Relaxation in a Completely Integrable Many-Body Quantum System: AnAb InitioStudy of the Dynamics of the Highly Excited States of 1D Lattice Hard-Core Bosons

Marcos Rigol, Vanja Dunjko, Vladimir Yurovsky, Maxim Olshanii
2007 Physical Review Letters  
In this Letter we pose the question of whether a many-body quantum system with a full set of conserved quantities can relax to an equilibrium state, and, if it can, what the properties of such state are. We confirm the relaxation hypothesis through a thorough ab initio numerical investigation of the dynamics of hard-core bosons on a one-dimensional lattice. Further, a natural extension of the Gibbs ensemble to integrable systems results in a theory that is able to predict the mean values of
more » ... ical observables after relaxation. Finally, we show that our generalized equilibrium carries more memory of the initial conditions than the usual thermodynamic one. This effect may have many experimental consequences, some of which having already been observed in the recent experiment on the non-equilibrium dynamics of one-dimensional hard-core bosons in a harmonic potential [T. Kinoshita, T. Wenger, D. S. Weiss, Nature (London) 440, 900 (2006)].
doi:10.1103/physrevlett.98.050405 pmid:17358832 fatcat:b2ljegzzjre7vfwtaczxzwkxpe