Electrodynamics of Amorphous Media at Low Temperatures

Amorphous solids exhibit intrinsic, local structural transitions, that give rise to the well known quantum-mechanical two-level systems at low temperatures. We explain the microscopic origin of the electric dipole moment of these two-level systems: The dipole emerges as a result of polarization fluctuations between near degenerate local configurations, which have nearly frozen in at the glass transition. An estimate of the dipole's magnitude, based on the random first order transition theory, is obtained and is found to be consistent with experiment. The interaction between the dipoles is estimated and is shown to contribute significantly to the Gr\"{u}neisen parameter anomaly in low $T$ glasses. In completely amorphous media, the dipole moments are expected to be modest in size despite their collective origin. In partially crystalline materials, however, very large dipoles may arise, possibly explaining the findings of Bauer and Kador, J. Chem. Phys. {\bf 118}, 9069 (2003).Comment: Submitted for publication; April 27, 2005 versio

Microscopic theory of network glasses

A molecular theory of the glass transition of network forming liquids is developed using a combination of self-consistent phonon and liquid state approaches. Both the dynamical transition and the entropy crisis characteristic of random first order transitions are mapped out as a function of the degree of bonding and the density. Using a scaling relation for a soft-core model to crudely translate the densities into temperatures, the theory predicts that the ratio of the dynamical transition temperature to the laboratory transition temperature rises as the degree of bonding increases, while the Kauzmann temperature falls relative to the laboratory transition. These results indicate why highly coordinated liquids should be "strong" while van der Waals liquids without coordination are "fragile".Comment: slightly revised version that has been accepted for publication in Phys. Rev. Let

Glassy Dynamics of Protein Folding

A coarse grained model of a random polypeptide chain, with only discrete torsional degrees of freedom and Hookean springs connecting pairs of hydrophobic residues is shown to display stretched exponential relaxation under Metropolis dynamics at low temperatures with the exponent $\beta\simeq 1/4$, in agreement with the best experimental results. The time dependent correlation functions for fluctuations about the native state, computed in the Gaussian approximation for real proteins, have also been found to have the same functional form. Our results indicate that the energy landscape exhibits universal features over a very large range of energies and is relatively independent of the specific dynamics.Comment: RevTeX, 4 pages, multicolumn, including 5 figures; larger computations performed, error bars improve

Fractal Analysis of Protein Potential Energy Landscapes

The fractal properties of the total potential energy V as a function of time t are studied for a number of systems, including realistic models of proteins (PPT, BPTI and myoglobin). The fractal dimension of V(t), characterized by the exponent \gamma, is almost independent of temperature and increases with time, more slowly the larger the protein. Perhaps the most striking observation of this study is the apparent universality of the fractal dimension, which depends only weakly on the type of molecular system. We explain this behavior by assuming that fractality is caused by a self-generated dynamical noise, a consequence of intermode coupling due to anharmonicity. Global topological features of the potential energy landscape are found to have little effect on the observed fractal behavior.Comment: 17 pages, single spaced, including 12 figure

The Intrinsic Quantum Excitations of Low Temperature Glasses

Several puzzling regularities concerning the low temperature excitations of glasses are quantitatively explained by quantizing domain wall motions of the random first order glass transition theory. The density of excitations agrees with experiment and scales with the size of a dynamically coherent region at $T_g$, being about 200 molecules. The phonon coupling depends on the Lindemann ratio for vitrification yielding the observed universal relation $l/\lambda \simeq 150$ between phonon wavelength $\lambda$ and mean free path $l$. Multilevel behavior is predicted to occur in the temperature range of the thermal conductivity plateau.Comment: 4 pages, submitted to PR

Microscopic Theory of Heterogeneity and Non-Exponential Relaxations in Supercooled Liquids

Recent experiments and computer simulations show that supercooled liquids around the glass transition temperature are "dynamically heterogeneous" [1]. Such heterogeneity is expected from the random first order transition theory of the glass transition. Using a microscopic approach based on this theory, we derive a relation between the departure from Debye relaxation as characterized by the $\beta$ value of a stretched exponential response function $\phi(t) =e^{-(t/ \tau_{KWW})^{\beta}}$, and the fragility of the liquid. The $\beta$ value is also predicted to depend on temperature and to vanish as the ideal glass transition is approached at the Kauzmann temperature.Comment: 4 pages including 3 eps figure

Solution of the local field equations for self-generated glasses

We present a self-consistent local approach to self generated glassiness which is based on the concept of the dynamical mean field theory to many body systems. Using a replica approach to self generated glassiness, we map the problem onto an effective local problem which can be solved exactly. Applying the approach to the Brazovskii-model, relevant to a large class of systems with frustrated micro-phase separation, we are able to solve the self-consistent local theory without using additional approximations. We demonstrate that a glassy state found earlier in this model is generic and does not arise from the use of perturbative approximations. In addition we demonstrate that the glassy state depends strongly on the strength of the frustrated phase separation in that model.Comment: 11 pages, 3 figure

Viscosity Dependence of the Folding Rates of Proteins

The viscosity dependence of the folding rates for four sequences (the native state of three sequences is a beta-sheet, while the fourth forms an alpha-helix) is calculated for off-lattice models of proteins. Assuming that the dynamics is given by the Langevin equation we show that the folding rates increase linearly at low viscosities \eta, decrease as 1/\eta at large \eta and have a maximum at intermediate values. The Kramers theory of barrier crossing provides a quantitative fit of the numerical results. By mapping the simulation results to real proteins we estimate that for optimized sequences the time scale for forming a four turn \alpha-helix topology is about 500 nanoseconds, whereas the time scale for forming a beta-sheet topology is about 10 microseconds.Comment: 14 pages, Latex, 3 figures. One figure is also available at http://www.glue.umd.edu/~klimov/seq_I_H.html, to be published in Physical Review Letter

Polarons as Nucleation Droplets in Non-Degenerate Polymers

We present a study of the nucleation mechanism that allows the decay of the metastable phase (trans-cisoid) to the stable phase (cis-transoid) in quasi one-dimensional non-degenerate polymers within the continuum electron-phonon model. The electron-phonon configurations that lead to the decay, i.e. the critical droplets (or transition state), are identified as polarons of the metastable phase. We obtain an estimate for the decay rate via thermal activation within a range of parameters consistent with experimental values for the gap of the cis-configuration. It is pointed out that, upon doping, the activation barriers of the excited states are quite smaller and the decay rate is greatly enhanced. Typical activation energies for electron or hole polarons are $\approx 0.1$ eV and the typical size for a critical droplet (polaron) is about $20 \AA$. Decay via quantum nucleation is also studied and it is found that the crossover temperature between quantum nucleation and thermal activation is of order $T_c \leq 40 ^oK$. Metastable configurations of non-degenerate polymers may provide examples for mesoscopic quantum tunneling.Comment: REVTEX 3.0, 28 PAGES, 3 FIGURES AVAILABLE UPON REQUEST, PITT 94-0