arXiv subjects

L. Angelani

Publications and source records attributed to L. Angelani.

35 records · Page 2Linked to original sources

arXiv2003

Character of Atomic Vibrations in a Lennard-Jones Glass

Lennard-Jones glasses (made on a computer by quenching from liquid state coordinates) are studied in harmonic approximation. Vibrational eigenfrequencies and eigenvectors are found by exact diagonalization for models with periodic boundaries and N=(500, 2048, and 6980) atoms. We analyze the density of states, mobility edge, and bond-stretching character of the normal modes. In agreement with older work of Grest, Nagel, and Rahman, the upper 7% of modes are localized, and the rest, delocalized. We find that modes can not be differentiated by any property or quantum number except their eigenfrequency. More specifically, in a given narrow frequency interval, all modes are globally identical. Transverse or longitudinal character, for example, disappears.

cond-mat.mtrl-sci↗

arXiv2003

Low-energy excess of vibrational states in v-SiO2: the role of transverse dynamics

The study of the effects of the density variations on the vibrational dynamics in vitreous silica is presented. A detailed analysis of the dynamical structure factor, as well as of the current spectra, allows the identification of a flattened transverse branch which is highly sensitive to the density variations. The experimental variations on the intensity and position of the Boson Peak (BP) in v-SiO2 as a function of density are reproduced and interpreted as being due to the shift and disappearance of the latter band. The BP itself is found to correspond to the lower energy tail of the excess states due to the piling up of vibrational modes at energies corresponding to the flattening of the transverse branch.

cond-mat.dis-nn↗

arXiv2003

General features of the energy landscape in Lennard-Jones like model liquids

Features of the energy landscape sampled by supercooled liquids are numerically analyzed for several Lennard-Jones like model systems. The properties of quasisaddles (minima of the square gradient of potential energy W=|grad V|^2), are shown to have a direct relationship with the dynamical behavior, confirming that the quasisaddle order extrapolates to zero at the mode-coupling temperature T_MCT. The same result is obtained either analyzing all the minima of W or the saddles (absolute minima of W), supporting the conjectured similarity between quasisaddles and saddles, as far as the temperature dependence of the properties influencing the slow dynamics is concerned. We find evidence of universality in the shape of the landscape: plots for different systems superimpose into master curves, once energies and temperatures are scaled by T_MCT. This allows to establish a quantitative relationship between T_MCT and potential energy barriers for LJ-like systems, and suggests a possible generalization to different model liquids.

cond-mat.soft↗

arXiv2003

Dynamics and geometric properties of the k-Trigonometric model

We analyze the dynamics and the geometric properties of the Potential Energy Surfaces (PES) of the k-Trigonometric Model (kTM), defined by a fully-connected k-body interaction. This model has no thermodynamic transition for k=1, a second order one for k=2, and a first order one for k>2. In this paper we i) show that the single particle dynamics can be traced back to an effective dynamical system (with only one degree of freedom); ii) compute the diffusion constant analytically; iii) determine analytically several properties of the self correlation functions apart from the relaxation times which we calculate numerically; iv) relate the collective correlation functions to the ones of the effective degree of freedom using an exact Dyson-like equation; v) using two analytical methods, calculate the saddles of the PES that are visited by the system evolving at fixed temperature. On the one hand we minimize |grad V|^2, as usually done in the numerical study of supercooled liquids and, on the other hand, we compute the saddles with minimum distance (in configuration space) from initial equilibrium configurations. We find the same result from the two calculations and we speculate that the coincidence might go beyond the specific model investigated here.

cond-mat.stat-mech↗

arXiv2003

Transverse acoustic nature of the excess of vibrational states in vitreous silica

We present a numerical simulation study of the density-dependence (rho = 2.2 - 4.0 g/cm^3) of the high-energy collective dynamics in vitreous silica at mesoscopic wavevectors (Q = 1 - 18 nm^-1). The density-dependence of the longitudinal and transverse current spectra provides evidence that the excess modes observed in the density of states of this and many other glasses, i.e. the Boson Peak, arises from the high-Q limit of the quasi-transverse acoustic branch. This conclusion emerges from the comparison of the numerical results with the experimentally observed energy-shift and intensity variation of the Boson Peak with increasing density.

