On a soluble model of an antiferromagnetic chain with Dzyaloshinsky interactions. II

Time-dependent properties of the one-dimensional XY model with Dzyaloshinsky interactions in the presence of a magnetic field in the z direction are investigated. Explicit expressions are derived for the time correlation functions of the z components of two spins and the time auto-correlation functions of M^z (= the z component of the magnetization). The ergodic behaviour of M^z in the thermodynamic limit is discussed in some detail. Furthermore an exact expression is derived for the time dependence of the average of M^z in a typical nonequilibrium situation. Finally the frequency-dependent susceptibility is evaluated.