Quantum response theory and momentum-space gravity

We present a quantum response approach to momentum-space gravity in dissipative multiband systems, which dresses both the quantum geometry–through an interband Weyl transformation–and the equations of motion. In addition to clarifying the roles of the contorsion and symplectic terms, we introduce the three-state quantum geometric tensor as a necessary element in the geometric classification of nonlinear responses and discuss the significance of the emergent terms from a gravitational point of view. We also identify a dual quantum geometric drag force in momentum space that provides an entropic source term for the multiband matrix of Einstein field equations.