Geometric energy transfer in two-component systems

TL;DR

This paper explores how wave function factorization into marginal and conditional parts reveals geometric aspects of energy transfer in two-component quantum systems, deriving identities for energy rate changes.

Contribution

It introduces a novel identity for the rate of change of the quantum metric term in wave function factorization, linking geometry and energy transfer.

Findings

The kinetic energy splits into gauge-dependent and metric-dependent terms.

An explicit identity for the energy rate change related to the quantum metric.

Insights into geometric energy transfer mechanisms in quantum systems.

Abstract

Factoring a wave function into marginal and conditional factors partitions the subsystem kinetic energy into two terms. The first depends solely on the marginal wave function, through its gauge-covariant derivative, while the second depends on the quantum metric of the conditional wave function over the manifold of marginal variables. We derive an identity for the rate of change of the second term.