Investigation of a newrepresentation of spin

Abstract: The Bose-Hubbard Model, a tight binding model within solid state theory can be solved exactly using a number theoretical approach. From this approach, in the two sited Bose-Hubbard model, the hopping term in the model takes the form of a Pauli x matrix. The hopping term can be interpreted as a two energy level system or a dimer with k+1 particles. The statistical properties of this dimer is investigated assuming Boltzmann distribution. The partition function and particle density on each site in the dimer is calculated for spin 1/2 system. The entropy and average energy is also calculated. The particle density is calculated and plotted as a function of temperature for the spin 1/2,1,3/2 and 2 system. At low temperature the particles are more likely to be found in the lower energy site and at high temperatures the particles is equally distributed at the both sites.