cond-mat.dis-nn↗

arXiv2003

Potential Energy Landscape in Lennard-Jones binary mixture model

The potential energy landscape in the Kob-Andersen Lennard-Jones binary mixture model has been studied carefully from liquid down to the supercooled regime, from T =2 down to T =0.46. One thousand of independent configurations along the time evolution have been examined at each investigated temperature. From the starting configuration we searched the nearest saddle (or quasi-saddle) and minimum of the potential energy. The vibrational densities of states for the starting and the two derived configurations have been evaluated. Besides the number of negative eigenvalues of saddle, other quantities show some signature of the approaching of the dynamical arrest temperature.

cond-mat.dis-nn↗

arXiv2002

Saddles and dynamics in a solvable mean-field model

We use the saddle-approach, recently introduced in the numerical investigation of simple model liquids, in the analysis of a mean-field solvable system. The investigated system is the k-trigonometric model, a k-body interaction mean field system, that generalizes the trigonometric model introduced by Madan and Keyes [J. Chem. Phys. 98, 3342 (1993)] and that has been recently introduced to investigate the relationship between thermodynamics and topology of the configuration space. We find a close relationship between the properties of saddles (stationary points of the potential energy surface) visited by the system and the dynamics. In particular the temperature dependence of saddle order follows that of the diffusivity, both having an Arrhenius behavior at low temperature and a similar shape in the whole temperature range. Our results confirm the general usefulness of the saddle-approach in the interpretation of dynamical processes taking place in interacting systems.

cond-mat.dis-nn↗

arXiv2002

Topological Signature of First Order Phase Transitions

We show that the presence and the location of first order phase transitions in a thermodynamic system can be deduced by the study of the topology of the potential energy function, V(q), without introducing any thermodynamic measure. In particular, we present the thermodynamics of an analytically solvable mean-field model with a k-body interaction which -depending on the value of k- displays no transition (k=1), second order (k=2) or first order (k>2) phase transition. This rich behavior is quantitatively retrieved by the investigation of a topological invariant, the Euler characteristic, of some submanifolds of the configuration space. Finally, we conjecture a direct link between the Euler characteristic and the thermodynamic entropy.

cond-mat.stat-mech↗

arXiv2002

Crossover between Equilibrium and Shear-controlled Dynamics in Sheared Liquids

We present a numerical simulation study of a simple monatomic Lennard-Jones liquid under shear flow, as a function of both temperature and shear rate. By investigating different observables we find that i) It exists a line in the (temperature-shear) plane that sharply marks the boarder between an ``equilibrium'' and a ``shear-controlled'' region for both the dynamic and the thermodynamic quantities; and ii) Along this line the structural relaxation time, is proportional to the inverse shear rate, i.e. to the typical time-scale introduced by the shear flow. Above the line the liquid dynamics is unaffected by the shear flow, while below it both temperature and shear rate control the particle motion.

cond-mat.soft↗

arXiv2002

Quasi-saddles as relevant points of the potential energy surface in the dynamics of supercooled liquids

The supercooled dynamics of a Lennard-Jones model liquid is numerically investigated studying relevant points of the potential energy surface, i.e. the minima of the square gradient of total potential energy $V$. The main findings are: ({\it i}) the number of negative curvatures $n$ of these sampled points appears to extrapolate to zero at the mode coupling critical temperature $T_c$; ({\it ii}) the temperature behavior of $n(T)$ has a close relationship with the temperature behavior of the diffusivity; ({\it iii}) the potential energy landscape shows an high regularity in the distances among the relevant points and in their energy location. Finally we discuss a model of the landscape, previously introduced by Madan and Keyes [J. Chem. Phys. {\bf 98}, 3342 (1993)], able to reproduce the previous findings.

cond-mat.soft↗

arXiv2002

Temperature-dependent vibrational heterogeneities in harmonic glasses

Numerical simulation is employed to study dynamical heterogeneities in model harmonic glasses whose atoms interact via three variants of the Lennard-Jones potential (monoatomic full Lennard-Jones, soft spheres, binary mixture). Heterogeneities are observed to exist in all three kinds of glasses, and in some cases they are observed to depend on temperature. The dimension of the heterogeneities is studied for the full Lennard-Jones case.

