Aging and metastability in the dynamics of quantum-group oscillators

A special quantum-group oscillator presents an upper bound in its energy spectrum, which is preceded by an accumulation of infinite levels. The standard Boltzmann–Gibbs (BG) statistical-mechanics formalism is inadequate for dealing with such systems, since the partition function diverges for any finite temperature. In the present work, the limits of applicability of the BG theory, for quantum-group oscillators, are analysed. The quantum-group oscillators are investigated through a conventional Monte Carlo simulation, in which the probability for jumping between states is based on the BG weight. As expected, for any finite temperature, the simulation always carries the system towards its upper-bound-energy state, after some time. However, it is shown that the system may live in a metastable state, characterized by a slowly varying value of energy, before approaching its maximum-energy state. Such a metastable state may present a long duration, for low temperatures, and exhibits aging. A modified dynamics is proposed, expected to work well only for low temperatures, which prevents the system from reaching the upper-bound-energy state. The modified dynamics yields results that coincide with those of the standard BG Monte Carlo in the metastable state, at low temperatures. It is argued that, depending on the time scale of interest, the metastable state may be considered as an effective equilibrium.