Researchers have extended the traditional Fermi-Dirac distribution to non-Hermitian systems. This new formalism provides a general framework to compute quantum many-body observables in equilibrium systems coupled to dissipative environments. The Fermi-Dirac distribution function describes the statistical distribution of particles over energy states in systems that obey the Pauli exclusion principle. Traditionally, this distribution is framed within the quantum mechanics paradigm, where the Hamiltonian of the quantum system is Hermitian. However, many physical systems, particularly those coupled to dissipative environments, are better described by non-Hermitian Hamiltonians. Typically, these operators exhibit complex energy eigenvalues tied to novel technological applications, like improved sensing capabilities and effective diode functionalities. In this Letter, Pei-Xin Shen, Zhide Lu, Jose L. Lado, and Mircea Trif introduced a non-Hermitian Femi-Dirac distribution (nHFDd). To verify its effectiveness, the researchers examined the issue of persistent current transport in superconducting-normal-superconducting junctions and normal metallic rings. Persistent currents, which are equilibrium currents that can flow indefinitely without an applied voltage, can be considerably influenced by external environments through dephasing processes. By utilizing the nHFDd function, the researchers derived an analytical formula for the persistent current that relies exclusively on the system's complex energy spectrum. It is worthwhile to remark that this new approach successfully corrects inaccuracies shown in previous methodologies, particularly at exceptional points—singularities in the parameter space where two or more eigenvalues and their corresponding eigenstates merge. At these points, traditional methods usually yield anomalies, but the new approach ensures that physical observables remain continuous and well-defined. This continuity at exceptional points is crucial for accurately describing quantum transport and other phenomena in non-Hermitian systems. Temperature effects and many-body interactions were also studied in this Letter. It was shown that the current amplitude is suppressed by thermal fluctuations and electron-electron scattering. Due to the analytic characteristics of the nHFDd, exceptional points cannot be identified in static observables, such as the current. However, the researchers demonstrate that they become apparent in dynamical quantities, such as the current susceptibility that is routinely measured in experiment. This work has significant implications for future research in quantum transport and non-Hermitian thermodynamics, as well as for the development of advanced quantum devices that can exploit non-Hermitian physics for enhancing their functionality.

This work has been published and selected as a Physical Review Letters Editors' Suggestion.