Extra Seminar - Würzburg ToCoTronics Colloquium

Persistent currents circulate continuously without requiring external power sources. In this presentation, I will explore how to extend their theory to incorporate dissipation within the scope of non-Hermitian quantum Hamiltonians. Using Green’s function formalism, I will show the emergence of a non-Hermitian Fermi-Dirac distribution that allows to derive an analytical expression for the persistent current that relies solely on the complex spectrum. This formula is then applied to two dissipative models supporting persistent currents: (i) a phase-biased superconducting-normal-superconducting junction; (ii) a normal ring threaded by a magnetic flux. I will demonstrate that the persistent currents in both systems exhibit no anomalies at any emergent exceptional points, whose signatures are only discernible in the current susceptibility. These findings are validated by exact diagonalization, and extended to account for finite temperatures and interaction effects. To conclude, I will highlight potential uses of the formalism in designing non-Hermitian devices and discuss possible extensions to non-equilibrium scenarios.