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We examine the Hall conductivity of macroscopic two-dimensional quantumsystem, and show that the observed quantities can sometimes violate thefluctuation dissipation theorem (FDT), even in the linear response (LR) regimeinfinitesimally close to equilibrium. The violation can be an order ofmagnitude larger than the Hall conductivity itself at low temperature and instrong magnetic field, which are accessible in experiments. We further extendthe results to general systems and give a necessary condition for suchlarge-scale violation to happen. This violation is a genuine quantum phenomenonthat appears on a macroscopic scale. Our results are not only bound to thedevelopment of the fundamental issues of nonequilibrium physics, but the ideais also meaningful for practical applications, since the FDT is widely used forthe estimation of noises from the LRs.

Macroscopic Quantum Violation of Fluctuation-Dissipation Theorem in Equilibrium