Two-regime dynamical behaviour in Lennard–Jones systems: Spectral and rescaled range analysis

In this work we present an analysis of temperature and pressure time series obtained by microcanonical (constant energy) molecular dynamics simulations. Simulations in the solid and fluid states were performed using a Lennard–Jones potential to describe atomic interactions. Several points of the system density–temperature phase diagram have been investigated for reduced densities ρ* in the range [0.2–1.4] and reduced temperatures T* in the range [1.5–2.5]. Power spectral analysis shows evidence of a two-regime power-law 1/fa behaviour with a large exponent at the high-frequency region and a smaller exponent at low frequencies. Rescaled range analysis (Hurst test) also reveals a two-regime behaviour. The exponent a depends on the system density and temperature. All time series exhibit essentially the same characteristics for short times (large frequencies). In contrast, at low frequencies, pressure is characterized by a faster loss of memory. The relation of the computed time series behaviour to the physical characteristics of the system (such as particle mean square displacement and characteristic times) is discussed.