By applying the concept of dynamical facilitation and analyzing the excitation lines that result from this facilitation, we investigate the origin of decoupling of transport coefficients in supercooled liquids. We illustrate our approach with two classes of models. One depicts diffusion in a strong glass former, and the other in a fragile glass former. At low temperatures, both models exhibit violation of the Stokes-Einstein relation, D ∼ τ −1 , where D is the self diffusion constant and τ is the structural relaxation time. In the strong case, the violation is sensitive to dimensionality d, going as D ∼ τ −2/3 for d = 1, and as D ∼ τ −0.95 for d = 3. In the fragile case, however, we argue that dimensionality dependence is weak, and show that for d = 1, D ∼ τ −0.73 . This scaling for the fragile case compares favorably with the results of a recent experimental study for a three-dimensional fragile glass former.

Single-molecule spectroscopy (SMS) is a powerful experimental technique used to investigate a wide range of physical, chemical, and biophysical phenomena. The merit of SMS is that it does not require ensemble averaging, which is found in standard spectroscopic techniques. Thus SMS yields insight into complex fluctuation phenomena that cannot be observed using standard ensemble techniques. We investigate theoretical aspects of SMS, emphasizing (a) dynamical fluctuations (e.g., spectral diffusion, photon-counting statistics, antibunching, quantum jumps, triplet blinking, and nonergodic blinking) and (b) single-molecule fluctuations in disordered systems, specifically distribution of line shapes of single molecules in low-temperature glasses. Special emphasis is given to single-molecule systems that reveal surprising connections to Levy statistics (i.e., blinking of quantum dots and single molecules in glasses). We compare theory with experiment and mention open problems. Our work demonstrates that the theory of SMS is a complementary field of research for describing optical spectroscopy in the condensed phase.

We investigate statistics of dynamical exchange events in coarse-grained models of supercooled liquids in spatial dimensions d=1, 2, and 3. The models, based upon the concept of dynamical facilitation, capture generic features of statistics of exchange times and persistence times. Here, distributions for both times are related and calculated for cases of strong and fragile glass formers over a range of temperatures. Exchange-time distributions are shown to be particularly sensitive to the model parameters and dimensions, and exhibit more structured and richer behavior than persistence-time distributions. Mean exchange times are shown to be Arrhenius, regardless of models and spatial dimensions. Specifically, tx approximately c-2, with c being the excitation concentration. Different dynamical exchange processes are identified and characterized from the underlying trajectories. We discuss experimental possibilities to test some of our theoretical findings.

Förster-Dexter theory for excitation energy transfer is generalized for the account of short time nonequilibrium kinetics due to the nonstationary bath relaxation. The final rate expression is presented as a spectral overlap between the time dependent stimulated emission and the stationary absorption profiles, which allows experimental determination of the time dependent rate. For a harmonic oscillator bath model, an explicit rate expression is derived and model calculations are performed in order to examine the dependence of the nonequilibrium kinetics on the excitation-bath coupling strength and the temperature. Relevance of the present theory with recent experimental findings and possible future theoretical directions are discussed.

We investigate the charging phenomena of an electric double layer capacitor (EDLC) by conducting both equilibrium and non-equilibrium molecular dynamics (MD) simulations.