Many-body quantum systems coupled to baths can display a variety of transport properties depending on the system and bath parameters. At the beginning of the presentation we will give an overview of some of the recent results on dissipatively boundary driven many-body quantum systems. We then focus our discussion on the emergence of current rectification in strongly interacting spin chains and show how this can lead to giant rectification and, for a particular setup, to perfect rectification beyond a critical value of the interaction. We then study how the rectification is affected by Hamiltonian and dissipative perturbations, showing in which scenarios one can still achieve giant rectification. References: G. Landi, D. Poletti, G. Schaller, arXiv:2104.14350 K.H. Lee et al., Phys. Rev. E 103, 052143 (2021) K.H. Lee et al, Entropy 22, 1311 (2020) V. Balachandran et al., Phys. Rev. Lett. 123, 020603 (2019) V. Balachandran et al., Phys. Rev. E 99, 032136 (2019) V. Balachandran et al., Phys. Rev. Lett. (2018)
Two dimensional photon gases trapped in dye-filled microcavities can undergo thermalization and nearly ideal equilibrium Bose-Einstein condensation. However, they are inherently driven-dissipative systems that can exhibit an intricate interplay between the thermalizing influence of the environment given by the dye solution and the pump and loss processes driving the system out of equilibrium. First we investigate how this interplay influences the selection of macroscopically occupied cavity modes in a homogeneously pumped system. Depending on the parameter regime, this selection can be related either to lasing of (typically multiple) modes or to equilibrium-like photon condensation in the ground mode. When the system is driven by an off-centered pump beam, we show how a robust mechanism for controlled two-mode emission can be achieved by tailoring the transverse potential landscape for the photons.