Quantum Pumping and Adiabatic Transport in Nanostructures

This thesis consists of a theoretical exploration of quantum transport phenomena and quantum dynamics in nanostructures. Specifically, we investigate adiabatic quantum pumping of charge in several novel types of nanostructures involving open quantum dots or graphene. For a bilayer of graphene we find that at the Dirac point and for a wide bilayer the pumped current scales linearly with the sample length when this length is much smaller than the interlayer coupling length, exhibits a maximum when both of these length scales are comparable, and crosses over to a logarithmic dependence if the sample length is much larger than the interlayer coupling length. This behavior is markedly different from the behavior of the conductance in a graphene bilayer. Futher we study possibilities for adiabatic evolution and computing in an extended version of the quantum Ising model, which includes beyond-nearest neighbour interactions and an additional site-dependent longitudinal magnetic field. We calculate the energy spectrum of this model, treating the interactions exactly and using perturbation theory in the longitudinal field and find that the presence of next-nearest-neighbour interactions enhances the minimal energy gap between the ground state and the first excited state