Disordered systems microscopic models

Chapter 8 by W. T. Coffey, Y. P. Kalmykov, and S. V. Titov, entitled Fractional Rotational Diffusion and Anomalous Dielectric Relaxation in Dipole Systems, provides an introduction to the theory of fractional rotational Brownian motion and microscopic models for dielectric relaxation in disordered systems. The authors indicate how anomalous relaxation has its origins in anomalous diffusion and that a physical explanation of anomalous diffusion may be given via the continuous time random walk model. It is demonstrated how this model may be used to justify the fractional diffusion equation. In particular, the Debye theory of dielectric relaxation of an assembly of polar molecules is reformulated using a fractional noninertial Fokker-Planck equation for the purpose of extending that theory to explain anomalous dielectric relaxation. Thus, the authors show how the Debye rotational diffusion model of dielectric relaxation of polar molecules (which may be described in microscopic fashion as the diffusion limit of a discrete time random walk on the surface of the unit sphere) may be extended via the continuous-time random walk to yield the empirical Cole-Cole, Cole-Davidson, and Havriliak-Negami equations of anomalous dielectric relaxation from a microscopic model based on a... 

When analyzing experimental EPR spectra of spin probes in micellar phase of complexes we used the model "Microscopic Order and Macroscopic Disorder" (MOMD) [33], This model is often used for description of EPR spectra of spin probes in micelles, dispersions, vesicles and other microscopically ordered but macroscopically disordered systems [34, 35],... 

Using the methods of classical statistical physics one may more or less rigorously solve problems where the system on a microscopic level is either in a state of complete chaos (perfect gas) or total order (solid perfectly crystalline bodies). In contrast, disordered media and processes in which there is neither crystalline order nor complete chaos on the microscopic level have not yet had an adequate description. This problem is connected with the condition that the macroscopic variables must considerably exceed the correlation scales of microscopic variables, a condition which is not met by disordered media. Consequently in order to describe such systems, fractal models and phased averaging on different scale levels (meso-levels) should be effective. 

II. Microscopic Models for Dielectric Relaxation in Disordered Systems... 

II. MICROSCOPIC MODELS FOR DIELECTRIC RELAXATION IN DISORDERED SYSTEMS... 

Finding polariton states in disordered planar microcavities microscopically is a difficult task which do not attempt here. As a first excursion into the study of disorder effects on polariton dynamics, here we will follow (32) to explore the dynamics in a simpler microscopic model of a ID microcavity. Such microcavities are interesting in themselves and can have experimental realizations from the results known in the theory of disordered systems (39) one can also anticipate that certain qualitative features may be common for ID and 2D systems (38). 

On physical grounds (see Section 10.3 and (15)) one should expect that low-energy polaritons in 2D organic microcavities would also be rendered strongly localized by disorder, as it would also follow from the general ideas of the theory of localization (39). Further work on microscopic models of two-dimensional polariton systems is required to quantify their localization regimes. 

To discuss this new type of ordered phase in spin glasses, one would like to have a microscopic model where the actual interactions and anisotropies are considered and the average over a realistic description of the site dilution disorder is performed. Clearly this is a difficult task and up to now no realistic model of a spin glass has been solved analytically. In addition, there exists another difficulty because a proper treatment of systems with quenched disorder like spin glasses involves averaging the free energy F rather than the partition function Z... 

It is well known that magnetoconductance (MC) is a sensitive local probe for investigating the microscopic transport parameters (e.g., scattering process, relaxation mechanism, etc.) in metallic and semiconducting systems [2]. The quantitative level of understanding of MC for disordered systems by using the localization-interaction model is rather useful for checking the appropriateness... 

The formulation of informative QSPR models adequate for multicomponent disordered systems is anything but trivial and their predictive and interpretative power depends critically on the information content of the descriptors utilized [22], The selection of descriptors for meaningful QSPR models implies the knowledge of what features of the stmcture are measured by a given descriptor and of how the microscopic properties influence the macroscopic (measured) properties in a mechanistic way. Without this knowledge it is hard to apply a reverse QSPR approach to optimize materials directly. 

As a final point, we note that typical surfaces are usually not crystalline but instead are covered by amorphous layers. These layers are much rougher at the atomic scale than the model crystalline surfaces that one would typically use for computational convenience or for fundamental research. The additional roughness at the microscopic level from disorder increases the friction between surfaces considerably, even when they are separated by a boundary lubricant.15 Flowever, no systematic studies have been performed to explore the effect of roughness on boundary-lubricated systems, and only a few attempts have been made to investigate dissipation mechanisms in the amorphous layers under sliding conditions from an atomistic point of view. 

In this work the main aspect has been concerned with the problem of electronic energy relaxation in polychro-mophoric ensembles of aromatic horaopolymers in dilute, fluid solution of a "good" solvent. In this morphological situation microscopic EET and trapping along the contour of an expanded and mobile coil must be expected to induce rather complex rate processes, as they proceed in typically low-dimensional, nonuniform, and finite-size disordered matter. A macroscopic transport observable, i.e., excimer fluorescence, must be interpreted, therefore, as an ensemble and configurational average over a convolute of individual disordered dynamical systems in a series of sequential relaxation steps. As a consequence, transient fluorescence profiles should exhibit a more complicated behavior, as it can be modelled, on the other hand, on the basis of linear rate equations and multiexponential reconvolution analysis. 

In this section we develop a microscopic quantum model which accounts both for positional and orientational disorder in such a system. Using the bosonic Hamiltonian for the system, we find the structure of the eigenstates (i.e. the weights of the electronic excitations on different molecules of the disordered medium) in the intervals where the wavevector of the cavity polaritons is a good quantum number. These weights will be used in Ch. 13 in consideration of the upper polariton nonradiative decay and also for estimations of the rate transition from incoherent states to the lowest energy polariton states. 

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