Molecular dynamics of nonergodic hard parallel squares with a Maxwellian velocity distribution

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Abstract
Molecular-dynamics calculations were done for hard parallel squares (HPS) at areas relative to close packing of 4.5, 2.0, 1.345, and 1.31. A Maxwellian velocity distribution (which was maintained in time) was used. A phase transition was found at 1.345 which, from these previous results, appears most likely to be a first-order transition. The normalized velocity autocorrelation function for the densities of 4.5 and 2.0 displayed a "long-time" tail whose decay approximates a minus-one power of the time. These results agreed with other molecular-dynamics simulations using a different initial velocity distribution but disagreed with Monte Carlo calculations. Speculation is presented on the ability of certain nonergodic systems such as the HPS to mimic the behavior of an ergodic system with regards to a number of properties.