We study the non-equilibrium dynamics of cold atoms held in an optical lattice potential. The expansion of an initially confined atom cloud occurs in two phases: an initial quadratic expansion followed by a ballistic behaviour at long times. Accounti
ng for this gives a good description of recent experimental results, and provides a robust method to extract the effective intersite tunneling from time-of-flight measurements.
We analyze the Coulomb interacting problem in undoped graphene layers by using an excitonic variational ansatz. By minimizing the energy, we derive a gap equation which reproduces and extends known results. We show that a full treatment of the exchan
ge term, which includes the renormalization of the Fermi velocity, tends to suppress the phase transition by increasing the critical coupling at which the excitonic instability takes place.
We study the bosonic analog of Andreev reflection at a normal-superfluid interface where the superfluid is a boson condensate. We model the normal region as a zone where nonlinear effects can be neglected. Against the background of a decaying condens
ate, we identify a novel contribution to the current of reflected atoms. The group velocity of this Andreev reflected component differs from that of the normally reflected one. For a three-dimensional planar or two-dimensional linear interface Andreev reflection is neither specular nor conjugate.
We propose that recent transport experiments revealing the existence of an energy gap in graphene nanoribbons may be understood in terms of Coulomb blockade. Electron interactions play a decisive role at the quantum dots which form due to the presenc
e of necks arising from the roughness of the graphene edge. With the average transmission as the only fitting parameter, our theory shows good agreement with the experimental data.
