Cooling processes for a 1D structural 'glass' model

Glass transitions in one-, two-, three-, and four-dimensional binary Lennard-Jones systems

We investigate the calorimetric liquid-glass transition by performing simulations of a binary Lennard-Jones mixture in one through four dimensions. Starting at a high temperature, the systems are cooled to T = 0 and heated back to the ergodic liquid state at constant rates. Glass transitions are observed in two, three and four dimensions as a hysteresis between the cooling and heating curves. This hysteresis appears in the energy and pressure diagrams, and the scanning rate dependence of the area and height of the hysteresis can be described using power laws. The one-dimensional system does not experience a glass transition but its specific heat curve resembles the shape of the D≥2 results in the supercooled liquid regime above the glass transition. As D increases, the radial distribution functions reflect reduced geometric constraints. Nearest neighbor distances become smaller with increasing D due to interactions between nearest and next-nearest neighbors. Simulation data for the glasses are compared with crystal and melting data obtained with a Lennard-Jones system with only one type of particle and we find that with increasing D crystallization becomes increasingly more difficult.

Topological solitons in nondegenerate one-component chains

The possibility of the existence of topological solitons in one-component chains with a nondegenerate potential of gradient type is proven. The existence and stability of the solitons are ensured by the competing nonlinear nearest-neighbor potential V1 and parabolic second-nearest-neighbor potential V2. Solitonic solutions have been found analytically for piecewise-parabolic V1 and numerically for smoothened nearest-neighbor (NN) potential V(1,delta). Numerical results for the soliton velocity and front width are in good agreement with analytical estimates. The solitons are shown to move at a unique velocity and actually maintain the constant profile as long as the NN potential is smooth enough. The impact of two solitons of different sign is inelastic and leads to their recombination. It is argued that the soliton propagation may constitute an elementary event of structural transformations in the chain.