From regular to erratic quantum dynamics in long spin 1/2 chains with an XY Hamiltonian

The dynamics of spin polarization driven by the XY Hamiltonian of a linear spin 1/2 chain of arbitrary length N was studied analytically and numerically. For an initial state with polarization localized on a single spin, Ijz, the dimension of the accessible Liouville subspace grows with N2. The polarization propagates along the chain in the form of spin-wave packets that gradually split into sub-packets bouncing back and forth at the ends. The initially regular appearance turns at longer times into an erratic behavior due to the complex interference of the spin-wave packets. Even for large N and long times the density operator exhibits large-amplitude fluctuations about its long-term average, which is non-ergodic in the sense that it is dependent on the initial conditions of the dynamics.