We study collisions between two strongly interacting atomic Fermi gas clouds. We observe exotic nonlinear hydrodynamic behavior, distinguished by the formation of a very sharp and stable density peak as the clouds collide and subsequent evolution into a box-like shape. We model the nonlinear dynamics of these collisions using quasi-1D hydrodynamic equations. Our simulations of the timedependent density profiles agree very well with the data and provide clear evidence of shock wave formation in this universal quantum hydrodynamic system.

We present the Born-Markov approximated Redfield quantum master equation (RQME) description for an open system of non-interacting particles (bosons or fermions) on an arbitrary lattice of N sites in any dimension and weakly connected to multiple reservoirs at different temperatures and chemical potentials. The RQME can be reduced to the Lindblad equation, of various forms, by making further approximations. By studying the N = 2 case, we show that RQME gives results which agree with exact analytical results for steady state properties and with exact numerics for time-dependent properties, over a wide range of parameters. In comparison, the Lindblad equations have a limited domain of validity in non-equilibrium. We conclude that it is indeed justified to use microscopically derived full RQME to go beyond the limitations of Lindblad equations in out-of-equilibrium systems. We also derive closed form analytical results for out-of-equilibrium time dynamics of two-point correlation functions. These results explicitly show the approach to steady state and thermalization. These results are experimentally relevant for cold atoms, cavity QED and far-from-equilibrium quantum dot experiments. PACS numbers:arXiv:1511.03778v4 [cond-mat.stat-mech]

We describe nonlinear phonon-thermoelectric devices where charge current and electronic and phononic heat currents are coupled, driven by voltage and temperature biases, when phonon-assisted inelastic processes dominate the transport. Our thermoelectric transistors and rectifiers can be realized in a gate-tunable double quantum-dot system embedded in a nanowire which is realizable within current technology. The inelastic electron-phonon scattering processes are found to induce pronounced charge, heat, and cross rectification effects, as well as a thermal transistor effect that, remarkably, can appear in the present model even in the linear-response regime without relying on the onset of negative differential thermal conductance.