  We consider two two-level systems (TLSs) coupled to the vacuum of guided
modes confined in a rectangular waveguide. Two TLSs are fixed at different
points in the waveguide and initially share an excitation. For the energy
separation of the TLSs far away from the cutoff frequencies of transverse
modes, two coupled delay-differential equations are obtained for the
probability amplitudes of the TLSs. The effects of the difference of TLSs'
energy separations and the inter-TLS distance on the time evolution of the
concurrence of the TLSs are examined.
