Abstract:
In this thesis, the ground state con guration of the Frenkel-Kontorova model with a scalloped external potential is investigated. The method of e ective potentials of Gri ths and Chou is extended by a novel approach involving the Burgers' equation of uid dynamics. This approach is then employed to predict the e ective potential at the end of a semi-in nite harmonic chain of particles in a periodic scalloped external potential. We explicitly construct the ground state con guration of particles, where the period of the particle spacing is close to that of the external potential. Our results are in agreement with previous exact results for this problem, thereby validating our method of approach.
