Relaxation of one-dimensional spin systems in a transverse variable magnetic field

A semiinfinite X-Y chain is considered with an impurity at the end which interacts with a transverse magnetic field. It is shown that by using a unitary transformation that includes a nonlinear canonical transformation of Fermi operators, such a system will reduce to the model of an ideal Fermi gas. The evolution of the impurity spin with time is investigated for a jump-like change in the transverse field. It is shown that the nature of the relaxation depends on the presence of a discrete level and its closeness to the edge of the continuous spectrum. The switching on and switching off of the field are analyzed. The evolution of the total spin in time is considered for an Ising chain on which a transverse circularly polarized field acts.

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