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 Mz (= the z component of the magnetization). The ergodic behaviour of Mz in the thermodynamic limit is discussed in some detail. Furthermore an exact expression is derived for the time dependence of the average of Mz in a typical nonequilibrium situation. Finally the frequency-dependent susceptibility is evaluated.