The Study Of Mobility Edges In A One-dimensional Incommensurate Model With P-wave Superfluid

This thesis focuses on the properties of the mobility edges in a one-dimensional p-wave superfluid on incommensurate lattices. We find that in a p-wave superflu-id system, the number of mobility edges increases with the increasing superfluid pairing order parameter. We identify the location of the mobility edges by a multifractal analysis.In the first chapter, we mainly introduce the background of the cold atomic physics, p-wave superfluid and one-dimensional disorder systems. In the mean-while, we detail some of the concept in the cold atom systems and the important developments in the cold atomic field in recent years.In the second chapter, we mainly introduce the background of the one-dimensional Kitaev chain, the concept of the Majorana fermions, and the topo-logical phase transition.In the third chapter, we mainly introduce the background of the disorder system in condensed matter physics. The main content are the Anderson local-ization, the phase transition of the one-dimensional incommensurate lattice(the Aubry-Andre model), and finally the mobility edge of the one-dimensional in-commensurate lattices.In the fourth chapter, we combine the one-dimensional Kitaev chain and the one-dimensional incommensurate lattices, where mobility edges exist, and focus on how a p-wave superfluid affects the mobility edges of the one-dimensional incommensurate lattices. Finally, we identify the location of the mobility edges by a multifractal analysis.Finally, a summary and outlook for our work are given.