Matrixvalued Boltzmann equation for the nonintegrable Hubbard chain
Abstract
The standard FermiHubbard chain becomes nonintegrable by adding to the nearest neighbor hopping additional longer range hopping amplitudes. We assume that the quartic interaction is weak and investigate numerically the dynamics of the chain on the level of the Boltzmann type kinetic equation. Only the spatially homogeneous case is considered. We observe that the huge degeneracy of stationary states in the case of nearest neighbor hopping is lost and the convergence to the thermal FermiDirac distribution is restored. The convergence to equilibrium is exponentially fast. However for small nextnearest neighbor hopping amplitudes one has a rapid relaxation towards the manifold of quasistationary states and slow relaxation to the final equilibrium state.
 Publication:

Physical Review E
 Pub Date:
 July 2013
 DOI:
 10.1103/PhysRevE.88.012108
 arXiv:
 arXiv:1302.2075
 Bibcode:
 2013PhRvE..88a2108F
 Keywords:

 05.30.Fk;
 67.10.Fj;
 Fermion systems and electron gas;
 Quantum statistical theory;
 Mathematical Physics;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 Physics  Computational Physics
 EPrint:
 9 figures