In the antiferromagnetic (AFM) bilayer model the quantum phase transition (QPT) between the ordered state and the disordered state is driven by a spin coupling tuning parameter for nearest neighbour interaction on the lattice. In this thesis, using a bond operator approach, we find the dispersion relation for the triplon quasi-particle deep in the disordered phase. Using this dispersion we find the scattering amplitude of two triplons in the disordered phase and find the bound state and its dependence on the lattice for the different spin channels. We find that the singlet channel (S = 0) is the most favourable bound state in this model.
Investigations into CP violation in the hadron sector may be done by studying CP - violating electromagnetic moments in molecular systems. Recently there have been experimental developments in using paramagnetic molecules to observe CP -violating phenomena, with a recent experiment strengthening the current limit of the electron electric dipole moment (EDM). These paramagnetic molecules allow us to study the lowest CP -violating magnetic moment of the nucleus, the nuclear magnetic quadrupole moment (MQM). The MQM is expected to improve the limits on fundamental CP - violating properties. In this thesis we focus on finding the contribution of core po- larisation to the nuclear MQM. We perform calculations of of T ,P −odd effects in the paramagnetic molecules TaN, ThO, ThF+, HfF+ ,YbF, HgF and BaF induced by MQMs with the core contribution. We compare these results to the valence only contribution and find that the core contribution has a large impact for deformed nuclei. We express the nuclear MQM and molecular frequency shifts in terms of the CP -violating quark EDMs, quark chromo-DMs and the $\theta$ term in QCD.