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Register a new userSpatio-temporal anomalous diffusion in heterogeneous media by NMR
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For the first time, the diffusion phase diagram in highly confined colloidal systems, predicted by Continuous Time Random Walk (CTRW), is experimentally obtained. Temporal and spatial fractional exponents, $alpha$ and $mu$, introduced within the framework of CTRW, are simultaneously measured by Pulse Field Gradient Nuclear Magnetic Resonance technique in samples of micro-beads dispersed in water. We find that $alpha$ depends on the disorder degree of the system. Conversely, $mu$ depends on both bead sizes and magnetic susceptibility differences within samples. Our findings fully match the CTRW predictions.
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The dynamical response of Coulomb-interacting particles in nano-clusters are analyzed at different temperatures characterizing their solid- and liquid-like behavior. Depending on the trap-symmetry, both the spatial and temporal correlations undergo slow, stretched exponential relaxations at long times, arising from spatially correlated motion in string-like paths. Our results indicate that the distinction between the `solid and `liquid is soft: While particles in a `solid flow producing dynamic heterogeneities, motion in `liquid yields unusually long tail in the distribution of particle-displacements. A phenomenological model captures much of the subtleties of our numerical simulations.
Anomalous transport in a circular comb is considered. The circular motion takes place for a fixed radius, while radii are continuously distributed along the circle. Two scenarios of the anomalous transport, related to the reflecting and periodic angular boundary conditions, are studied. The first scenario with the reflection boundary conditions for the circular diffusion corresponds to the conformal mapping of a 2D comb Fokker-Planck equation on the circular comb. This topologically constraint motion is named umbrella comb model. In this case, the reflecting boundary conditions are imposed on the circular (rotator) motion, while the radial motion corresponds to geometric Brownian motion with vanishing to zero boundary conditions on infinity. The radial diffusion is described by the log-normal distribution, which corresponds to exponentially fast motion with the mean squared displacement (MSD) of the order of $e^t$. The second scenario corresponds to the circular diffusion with periodic boundary conditions and the outward radial diffusion with vanishing to zero boundary conditions at infinity. In this case the radial motion corresponds to normal diffusion. The circular motion in both scenarios is a superposition of cosine functions that results in the stationary Bernoulli polynomials for the probability distributions.
We propose a spatio-temporal characterization of the entanglement dynamics in many-body localized (MBL) systems, which exhibits a striking resemblance with dynamical heterogeneities in classical glasses. Specifically, we find that the relaxation times of local entanglement, as measured by the concurrence, are spatially correlated giving rise to a dynamical correlation length for quantum entanglement. Our work provides a yet unrecognized connection between the behavior of classical glasses and the genuine quantum dynamics of MBL systems.
We study relaxation dynamics of a three dimensional elastic manifold in random potential from a uniform initial condition by numerically solving the Langevin equation.We observe growth of roughness of the system up to larger wavelengths with time.We analyze structure factor in detail and find a compact scaling ansatz describing two distinct time regimes and crossover between them. We find short time regime corresponding to length scale smaller than the Larkin length $L_c$ is well described by the Larkin model which predicts a power law growth of domain size $L(t)$. Longer time behavior exhibits the random manifold regime with slower growth of $L(t)$.
We investigate the origin of the breakdown of the Stokes-Einstein relation (SER) between diffusivity and viscosity in undercooled melts. A binary Lennard-Jones system, as a model for a metallic melt, is studied by molecular dynamics. A weak breakdown at high temperatures can be understood from the collectivization of motion, seen in the isotope effect. The strong breakdown at lower temperatures is connected to an increase in dynamic heterogeneity. On relevant timescales some particles diffuse much faster than the average or than predicted by the SER. The van-Hove self correlation function allows to unambiguously identify slow particles. Their diffusivity is even less than predicted by the SER. The time-span of these particles being slow particles, before their first conversion to be a fast one, is larger than the decay time of the stress correlation. The contribution of the slow particles to the viscosity rises rapidly upon cooling. Not only the diffusion but also the viscosity shows a dynamically heterogeneous scenario. We can define a slow viscosity. The SER is recovered as relation between slow diffusivity and slow viscosity.
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