Non-exponential relaxation for anomalous diffusion

We study the relaxation process in normal and anomalous diffusion regimes for systems described by a generalized Langevin equation (GLE). We demonstrate the existence of a very general correlation function which describes the relaxation phenomena. Such function is even; therefore, it cannot be an exponential or a stretched exponential. However, for a proper choice of the parameters, those functions can be reproduced within certain intervals with good precision. We also show the passage from the non-Markovian to the Markovian behaviour in the normal diffusion regime. For times longer than the relaxation time, the correlation function for anomalous diffusion becomes a power law for broad-band noise.Comment: 6 pages, 2 figure

Electron Glass Dynamics

Examples of glasses are abundant, yet it remains one of the phases of matter whose understanding is very elusive. In recent years, remarkable experiments have been performed on the dynamical aspects of glasses. Electron glasses offer a particularly good example of the 'trademarks' of glassy behavior, such as aging and slow relaxations. In this work we review the experimental literature on electron glasses, as well as the local mean-field theoretical framework put forward in recent years to understand some of these results. We also present novel theoretical results explaining the periodic aging experiment.Comment: Invited review to appear in Annual Review of Condensed Matter Physic

Characterization of the Dynamics of Glass-forming Liquids from the Properties of the Potential Energy Landscape

We develop a framework for understanding the difference between strong and fragile behavior in the dynamics of glass-forming liquids from the properties of the potential energy landscape. Our approach is based on a master equation description of the activated jump dynamics among the local minima of the potential energy (the so-called inherent structures) that characterize the potential energy landscape of the system. We study the dynamics of a small atomic cluster using this description as well as molecular dynamics simulations and demonstrate the usefulness of our approach for this system. Many of the remarkable features of the complex dynamics of glassy systems emerge from the activated dynamics in the potential energy landscape of the atomic cluster. The dynamics of the system exhibits typical characteristics of a strong supercooled liquid when the system is allowed to explore the full configuration space. This behavior arises because the dynamics is dominated by a few lowest-lying minima of the potential energy and the potential energy barriers between these minima. When the system is constrained to explore only a limited region of the potential energy landscape that excludes the basins of attraction of a few lowest-lying minima, the dynamics is found to exhibit the characteristics of a fragile liquid.Comment: 13 pages, 6 figure

A Hybrid model for the origin of photoluminescence from Ge nanocrystals in SiO2_2 matrix

In spite of several articles, the origin of visible luminescence from germanium nanocrystals in SiO$_2$ matrix is controversial even today. Some authors attribute the luminescence to quantum confinement of charge carriers in these nanocrystals. On the other hand, surface or defect states formed during the growth process, have also been proposed as the source of luminescence in this system. We have addressed this long standing query by simultaneous photoluminescence and Raman measurements on germanium nanocrystals embedded in SiO$_2$ matrix, grown by two different techniques: (i) low energy ion-implantation and (ii) atom beam sputtering. Along with our own experimental observations, we have summarized relevant information available in the literature and proposed a \emph{Hybrid Model} to explain the visible photoluminescence from nanocrystalline germanium in SiO$_2$ matrix.Comment: 23 pages, 8 figure

Anomalous Rotational Relaxation: A Fractional Fokker-Planck Equation Approach

In this study we obtained analytically relaxation function in terms of rotational correlation functions based on Brownian motion for complex disordered systems in a stochastic framework. We found out that rotational relaxation function has a fractional form for complex disordered systems, which indicates relaxation has non-exponential character obeys to Kohlrausch-William-Watts law, following the Mittag-Leffler decay.Comment: Revtex4, 9 pages. Paper was revised. References adde

Relation between positional specific heat and static relaxation length: Application to supercooled liquids

A general identification of the {\em positional specific heat} as the thermodynamic response function associated with the {\em static relaxation length} is proposed, and a phenomenological description for the thermal dependence of the static relaxation length in supercooled liquids is presented. Accordingly, through a phenomenological determination of positional specific heat of supercooled liquids, we arrive at the thermal variation of the static relaxation length $\xi$, which is found to vary in accordance with $\xi \sim (T-T_0)^{-\nu}$ in the quasi-equilibrium supercooled temperature regime, where $T_0$ is the Vogel-Fulcher temperature and exponent $\nu$ equals unity. This result to a certain degree agrees with that obtained from mean field theory of random-first-order transition, which suggests a power law temperature variation for $\xi$ with an apparent divergence at $T_0$. However, the phenomenological exponent $\nu = 1$, is higher than the corresponding mean field estimate (becoming exact in infinite dimensions), and in perfect agreement with the relaxation length exponent as obtained from the numerical simulations of the same models of structural glass in three spatial dimensions.Comment: Revised version, 7 pages, no figures, submitted to IOP Publishin

Electronic transport in field-effect transistors of sexithiophene

The electronic conduction of thin-film field-effect-transistors (FETs) of sexithiophene was studied. In most cases the transfer curves deviate from standard FET theory; they are not linear, but follow a power law instead. These results are compared to conduction models of "variable-range hopping" and "multi-trap-and-release". The accompanying IV curves follow a Poole-Frenkel (exponential) dependence on the drain voltage. The results are explained assuming a huge density of traps. Below 200 K, the activation energy for conduction was found to be ca. 0.17 eV. The activation energies of the mobility follow the Meyer-Neldel rule. A sharp transition is seen in the behavior of the devices at around 200 K. The difference in behavior of a micro-FET and a submicron FET is shown. (C) 2004 American Institute of Physics

The impact of the molecular weight on the nonequilibrium glass transition dynamics of poly(phenylmethyl siloxane) in cylindrical nanopores

Changes in the glass transition dynamics caused by nanoconfinement reveal pronounced out-of-equilibrium features. Therefore, the confinement effects weaken with time. Using dielectric spectroscopy, we have investigated the impact of molecular weight on the equilibration kinetics of the studied polymer embedded within anodic aluminum oxide nanoporous templates. For our research, we have used poly(phenylmethyl siloxane) (PMPS) with low (Mw = 2530 g/mol) and high (Mw = 27,800 g/mol) molecular weight. We have found that the observed faster dynamics of the nanopore-confined systems weakens with time, and ultimately it is possible to regain the bulk-like mobility. The equilibration time increases by reducing the pore size and lowering the annealing temperature much below the glass transition temperature of the interfacial layer, Tg_interface. The experimental data analysis has also revealed that the molecular weight of the nanopore-confined polymer influences the recovery of the bulk segmental relaxation time, τα. Low-molecular-weight PMPS rearrange and reach denser packing of the polymer chains with greater ease than the high-molecular-weight one. Finally, we have also demonstrated that the molecular weight affects the relationship between the time constant characterizing the equilibration kinetics and the characteristic time of viscous flow in cylindrical channels of nanometer size