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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• Non-Hermitian multiterminal phase-biased Josephson junctions
• Interplay between Majorana and Shiba states in a minimal Kitaev chain coupled to a superconductor
• Non-Hermitian minimal Kitaev chains
• Josephson effect and critical currents in trivial and topological full-shell hybrid nanowires
• Andreev non-Hermitian Hamiltonian for open Josephson junctions from Green's functions
• Design nearly optimal quantum algorithm for linear differential equations via Lindbladians
• Non-Hermitian superconducting diode effect
• Many-body Liouvillian dynamics with a non-Hermitian tensor-network kernel polynomial algorithm
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• Supercurrent from the imaginary part of the Andreev levels in non-Hermitian Josephson junctions
• Non-Hermitian Josephson junctions with four Majorana zero modes
• Non-Hermitian skin effect and electronic nonlocal transport
• 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