One of the simplest ways of driving a quantum system out of equilibrium is via a quantum quench where some parameter of the Hamiltonian is changed suddenly. In this talk I will first discuss how quenches involving some exactly solvable models such as the XX spin-chain and the Luttinger liquid can give rise to intriguing non-equilibrium states characterized by a net current flow and new power-law exponents. Following this I will discuss the effect of non-linearities such as that arising from a periodic potential. The effect of the non-linearity will be treated within a renormalization group approach.

Dept. of Physics, New York University