In this talk, I will introduce the theory of persistent current transport in non-Hermitian quantum systems, building on the foundation of Hermitian superconducting-normal-superconducting junctions. These systems, which emulate topological spin Josephson junctions after applying the Jordan-Wigner transformation, serve as a natural starting point for exploring Hermitian quantum transport. I will then extend the system to incorporate dissipation using non-Hermitian quantum Hamiltonians. By employing Green's function formalism, I will show the emergence of a non-Hermitian Fermi-Dirac distribution that allows us to derive an analytical expression for the persistent current that depends solely on the complex spectrum. This formula is applied to two dissipative models: (i) a phase-biased superconducting-normal-superconducting junction, and (ii) a normal mesoscopic ring threaded by a magnetic flux. I will demonstrate that the persistent currents in both systems exhibit no anomalies at emergent exceptional points, whose signatures instead become apparent in the current susceptibility. These results, validated by exact
diagonalization, are further extended to include finite temperature and interaction effects. I will conclude by discussing potential applications of this formalism in designing non-Hermitian devices and
exploring non-equilibrium quantum transport.

References:

[1] P.-X. Shen, S. Hoffman, and M. Trif, Theory of topological spin Josephson junctions, Phys. Rev. Res. 3, 013003 (2021).

[2] P.-X. Shen, Z. Lu, J. L. Lado, and M. Trif, Non-Hermitian Fermi-Dirac Distribution in Persistent Current Transport, Phys. Rev. Lett. 133, 086301 (2024) (Editors' Suggestion).