Fractional quantum Hall systems host quasiparticles carrying fractional charge and obeying anyonic statistics—excitations that interpolate between bosons and fermions. While fractional charge has been accurately measured, the direct observation of anyonic braiding remains an open challenge. Two main approaches have been pursued: spatial braiding in interferometers, which are highly sensitive to Coulomb and geometric effects, and temporal braiding through current cross-correlations in Hanbury–Brown–Twiss or “anyon collider” setups, which suffer from model-dependent interpretations. The Unifying Nonequilibrium Perturbative Theory (UNEPT) offers a comprehensive framework to describe these systems beyond the Tomonaga–Luttinger liquid model that fails to capture most experimental situations. It yields a novel braiding fluctuation–dissipation theorem (FDT) that enables extraction of the anyonic braiding phase from measurable quantities such as noise and admittance. This project aims, on one hand, to extend this braiding FDT to time- and space-resolved probes of braiding under finite DC and AC drives, and on the other, to apply UNEPT to interferometric geometries to address spatial braiding, shown recently to be more robust than its temporal counterpart. The student will receive training in advanced quantum transport theory and collaborate with experimental groups to design realistic detection protocols for anyonic statistics.