Semiclassical Wave-Packet Dynamics in Phase-Space Geometry: Quantum Metric Effects

TL;DR

This paper develops a comprehensive formalism to incorporate quantum metric effects into wave-packet dynamics, revealing new corrections to energy, phase-space density, and transport phenomena in quantum materials.

Contribution

It introduces a general expansion-based framework that treats real- and momentum-space geometries equally, deriving quantum-metric corrections and associated transport responses.

Findings

Quantum-metric corrections modify wave-packet energy and phase-space density.

A kinetic equation incorporating quantum-metric effects is derived.

Identification of a metric-gradient-induced polarization and Hall response.

Abstract

Quantum geometry governs a wide range of transport and optical phenomena in quantum materials. Recent works have explored analogue electromagnetism and gravity in terms of the quantum geometric tensor, whose real and imaginary parts correspond to the quantum metric and the Berry curvature. By treating real- and momentum-space geometries on an equal footing, we develop a comprehensive and general formalism based on an expansion in $\hbar$, equivalent to an expansion in spatial derivatives. We derive the quantum-metric corrections to the wave-packet energy, the Berry connection, and the phase-space density of states, similar to the field-induced corrections in nonlinear response. A kinetic equation that captures quantum-metric effects across the full phase space then follows naturally. We further identify a polarization induced by gradients of the metric and a linear Hall response originating from its mixed components. Our framework provides a foundation for investigating thermodynamic and transport properties in systems where real- and momentum-space quantum geometries coexist.