Structural relaxation in a supercooled molecular liquid

We perform molecular-dynamics simulations of a molecular system in supercooled states for different values of inertia parameters to provide evidence that the long-time dynamics depends only on the equilibrium structure. This observation is consistent with the prediction of the mode-coupling theory for the glass transition and with the hypothesis that the potential energy-landscape controls the slow dynamics. We also find that dynamical properties at intermediate wavenumber depend on the spatial correlation of the molecule's geometrical center.Comment: 7 pages, 4 figures, Europhys. Lett. in pres

A mode-coupling theory for the glassy dynamics of a diatomic probe molecule immersed in a simple liquid

Generalizing the mode-coupling theory for ideal liquid-glass transitions, equations of motion are derived for the correlation functions describing the glassy dynamics of a diatomic probe molecule immersed in a simple glass-forming system. The molecule is described in the interaction-site representation and the equations are solved for a dumbbell molecule consisting of two fused hard spheres in a hard-sphere system. The results for the molecule's arrested position in the glass state and the reorientational correlators for angular-momentum index $\ell = 1$ and $\ell = 2$ near the glass transition are compared with those obtained previously within a theory based on a tensor-density description of the molecule in order to demonstrate that the two approaches yield equivalent results. For strongly hindered reorientational motion, the dipole-relaxation spectra for the $\alpha$-process can be mapped on the dielectric-loss spectra of glycerol if a rescaling is performed according to a suggestion by Dixon et al. [Phys. Rev. Lett. {\bf 65}, 1108 (1990)]. It is demonstrated that the glassy dynamics is independent of the molecule's inertia parameters.Comment: 19 pages, 10 figures, Phys. Rev. E, in prin

Structural Relaxation and Mode Coupling in a Simple Liquid: Depolarized Light Scattering in Benzene

We have measured depolarized light scattering in liquid benzene over the whole accessible temperature range and over four decades in frequency. Between 40 and 180 GHz we find a susceptibility peak due to structural relaxation. This peak shows stretching and time-temperature scaling as known from $\alpha$ relaxation in glass-forming materials. A simple mode-coupling model provides consistent fits of the entire data set. We conclude that structural relaxation in simple liquids and $\alpha$ relaxation in glass-forming materials are physically the same. A deeper understanding of simple liquids is reached by applying concepts that were originally developed in the context of glass-transition research.Comment: submitted to New J. Phy

Magneto-Transport in the Two-Dimensional Lorentz Gas

We consider the two-dimensional Lorentz gas with Poisson distributed hard disk scatterers and a constant magnetic field perpendicular to the plane of motion. The velocity autocorrelation is computed numerically over the full range of densities and magnetic fields with particular attention to the percolation threshold between hopping transport and pure edge currents. The Ohmic and Hall conductance are compared with mode-coupling theory and a recent generalized kinetic equation valid for low densities and small fields. We argue that the long time tail as $t^{-2}$ persists for non-zero magnetic field.Comment: 7 pages, 14 figures. Uses RevTeX and epsfig.sty. Submitted to Physical Review

Structural relaxation in a system of dumbbell molecules

The interaction-site-density-fluctuation correlators, the dipole-relaxation functions, and the mean-squared displacements of a system of symmetric dumbbells of fused hard spheres are calculated for two representative elongations of the molecules within the mode-coupling theory for the evolution of glassy dynamics. For large elongations, universal relaxation laws for states near the glass transition are valid for parameters and time intervals similar to the ones found for the hard-sphere system. Rotation-translation coupling leads to an enlarged crossover interval for the mean-squared displacement of the constituent atoms between the end of the von Schweidler regime and the beginning of the diffusion process. For small elongations, the superposition principle for the reorientational $\alpha$-process is violated for parameters and time intervals of interest for data analysis, and there is a strong breaking of the coupling of the $\alpha$-relaxation scale for the diffusion process with that for representative density fluctuations and for dipole reorientations.Comment: 15 pages, 14 figures, Phys. Rev. E in pres

Frustrated spin-12\frac{1}{2} Heisenberg magnet on a square-lattice bilayer: High-order study of the quantum critical behavior of the J1J_{1}--J2J_{2}--J1⊥J_{1}^{\perp} model

