Institute for Theoretical Physics • University of Cologne

The prospect of intrinsically protected quantum computing is driving the research on topological quantum systems. Materials with a topologically nontrivial band structure are however difficult to manufacture experimentally. We recently showed that topological materials can be engineered by quite simple means, when considering a different space: superconducting junctions have the phase difference and the number of transported charges across the junction as conjugate variables. In the main part of the talk, I will present the example of a four-terminal junction whose energy spectrum exhibits Weyl singularities in the space of three independent phases, which thus play the role of quasimomenta. The nonzero Chern number can be directly probed through a transport measurement, namely, through a quantised transconductance. In the final part of the talk, I will provide an outlook on future directions. For one, electric circuits may be used to study topological phase transitions specific to open systems out of equilibrium, and secondly, they may exhibit a so far unexplored connection between topology and quantum thermodynamics.

The grand canonical ensemble lies at the core of quantum and classical  statistical mechanics. A small system thermalizes to this ensemble while exchanging heat and particles with a bath. A quantum system may exchange  quantities represented by operators that fail to commute. Whether such  a ​ ​ system thermalizes and what form the thermal state has are questions  about ​ ​ truly quantum thermodynamics. Here we investigate this thermal  state from ​ ​ three perspectives. First, we introduce an approximate microcanonical ensemble. If this ensemble characterizes the system- and-bath composite, tracing out the bath yields the system's thermal  state. This state is expected to be the equilibrium point, we argue,  of typical dynamics. Finally, we define a resource-theory model for thermodynamic exchanges of noncommuting observables. Complete passivity ​-- ​ the inability to extract work from equilibrium states ​ ​ -- ​, ​ implies  the thermal state's form, too. Our work opens new avenues into  equilibrium in the presence of quantum noncommutation. ​ [Based on arXiv:1512.01189]​