The extinction of the contact process in lattice models with quenched disorder is analysed in the limit of small density of infected sites. It is shown that the problem in such a regime can be mapped to the quantum-mechanical one characterized by the Anderson Hamiltonian for an electron in a random lattice. It is demonstrated both analytically (self-consistent mean-field) and numerically (by direct diagonalization of the Hamiltonian and by means of cellular automata simulations) that disorder enhances the contact process given the mean values of random parameters are not influenced by disorder.

S. N. Taraskin J. J. Ludlam C. J. Neugebauer C. A. Gilligan

A structural model of a one-component $\sigma$-phase crystal has been constructed by means of molecular dynamics simulation. The phonon dispersion curves and the vibrational density of states were computed for this model. The dependence of the vibrational properties on the thermodynamical parameters was investigated. The vibrational density of states of the $\sigma$-phase structure is found to be similar to that of a one-component glass with icosahedral local order. On the basis of this comparison it is concluded that the $\sigma$ phase can be considered to be a good crystalline reference structure for this glass.

S. I. Simdyankin S. N. Taraskin M. Dzugutov S. R. Elliott

In the framework of the band theory, we consider two tight-binding models of insulators. The first one, proposed recently by Taraskin et al, is a translationally invariant system, built out of two independent non-overlapping bands of single-particle orbitals that are coupled by a weak inter-band hybridization. This kind of insulator exhibits unphysical properties: we show, in particular, that the one-body density matrix does not depend on the width of the gap between the bands. Consequently, there is no delocalization effect with increasing metallicity. In the second model there are also two bands. However, they are not imposed by construction but are created from a band of single-particle orbitals due to the breaking of the translational symmetry by a periodic potential. These bands are separated by a gap for all nonzero values of the unique energy parameter of the model. We demonstrate that the one-body density matrix has the same structure as in the first model. As a result, the large distance asymptotic formulae derived by Taraskin et al in dimensions $D=1,2,3$, apply as well, but only for very large gap widths. In D=1 and in the diagonal direction of D=2 cases, we derive a stronger asymptotic formula, valid for all gap widths. The both kinds of asymptotic formulae are composed of a dimension-dependent power-law factor and a gap-dependent exponentially decaying factor. The latter asymptotics implies that the exponential decay rate vanishes linearly with the vanishing gap. In non-diagonal directions, we have found numerically that the linear scaling is replaced by the square root one. Independently of the direction, the exponential decay rate grows logarithmically with the gap width, for sufficiently large gaps.

Janusz Jedrzejewski Taras Krokhmalskii

A model for cooperative sequential adsorption that incorporates nearest-neighbor exclusion and next-nearest neighbor interaction is presented. It is analyzed for the case of one-dimensional dimer and two-dimensional monomer adsorption. Analytic solutions found for certain values of the interaction strength are used to investigate jamming coverage and temporal approach to jamming in the one-dimensional case. In two dimensions, the series expansion of the coverage $\theta(t)$ is presented and employed to provide estimates for the jamming coverage as a function of interaction strength. These estimates are supported by Monte Carlo simulation results.

C. J. Neugebauer S. N. Taraskin

The jump-walking Monte-Carlo algorithm is revisited and updated to study the equilibrium properties of systems exhibiting quasi-ergodicity. It is designed for a single processing thread as opposed to currently predominant algorithms for large parallel processing systems. The updated algorithm is tested on the Ising model and applied to the lattice-gas model for sorption in aerogel at low temperatures, when dynamics of the system is critically slowed down. It is demonstrated that the updated jump-walking simulations are able to produce equilibrium isotherms which are typically hidden by the hysteresis effect characteristic of the standard single-flip simulations.

Zilvinas Rimas Sergei Taraskin

It is demonstrated that the width of the uncorrelated atomic-charge distribution in glasses can be extracted from the frequency dependence of the coupling coefficient for the far-infrared absorption measured experimentally by the time-domain terahertz spectroscopy technique. This value for As2S3 glass is found to be 0.12 (e). A density functional theory-based tight-binding molecular dynamics model of As2S3 glass qualitatively supports these findings.

S. N. Taraskin S. I. Simdyankin S. R. Elliott

The one-dimensional contact process with weak to intermediate quenched disorder in its transmission rates is investigated via quasi-stationary Monte Carlo simulation. We address the contested questions of both the nature of dynamical scaling, conventional or activated, as well as of universality of critical exponents by employing a scaling analysis of the distribution of lifetimes and the quasi-stationary density of infection. We find activated scaling to be the appropriate description for all disorder strengths considered. Critical exponents are disorder dependent and approach the values expected for the limit of strong disorder as predicted by strong-disorder renormalization group analysis of the process. However, even for the strongest disorder under consideration no strong-disorder exponents are found.

S V Fallert S N Taraskin

We performed terahertz time-domain spectroscopy, low-frequency Raman scattering, and Brillouin light scattering on vitreous glucose to investigate the boson peak (BP) dynamics. In the spectra of {\alpha}({\nu})/{\nu}2 [{\alpha}({\nu}) is the absorption coefficient], the BP is clearly observed around 1.1 THz. Correspondingly, the complex dielectric constant spectra show a universal resonancelike behavior only below the BP frequency. As an analytical scheme, we propose the relative light-vibration coupling coefficient (RCC), which is obtainable from the combination of the far-infrared and Raman spectra. The RCC reveals that the infrared light-vibration coupling coefficient CIR({\nu}) of the vitreous glucose behaves linearly on frequency which deviates from Taraskin's model of CIR({\nu}) = A + B{\nu}2 [S. N. Taraskin et al., Phys. Rev. Lett. 97, 055504 (2006)]. The linearity of CIR({\nu}) might require modification of the second term of the model. The measured transverse sound velocity shows an apparent discontinuity with the flattened mode observed in the inelastic neutron scattering study [N. Violini et al., Phys. Rev. B 85, 134204 (2012)] and suggests a coupling between the transverse acoustic and flattened modes.

Mikitoshi Kabeya Tatsuya Mori Yasuhiro Fujii Akitoshi Koreeda Byoung Wan Lee Jae-Hyeon Ko Seiji Kojima

This paper describes a method for extracting rapidly varying, superimposed amplitude- and frequency-modulated signal components. The method is based upon the continuous wavelet transform (CWT) and uses a new wavelet which is a modification to the well-known Morlet wavelet to allow analysis at high resolution. In order to interpret the CWT of a signal correctly, an approximate analytic expression for the CWT of an oscillatory signal is examined via a stationary-phase approximation. This analysis is specialized for the new wavelet and the results are used to construct expressions for the amplitude and frequency modulations of the components in a signal from the transform of the signal. The method is tested on a representative, variable-frequency signal as an example before being applied to a function of interest in our subject area - a structural correlation function of a disordered material - which immediately reveals previously undetected features.

J. D. Harrop S. N. Taraskin S. R. Elliott

The lattice gas model of condensation in a heterogeneous pore system, represented by a random graph of cells, is studied using an exact analytical solution. A binary mixture of pore cells with different coordination numbers is shown to exhibit two phase transitions as a function of chemical potential in a certain temperature range. Heterogeneity in interaction strengths is demonstrated to reduce the critical temperature and, for large enough degree of disorder, divides the cells into ones which are either on average occupied or unoccupied. Despite treating the pore space loops in a simplified manner, the random-graph model provides a good description of condensation in porous structures containing loops. This is illustrated by considering capillary condensation in a structural model of mesoporous silica SBA-15.

Thomas P. Handford Alexander Dear Francisco J. Pérez-Reche Sergei N. Taraskin