Quantum geometry from the Moyal product: quantum kinetic equation and non-linear response
Abstract
We systematically derive the dissipationless quantum kinetic equation for a multi-band free fermionic system with U(1) symmetry. Using the Moyal product formalism, we fully band-diagonalize the dynamics. Expanding to the second order in gradients, which is beyond the semiclassical limit, we give a complete analysis of the band-resolved thermodynamics and transport properties, especially those arising from the quantum geometric tensor. We apply our framework to a Bloch band theory under electric fields near equilibrium and find the linear and nonlinear transport coefficients. We also obtain the dynamical density-density response functions in the metallic case, including quantum metric corrections. Our results and approach can be applied very generally to multi-band problems even in situations with spatially varying Hamiltonians and distributions.
Cite
@article{arxiv.2504.10447,
title = {Quantum geometry from the Moyal product: quantum kinetic equation and non-linear response},
author = {Takamori Park and Xiaoyang Huang and Lucile Savary and Leon Balents},
journal= {arXiv preprint arXiv:2504.10447},
year = {2026}
}
Comments
Corrected errors in Eq (3.31). Added Appendix F, N