Exact time-correlation functions of quantum ising chain in a kicking transversal magnetic field - Spectral analysis of the adjoint propagator in Heisenberg picture

Spectral analysis of the adjoint propagator in a suitable Hilbert space (an d Lie algebra) of quantum observables in Heisenberg picture is discussed as an alternative approach to characterize infinite temperature dynamics of n on-linear quantum many-body systems or quantum fields, and to provide a bri dge between ergodic properties of such systems and the results of classical ergodic theory. We begin by reviewing some recent analytic and numerical r esults along this lines. In some cases the Heisenberg dynamics inside the s ubalgebra of the relevant quantum observables can be mapped explicitly into the (conceptually much simpler) Schrodinger dynamics of a single one-(or f ew)-dimensional quantum particle. The main body of the paper is concerned w ith an application of the proposed method in order to work out explicitly t he general spectral measures and the time correlation functions in a quantu m Ising spin 1/2 chain in a periodically kicking transversal magnetic field , including the results for the simpler autonomous case of a static magneti c field in the appropriate limit. The main result, being a consequence of a purely continuous non-trivial part of the spectrum, is that the general ti me-correlation functions decay to their saturation values as t(-3/2).