Nature of vibrational eigenmodes in topologically disordered solids

We use a local projectional analysis method to investigate the effect of topological disorder on the vibrational dynamics in a model glass simulated by molecular dynamics. Evidence is presented that the vibrational eigenmodes in the glass are generically related to the corresponding eigenmodes of its crystalline counterpart via disorder-induced level-repelling and hybridization effects. It is argued that the effect of topological disorder in the glass on the dynamical matrix can be simulated by introducing positional disorder in a crystalline counterpart.Comment: 7 pages, 6 figures, PRB, to be publishe

Polytetrahedral Clusters

By studying the structures of clusters bound by a model potential that favours polytetrahedral order, we find a previously unknown series of `magic numbers' (i.e. sizes of special stability) whose polytetrahedral structures are characterized by disclination networks that are analogous to hydrocarbons.Comment: 4 pages, 4 figure

Phason elasticity of a three-dimensional quasicrystal: transfer-matrix method

We introduce a new transfer matrix method for calculating the thermodynamic properties of random-tiling models of quasicrystals in any number of dimensions, and describe how it may be used to calculate the phason elastic properties of these models, which are related to experimental measurables such as phason Debye-Waller factors, and diffuse scattering wings near Bragg peaks. We apply our method to the canonical-cell model of the icosahedral phase, making use of results from a previously-presented calculation in which the possible structures for this model under specific periodic boundary conditions were cataloged using a computational technique. We give results for the configurational entropy density and the two fundamental elastic constants for a range of system sizes. The method is general enough allow a similar calculation to be performed for any other random tiling model.Comment: 38 pages, 3 PostScript figures, self-expanding uuencoded compressed tar file, LaTeX using RevTeX macros and epsfig.st

Relationship between Structure, Entropy and Diffusivity in Water and Water-like Liquids

Anomalous behaviour of the excess entropy ($S_e$) and the associated scaling relationship with diffusivity are compared in liquids with very different underlying interactions but similar water-like anomalies: water (SPC/E and TIP3P models), tetrahedral ionic melts (SiO$_2$ and BeF$_2$) and a fluid with core-softened, two-scale ramp (2SRP) interactions. We demonstrate the presence of an excess entropy anomaly in the two water models. Using length and energy scales appropriate for onset of anomalous behaviour, the density range of the excess entropy anomaly is shown to be much narrower in water than in ionic melts or the 2SRP fluid. While the reduced diffusivities ($D^*$) conform to the excess entropy scaling relation, $D^* =A\exp (\alpha S_e)$ for all the systems (Y. Rosenfeld, Phys. Rev. A {\bf 1977}, {\it 15}, 2545), the exponential scaling parameter, $\alpha$, shows a small isochore-dependence in the case of water. Replacing $S_e$ by pair correlation-based approximants accentuates the isochore-dependence of the diffusivity scaling. Isochores with similar diffusivity scaling parameters are shown to have the temperature dependence of the corresponding entropic contribution. The relationship between diffusivity, excess entropy and pair correlation approximants to the excess entropy are very similar in all the tetrahedral liquids.Comment: 24 pages, 4 figures, to be published in Journal of Physical Chemistry

Physical Origin of the Boson Peak Deduced from a Two-Order-Parameter Model of Liquid

We propose that the boson peak originates from the (quasi-) localized vibrational modes associated with long-lived locally favored structures, which are intrinsic to a liquid state and are randomly distributed in a sea of normal-liquid structures. This tells us that the number density of locally favored structures is an important physical factor determining the intensity of the boson peak. In our two-order-parameter model of the liquid-glass transition, the locally favored structures act as impurities disturbing crystallization and thus lead to vitrification. This naturally explains the dependence of the intensity of the boson peak on temperature, pressure, and fragility, and also the close correlation between the boson peak and the first sharp diffraction peak (or prepeak).Comment: 5 pages, 1 figure, An error in the reference (Ref. 7) was correcte

Thermodynamic formalism for systems with Markov dynamics

The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function within the framework of discrete time Markov chains was not suitable for continuous time Markov dynamics. Here we propose another interpretation of the definition that allows us to apply the thermodynamic formalism to continuous time. We also generalize the formalism --a dynamical Gibbs ensemble construction-- to a whole family of observables and their associated large deviation functions. This allows us to make the connection between the thermodynamic formalism and the observable involved in the much-studied fluctuation theorem. We illustrate our approach on various physical systems: random walks, exclusion processes, an Ising model and the contact process. In the latter cases, we identify a signature of the occurrence of dynamical phase transitions. We show that this signature can already be unravelled using the simplest dynamical ensemble one could define, based on the number of configuration changes a system has undergone over an asymptotically large time window.Comment: 64 pages, LaTeX; version accepted for publication in Journal of Statistical Physic