Growth Of Mean Square Displacement Research Articles

Slow dynamics of a mobile impurity interacting with an Anderson insulator

We investigate dynamics of a single mobile impurity immersed in a bath of Anderson localized particles and focus on the regime of relatively strong disorder and interactions. In that regime, the dynamics of the system is particularly slow, suggesting, at short times, an occurrence of many-body localization. Considering longer time scales, we show that the latter is a transient effect and that, eventually, the impurity spreads sub-diffusively and induces a gradual delocalization of the Anderson insulator. The phenomenology of the system in the considered regime of slow dynamics includes a sub-diffusive growth of mean square displacement of the impurity, power-law decay of density correlation functions of the Anderson insulator and a power-law growth of entanglement entropy in the system. We observe a similar regime of slow dynamics also when the disorder in the system is replaced by a sufficiently strong quasi-periodic potential.

Molecular dynamics study of pristine and defective hexagonal BN, SiC and SiGe monolayers

The structural and thermodynamical properties of 2D honeycomb hybrids are investigated over a wide temperatures range by carrying out atomistic simulations using Tersoff-type interatomic empirical potential. The variance of the radial distribution as well as the height correlation functions in terms of temperature and buckling parameter are discussed for the SiC, SiGe and BN compounds. A non-monotonic growth of mean square displacement is observed when increasing the defect concentration. The energetic of Stone–Wales defects and vacancies as well as the magnitude of thermally excited ripples for both pristine and defective monolayers increase significantly at higher temperatures, which is caused by the increase in bond lengths and atom’s velocities, resulting in higher kinetic energy. It follows that thermal rippling is intricately related to thermal expansion.

Breakdown of universal Lindemann criterion in the melting of Lennard-Jones polydisperse solids

It is commonly believed that melting occurs when mean square displacement (MSD) of a particle of crystalline solid exceeds a threshold value. This is known as the Lindemann criterion, first introduced in the year of 1910 by Lindemann. However, Chakravarty et al., demonstrated that this common wisdom is inadequate because the MSD at melting can be temperature dependent when pressure is also allowed to vary along the coexistence line of the phase diagram [Chakravarty C, Debenedetti P G and Stillinger F H 2007 J. Chem. Phys. 126 204508]. We show here by extensive molecular dynamics simulation of both two and three dimensional polydisperse Lennard-Jones solids that particles on the small and large limits of size distribution exhibit substantially different Lindemann ratio at melting. Despite all the dispersion in MSD, melting is found to be first order in both the dimensions at 5–10% dispersity in size. Sharpness of the transition is incommensurate with the different rate of growth of MSD. The increased MSD values of smaller particles play a role in the segregation of them prior to melting.