Linear Response and Quantum Geometry Beyond Hermiticity

Building on the non-Hermitian Fermi-Dirac distribution introduced in [Phys. Rev. Lett. 133, 086301 (2024)], we develop a unified susceptibility framework for quantum systems effectively described by non-Hermitian Hamiltonians. This formulation yields both real and imaginary response components and remains well-defined at exceptional points. We demonstrate its scope through three advances: (1) for Josephson junctions and mesoscopic rings, we obtain the full current susceptibility; in the uniform-decay, weak-dissipation, well-separated-level limit, it recovers known results without phenomenological kinetics; (2) the Hall conductance in non-Hermitian bands is no longer quantized at finite dephasing yet preserves a biorthogonal geometric structure; and (3) the interacting dielectric response, obtained through the random phase approximation, reveals geometric contributions from the non-Hermitian Fubini–Study metric. Our approach connects linear response, dissipation, and topology within a single framework, offering a direct bridge from effective non-Hermitian models to measurable transport signatures.