system

With the help of an approach based on an analytic study of the partition function and related observable expectation values, we address the problem of the thermal stability of nonlinear structures. We develop an useful analogy with magnetic systems, present explicit calculations for a simple case, and address the existing debate in the literature concerning whether thermal interaction aids or hampers the existence of selftrapped states. An unambiguous demonstration of selftrapping being aided in one regime but hampered in another emerges from our analysis.Work supported in part by the NATO Scientific Affairs Division