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Exact time-correlation functions of quantum Ising chain in a kicking transversal magnetic field
Spectral analysis of the {\em adjoint} propagator in a suitable Hilbert space
(and Lie algebra) of quantum observables in Heisenberg picture is discussed as
an alternative approach to characterize infinite temperature dynamics of
non-linear quantum many-body systems or quantum fields, and to provide a bridge
between ergodic properties of such systems and the results of classical ergodic
theory. We begin by reviewing some recent analytic and numerical results along
this lines. In some cases the Heisenberg dynamics inside the subalgebra of the
relevant quantum observables can be mapped explicitly into the (conceptually
much simpler) Schr\" odinger dynamics of a single one-(or few)-dimensional
quantum particle. The main body of the paper is concerned with an application
of the proposed method in order to work out explicitly the general spectral
measures and the time correlation functions in {\em a quantum Ising spin 1/2
chain in a periodically kicking transversal magnetic field}, including the
results for the simpler autonomous case of a static magnetic 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 time-correlation
functions decay to their saturation values as .Comment: 12 pages with 4 eps-figure
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