We propose an approach to investigate non-equilibrium photon dynamics driven by mechanical motion in a recently developed optomechanical setup with a membrane between two mirrors. The presence of a photon in the left or the right half of the cavity can be identified with the two states of a two-level system, loosely speaking. Mechanical driving can shuttle photons between the two halves of the cavity and opens up the whole domain of strongly driven quantum systems to the field of optomechanics. Depending on the driving strength we predict the possibility to observe an Autler-Townes splitting as well as Landau-Zener-Stueckelberg dynamics originally known from atomic two-state systems.
[more] We show that a realistic description of the classic Kondo systems of iron impurities in the noble metals gold and silver is given by the fully screened, 3-channel spin 3/2 Kondo model. It yields excellent agreement between theory and experiment for the temperature dependence of both the resistivity and the decoherence rate, studied via weak localization. This result sets a benchmark for the level of quantitative understanding attainable for the Kondo effect in real materials.
[more] We work out a Hamiltonian scaling theory for the steady state of the Kondo model with voltage bias V. We focus on the spin dynamics and in particular on the static spin susceptibility. This yields key insights into the differences between equilibrium and non-equilibrium behavior in this paradigm model for correlated quantum impurities.

Static spin susceptibility as a function of Teff = V/(1+r)(1+r-1), where r describes the asymmetry of the coupling to the two leads. Curves are for r=1.0 (symmetric coupling), 1.4, 1.8, 2.2, 2.6, 3.0 from bottom to top. The dashed line shows an asymptotically exact result in the limit of vanishing voltage bias.
[more] Motivated by recent experiments in ultracold atomic gases that explore the nonequilibrium dynamics of interacting quantum many-body systems, we investigate the opposite limit of Landau's Fermi liquid paradigm: We study a Hubbard model with a sudden interaction quench, that is the interaction is switched on at time t=0. Using the flow equation method, we are able to study the real time dynamics for weak interaction U in a systematic expansion and find three clearly separated time regimes:
i) An initial buildup of correlations where the quasiparticles are formed.
ii) An intermediate quasi-steady regime resembling a zero temperature Fermi liquid with a nonequilibrium quasiparticle distribution function.
iii) The long time limit described by a quantum Boltzmann equation leading to thermalization with a temperature T proportional to U.
[more]