# Semiclassical kinetic theory for systems with non-trivial quantum geometry and the expectation value of physical quantities

Source: [Semiclassical kinetic theory for systems with non-trivial quantum geometry and the expectation value of physical quantities](<https://www.sota2.com/research/paper/68fa44e81e209131ce914a12>)

Collection index: [llms.txt](<https://www.sota2.com/research/llms.txt>)

Data updated: 2025-10-25T05:02:07.778Z

Authors: Thierry Valet, Roberto Raimondi

Published: 2022-10-18T14:45:49.000Z

## Abstract

Starting from the Keldysh theory, for a general low energy $N$-band Hamiltonian in the clean limit, we perform a manifestly $\\smash{U(1) \\times SU(N)}$ gauge invariant semiclassical expansion. A generalized Berry curvature tensor is shown to control a redistribution of spectral weights. New expressions for certain physical quantities ensue, establishing the limits of a previously proposed correction to the density of states. In the two-band case, we derive a completely general semiclassical kinetic theory including all $O(\\hbar)$ quantum corrections. As an application, we show how one can recover, out of a single simple calculation, the chiral anomaly, intrinsic anomalous Hall conductivity and chiral magnetic effect, in all generality. The demonstrated flexibility and efficiency of our formalism derives from the insulation it provides from the underlying complexity of the quantum kinetics, notwithstanding its rigorous connection to this deeper level.

## Recorded benchmark results

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## Original sources and implementation

[Original paper](<https://arxiv.org/abs/2210.09905>)

[PDF](<https://arxiv.org/pdf/2210.09905.pdf>)