Non-Hermitian Fermi-Dirac Distribution in Persistent Current Transport

Abstract

Persistent currents circulate continuously without requiring external power sources. Here, we extend their theory to include dissipation within the framework of non-Hermitian quantum Hamiltonians. Using Green's function formalism, we introduce a non-Hermitian Fermi-Dirac distribution and derive an analytical expression for the persistent current that relies solely on the complex spectrum. We apply our formula to two dissipative models supporting persistent currents: (i) a phase-biased superconducting-normal-superconducting junction; (ii) a normal ring threaded by a magnetic flux. We show that the persistent currents in both systems exhibit no anomalies at any emergent exceptional points, whose signatures are only discernible in the current susceptibility. We validate our findings by exact diagonalization and extend them to account for finite temperatures and interaction effects. Our formalism offers a general framework for computing quantum many-body observables of non-Hermitian systems in equilibrium, with potential extensions to non-equilibrium scenarios.

5+9 pages, 4+5 figures, published in Phys. Rev. Lett. with Editors' Suggestion

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• Design nearly optimal quantum algorithm for linear differential equations via Lindbladians
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• Chemical master equation parameter exploration using DMRG
• Edge states and persistent current in a PT-symmetric extended Su-Schrieffer-Heeger model with generic boundary conditions
• Physical constraints on effective non-Hermitian systems