The zero-temperature phase diagram of the spin-$\frac{1}{2}$ $J_{1}$--$J_{2}$--$J_{1}^{\perp}$ model on an $AA$-stacked square-lattice bilayer is studied using the coupled cluster method implemented to very high orders. Both nearest-neighbor (NN) and frustrating next-nearest-neighbor Heisenberg exchange interactions, of strengths $J_{1}>0$ and $J_{2} \equiv \kappa J_{1}>0$, respectively, are included in each layer. The two layers are coupled via a NN interlayer Heisenberg exchange interaction with a strength $J_{1}^{\perp} \equiv \delta J_{1}$. The magnetic order parameter $M$ (viz., the sublattice magnetization) is calculated directly in the thermodynamic (infinite-lattice) limit for the two cases when both layers have antiferromagnetic ordering of either the N\'{e}el or the striped kind, and with the layers coupled so that NN spins between them are either parallel (when $\delta 0$) to one another. Calculations are performed at $n$th order in a well-defined sequence of approximations, which exactly preserve both the Goldstone linked cluster theorem and the Hellmann-Feynman theorem, with $n \leq 10$. The sole approximation made is to extrapolate such sequences of $n$th-order results for $M$ to the exact limit, $n \to \infty$. By thus locating the points where $M$ vanishes, we calculate the full phase boundaries of the two collinear AFM phases in the $\kappa$--$\delta$ half-plane with $\kappa > 0$. In particular, we provide the accurate estimate, ($\kappa \approx 0.547,\delta \approx -0.45$), for the position of the quantum triple point (QTP) in the region $\delta < 0$. We also show that there is no counterpart of such a QTP in the region $\delta > 0$, where the two quasiclassical phase boundaries show instead an ``avoided crossing'' behavior, such that the entire region that contains the nonclassical paramagnetic phases is singly connected

The mean-squared displacement of a molecule moving in a glassy system

The mean-squared displacement (MSD) of a hard sphere and of a dumbbell molecule consisting of two fused hard spheres immersed in a dense hard-sphere system is calculated within the mode-coupling theory for ideal liquid-glass transitions. It is proven that the velocity correlator, which is the second time derivative of the MSD, is the negative of a completely monotone function for times within the structural-relaxation regime. The MSD is found to exhibit a large time interval for structural relaxation prior to the onset of the $\alpha$-process which cannot be described by the asymptotic formulas for the mode-coupling-theory-bifurcation dynamics. The $\alpha$-process for molecules with a large elongation is shown to exhibit an anomalously wide cross-over interval between the end of the von-Schweidler decay and the beginning of normal diffusion. The diffusivity of the molecule is predicted to vary non-monotonically as function of its elongation.Comment: 18 pages, 12 figures, Phys. Rev. E, in prin

An exactly solvable toy model that mimics the mode coupling theory of supercooled liquid and glass transition

A toy model is proposed which incorporates the reversible mode coupling mechanism responsible for ergodic-nonergodic transition with trivial Hamiltonian in the mode coupling theory (MCT) of structural glass transition. The model can be analyzed without relying on uncontrolled approximations inevitable in the current MCT. The strength of hopping processes can be easily tuned and the ideal glass transition is reproduced only in a certain range of the strength. On the basis of the analyses of our model we discuss about a sharp ergodic-nonergodic transition and its smearing out by "hopping".Comment: 5 pages, 2 ps-figures, inappropriate terms replace

Fragile to strong crossover coupled to liquid-liquid transition in hydrophobic solutions

Using discrete molecular dynamics simulations we study the relation between the thermodynamic and diffusive behaviors of a primitive model of aqueous solutions of hydrophobic solutes consisting of hard spheres in the Jagla particles solvent, close to the liquid-liquid critical point of the solvent. We find that the fragile-to-strong dynamic transition in the diffusive behavior is always coupled to the low-density/high-density liquid transition. Above the liquid-liquid critical pressure, the diffusivity crossover occurs at the Widom line, the line along which the thermodynamic response functions show maxima. Below the liquid-liquid critical pressure, the diffusivity crossover occurs when the limit of mechanical stability lines are crossed, as indicated by the hysteresis observed when going from high to low temperature and vice versa. These findings show that the strong connection between dynamics and thermodynamics found in bulk water persists in hydrophobic solutions for concentrations from low to moderate, indicating that experiments measuring the relaxation time in aqueous solutions represent a viable route for solving the open questions in the field of supercooled water.Comment: 6 pages, 4 figures. Accepted for publication on Physical Review

Self-diffusion in sheared colloidal suspensions: violation of fluctuation-dissipation relation

Using memory-function formalism we show that in sheared colloidal suspensions the fluctuation-dissipation theorem for self-diffusion, i.e. Einstein's relation between self-diffusion and mobility tensors, is violated and propose a new way to measure this violation in Brownian Dynamics simulations. We derive mode-coupling expressions for the tagged particle friction tensor and for an effective, shear-rate dependent temperature