From Non-Hermitian Linear Response to Dynamical Correlations and Fluctuation-Dissipation Relations in Quantum Many-Body Systems

Quantum many-body systems are characterized by their correlations. While equal-time correlators and unequal-time commutators between operators standard observables, the direct access to anti-commutators poses a formidable experimental challenge. Here, we propose general technique for measuring using linear response of system non-Hermitian perturbation. We illustrate protocol at example Bose-Hubbard model, where approach thermal equilibrium in closed quantum can be tracked both sides fluctuation-dissipation relation. relate scheme Zeno effect weak measurements, possible implementations cold-atom system. Our proposal provides way characterizing dynamical correlations with potential applications understanding strongly correlated matter as well novel technologies.