arXiv subjects

V. Halpern

Publications and source records attributed to V. Halpern.

5 recordsLinked to original sources

arXiv2006

Slow dynamics and correlation functions

The slow dynamics of a system as it approaches a phase transition, associated with the slowing down in the decay of a correlation function, can be caused by a sharp increase in the probability of a particle's returning to its original state following a transition, rather than to a slowing down in the transition rates as is usually assumed. The results of our calculations show that this is the case for the ferromagnetic Potts model. The implications of this result for various theories of the glass transition are discussed.

cond-mat.other↗

arXiv2006

The connection between non-exponential relaxation and fragility in supercooled liquids

Among the outstanding problems in the theory of supercooled liquids are the reasons for the rapid increase in their viscosity and relaxation times as the temperature is lowered towards the glass transition temperature, the non-exponential time dependence of the relaxation, and the possible connection between these two properties. The ferromagnetic Potts model on a square latice is a simple system that is found to exhibit these properties. Our calculations show that in this system the connection between them is associated with the dependence on temperature and time of the average environment of the sites. Some of the consequences of this for understanding the behavior of supercooled liquids are discussed.

cond-mat.dis-nn↗

arXiv2006

Correlated weak bonds as a source of the Boson peak in glasses

Many attempts to explain the Boson peak in the vibrational spectra of glasses consider models of a lattice of harmonic oscillators connected by spring constants of varying strength and randomly distributed. However, in real glasses one expects that some molecules will be connected to their neighbors by more than one weak bond, so that a realistic model should consider oscillators with several weak springs. In this paper, a t-matrix formalism is used to study the effect of such correlated weak springs in a scalar model on a simple cubic lattice with a binary distribution of spring constants. Our results, which are confirmed by computer simulations, show that a concentration of c oscillators with z weak springs and 6-z strong ones leads to a low frequency peak in the reduced density of states (Boson peak) even when the total concentration of weak springs cz is less than 10%., No such peak has been found at these low concentrations in previously reported calculations which used effective medium methods. For a given value of cz, this peak becomes more pronounced and moves to much lower frequencies as z increases.

cond-mat.dis-nn↗

arXiv2005

A new approach to strongly correlated disorder

Problems involving disordered systems are usually analyzed for systems with random disorder. However, there are many systems in which the main disorder involves clusters with correlated differences between their properties and those of the average system. A new approximation, the average trace approximation, is proposed for calculating the diagonal elements of the Green function, and hence the density of states, in such systems. As an example, application of the method to a simple cubic array of harmonic oscillators shows that correlation in the disorder leads to a peak in the low frequency density of states, a result confirmed by computer simulations.

cond-mat.dis-nn↗

arXiv2003

Rate equations for cluster formation in supercooled liquids

The formation of clusters in supercooled liquids close to the glass transition temperature is described by rate equations in which the coefficients are determined on physical grounds rather than in terms of thermodynamic quantities such as free energies and surface tensions. In particular, the density of free molecules in the liquid as a function of temperature is determined self-consistently. Calculations for a very simple model indicate that such rate equations are capable of producing physically reasonable results. Our results suggest that the difference between strong and fragile liquids may be associated with the strength of the binding of a surface molecule to a cluster, and they also provide indications about the nature of the glass transition and the structure of the resulting glass.

cond-mat.dis-nn↗