03-30E

With the help of the Jordan-Wigner transformation the spin-$\frac {1}{2}$ $XY$ chains can be reformulated in terms of noninteracting spinless fermions and as a result many statistical-mechanics calculations can be performed rigorously, i.e. without making any simplifying approximations. We are interested in dynamic properties of such chains (time-dependent spin correlation functions, dynamic structure factors, dynamic susceptibilities) which are of great importance for interpretation of experimental data. We have worked out a number of dynamic quantities explicitly as well as have performed a general analysis of the two-fermion continua which are relevant for different dynamic quantities.