Cold atoms in double-well optical lattices
  Cold atoms, loaded into an optical lattice with double-well sites, are considered. Pseudospin representation for an effective Hamiltonian is derived. The system in equilibrium displays two phases, ordered and disordered. The second-order phase transition between the phases can be driven either by temperature or by changing the system parameters. Collective pseudospin excitations have a gap disappearing at the phase-transition point. Dynamics of atoms is studied, when they are loaded into the lattice in an initially nonequilibrium state. It is shown that the temporal evolution of atoms, contrary to their equilibrium thermodynamics, cannot be described in the mean-field approximation, since it results in a structurally unstable dynamical system, but a more accurate description is necessary taking account of attenuation effects. 
V.I. Yukalov and E.P. Yukalova