Quantum impurities in non-equilibrium steady states 

With the present experimental interest in quantum dots and other mesoscopic objects submitted to electric currents, an efficient theoretical framework for studying quantum impurities in non-equilibrium steady states is much needed. After reviewing the topic of quantum impurities with relevant experiments and theoretical ideas, I will present aspects of some recent progress I made. It is a new theoretical framework that I developed recently in the interacting resonant level model (IRLM). I will explain how a non-equilibrium steady-state  (Hershfield's) density matrix can be defined, why it is related the physical (Schwinger-Keldysh) construction of steady states, and how the dynamics can be encoded into conditions on the Hilbert space ("impurity conditions"). Then I will show how these simple but slightly abstract concepts immediately give the full perturbative series (as multiple integrals), without using Feynmann diagrams or Keldysh time-ordering; I will discuss the RG-improved results in the IRLM. Finally, if time allows, I will discuss how these same concepts can be used to answer the question of integrability in equilibrium and in non-equilibrium steady states.