## LABORATOIRE DE PHYSIQUE THEORIQUE DE LA MATIERE CONDENSEE

Pedro Ribeiro
Centro de Física das Interações Fundamentais, Instituto Superior Técnico, Universidade de Lisboa

Non-equilibrium-induced pattern formation in strongly interacting electronic systems in one dimension.

Quantum phases of matter are typically defined for systems in thermal equilibrium. Strong non-equilibrium conditions eventually drive a system away from its linear response regime, strongly affecting the properties of the underlying equilibrium phase. A well known example arising in classical fluid mechanics is Rayleigh-Bernard convection, where a fluid placed between two plates at different temperatures develops an instability towards the formation of convection rolls of a specific wave-length.
In this talk I will report on recent results regarding the effects of large bias voltages applied across an half-filled Hubbard chain. At equilibrium this system shows a charge gap and strong antiferromagnetic correlations. I will show that out of equilibrium the wave-vector maximizing the spin-susceptibility shifts from it equilibrium value $q=\pi$, as a function of the applied voltage and of temperature. I will describe the rich mean-field diagram obtained upon increasing the electron-electron interaction term. Some of phases found here are examples of non-equilibrium-induced spacial pattern formation. I will briefly comment on the properties and stability of these phases. Finally I will proceed to argue that, although no symmetry breaking arises in the 1D Hubbard model, these results suggest a modulation of the charge gap that may be observed experimentally by STM on engineered atomic chains and nano-wires.