Individual colloidal particles have been studied experimentally in a one dimensional random potential with energies that follow a Gaussian distribution. This rough, noise-like potential has been realised using a holographic optical set-up, which allows the width of the distribution to be varied. For different widths, the particle trajectories were followed and the particle dynamics characterised by, for example, the mean square displacement, non-Gaussian parameter, van Hove function, time-dependent diffusion coefficient and residence time distribution. The values obtained for these observables are consistent with the static properties of the system, in particular the barrier height distribution, which was obtained by a detailed characterisation of the tweezer-like set-up. The dynamics display three distinct behaviours: at short times normal diffusion, subsequently an extended regime of localisation within the different minima of the potential and finally a very slow approach towards long-time diffusive behaviour, for which diffusion coefficients consistent with theoretical predictions have been found.

The growth of quasicrystals, i.e., aperiodic structures with long-range order, seeded from the melt is investigated using a dynamical phase field crystal model. Depending on the thermodynamic conditions, two different growth modes are detected, namely defect-free growth of the stable quasicrystal and a mode dominated by phasonic flips which are incorporated as local defects into the grown structure such that random tiling-like ordering emerges. The latter growth mode is unique to quasicrystals and can be verified in experiments on one-component mesoscopic systems.PACS numbers: 61.44. Br,81.10.Aj,82.70.Dd Quasicrystals are aperiodic structures that possess long range positional and orientational order [1,2]. Since their discovery by Shechtman [1], hundreds of quasicrystals have been reported and confirmed. Most of them are metallic alloys (see, e.g., [3,4]) but more recently they have also beend found in soft-matter systems that are made, e.g., by amphiphilic molecules [5], supramolecular dendritic systems [6,7], or by star block copolymers [8,9]. Such soft matter quasicrystals can provide scaffolds for photonic materials [10] and serve as well-characterized mesoporous matrices [11,12]. In general, quasicrystals occur either as defect-free structures stabilized by energy [13][14][15][16][17] or as locally disordered phases, leading to random tiling like structures, stabilized by entropy [18].One of the key issues for quasicrystal formation is to understand their growth mechanism out of an undercooled melt. Unlike ordinary growth of periodic crystals where a layer-by-layer mode is possible, quasicrystals lack any strict sequential growth mode due to their aperiodicity which renders their formation quite complex. Based on atomistic simulations, it has been proposed that instead first clusters are formed in the fluid which then assemble in the growing solid-fluid interface [19] but the fundamentals and details for quasicrystal growth are far from being understood. In particular, the incorporation of defects into the emerging structure during the growth process plays the leading role to discriminate between grown defect-free and random-tiling-like quasicrystals.In this letter we explore the growth behavior of quasicrystals using an appropriate dynamical phase field crystal model with two incommensurate length scales which exhibits stable defect-free quasicrystals in equilibrium. Depending on the thermodynamic conditions (such as undercooling and distance from the triple point), we find two different growth regimes for quasicrystals. There is either a defect-free growth into the stable quasicrystal or a mode dominated by phasonic flips which are incorporated as local defects into the grown structure such that a metastable random tiling-like ordering emerges. The latter growth mode is unique to quasicrystals and can be verified in experiments on one component mesoscopic systems which exhibit quasicrystalline order. Our findings do not only provide a microscopic (i.e. particleresolved) understanding of the growth pro...

We propose an analytical method to determine the shape of density profiles in the asymptotic long time limit for a broad class of coupled continuous time random walks which operate in the ballistic regime. In particular, we show that different scenarios of performing a random walk step, via making an instantaneous jump penalized by a proper waiting time or via moving with a constant speed, dramatically effect the corresponding propagators, despite the fact that the end points of the steps are identical. Furthermore, if the speed during each step of the random walk is itself a random variable, its distribution gets clearly reflected in the asymptotic density of random walkers. These features are in contrast with more standard non-ballistic random walks.

We show that the dynamics of soft-sphere systems with purely repulsive interactions can be described by introducing an effective hard-sphere diameter determined using the Andersen-Weeks-Chandler approximation. We find that this approximation, known to describe static properties of liquids, also gives a good description of a dynamical quantity, the relaxation time, even in the vicinity of the glass transition.