cond-mat.dis-nn↗

arXiv2001

Off-equilibrium dynamics in the energy landscape of a simple model glass

The aging dynamics of a simple model glass is numerically investigated observing how it takes place in the potential energy landscape $V$. Partitioning the landscape in basins of minima of $|\nabla V|^2$, we are able to elucidate some interesting topological properties of the aging process. The main result is the characterization of the long time behavior as a jump dynamics between basins of attraction of minima. Moreover we extract some information about the landscape itself, determining quantitatively few parameters describing it, such as the mean energy barrier value and the mean square distance between adjacent minima.

cond-mat.soft↗

arXiv2000

Topological Description of the Aging Dynamics in Simple Glasses

We numerically investigate the aging dynamics of a monatomic Lennard-Jones glass, focusing on the topology of the potential energy landscape which, to this aim, has been partitioned in basins of attraction of stationary points (saddles and minima). The analysis of the stationary points visited during the aging dynamics shows the existence of two distinct regimes: i) at short times, t t_c, the system mainly lies in basins pertaining to minima of slowly decreasing energy. The dynamics for t>t_c can be represented by a simple random walk on a network of minima with a jump probability proportional to the inverse of the waiting time.

cond-mat.dis-nn↗

arXiv2000

Saddles in the energy landscape probed by supercooled liquids

We numerically investigate the supercooled dynamics of two simple model liquids exploiting the partition of the multi-dimension configuration space in basins of attraction of the stationary points (inherent saddles) of the potential energy surface. We find that the inherent saddles order and potential energy are well defined functions of the temperature T. Moreover, decreasing T, the saddle order vanishes at the same temperature (T_MCT) where the inverse diffusivity appears to diverge as a power law. This allows a topological interpretation of T_MCT: it marks the transition from a dynamics between basins of saddles (T>T_MCT) to a dynamics between basins of minima (T<T_MCT).

cond-mat.dis-nn↗

arXiv2000

Frustration and sound attenuation in structural glasses

Three classes of harmonic disorder systems (Lennard-Jones like glasses, percolators above threshold, and spring disordered lattices) have been numerically investigated in order to clarify the effect of different types of disorder on the mechanism of high frequency sound attenuation. We introduce the concept of frustration in structural glasses as a measure of the internal stress, and find a strong correlation between the degree of frustration and the exponent alpha that characterizes the momentum dependence of the sound attenuation $Gamma(Q)$$\simeq$$Q^α$. In particular, alpha decreases from about d+1 in low-frustration systems (where d is the spectral dimension), to about 2 for high frustration systems like the realistic glasses examined.

cond-mat.dis-nn↗

arXiv2000

Off-Equilibrium Effective Temperature in Monatomic Lennard-Jones Glass

The off-equilibrium dynamics of a monatomic Lennard-Jones glass is investigated after sudden isothermal density jumps (crunch) from well equilibrated liquid configurations towards the glassy state. The generalized fluctuation-dissipation relation has been studied and the temperature dependence of the violation factor m is found in agreement with the one step replica symmetry breaking scenario, i.e. at low temperature m(T) is found proportional to T up to an off-equilibrium effective temperature T_eff, where m(T_eff)=1. We report T_eff as a function of the density and compare it with the glass transition temperatures T_g as determined by equilibrium calculations.

cond-mat.dis-nn↗

arXiv1999

Potential Energy Landscape and Long Time Dynamics in a Simple Model Glass

We analyze the properties of a Lennard-Jones system at the level of the potential energy landscape. After an exhaustive investigation of the topological features of the landscape of the systems, obtained studying small size sample, we describe the dynamics of the systems in the multi-dimensional configurational space by a simple model. This consider the configurational space as a connected network of minima where the dynamics proceeds by jumps described by an appropriate master equation. Using this model we are able to reproduce the long time dynamics and the low temperature regime. We investigate both the equilibrium regime and the off-equilibrium one, finding those typical glassy behavior usually observed in the experiments such as: {\it i)} stretched exponential relaxation, {\it ii)} temperature-dependent stretching parameter, {\it iii)} breakdown of the Stokes-Einstein relation, and {\it iv)} appearance of a critical temperature below which one observes deviation from the fluctuation-dissipation relation as consequence of the lack of equilibrium in the system.

cond-mat.dis-nn↗