Time evolution of quasi-stationary states

J. Révai

Antonio Rodríguez, Fernando Dantas Nobre, Constantino Tsallis

This paper studies the duration of quasi-stationary states, typical of long-range-interacting Hamiltonians where negative specific heat emerges. For the classical Heisenberg d-dimensional model, the authors show a universal behavior on the time evolution of the average kinetic energy per particle as a function of dimension, system size, and range of the interactions.

Duccio Fanelli

V.S. Rudakov

Maurizio Fagotti

Locally quasi-stationary states (LQSS) were introduced as inhomogeneous generalisations of stationary states in integrable systems. Roughly speaking, LQSSs look like stationary states, but only locally. Despite their key role in hydrodynamic descriptions, an unambiguous definition of LQSSs was not given. By solving the dynamics in inhomogeneous noninteracting spin chains, we identify the set of LQSSs as a subspace that is invariant under time evolution, and we explicitly construct the latter in a generalised XY model. As a by-product, we exhibit an exact generalised hydrodynamic theory (including ``quantum corrections'').

R. G. Winter

To elucidate the time development of quasi-stationary states, a simple barrier penetration problem has been studied. Both approximate expressions and numerical results for some parameters were obtained for the decay rate. First, irregular oscillations occur for a short time. Second, the exponential region follows. Third, further oscillations occur during which the decay rate dips to negative values, so that the probability of finding the undecayed system increases briefly at several times. Fourth and finally, the decay rate decreases like an inverse power of the time.