AI 中文总结
本文针对凝聚态能量与电荷转移的精度阶次未知问题，采用绝热微扰理论推导相关公式，计算电子-离子体系的非绝热电导率与德鲁德权重，为该领域提供了可控精度的理论框架。
AI 中文摘要
凝聚态体系中的能量与电荷转移通常用准粒子描述，结果关于电子-原子核质量比ε（绝热小参数）的精度阶次通常未知。为量化ε的可控精度下的能量转移，本文采用绝热微扰理论推导原子核动能变化率公式。应用一系列近恒等幺正变换，可更高阶地解耦电子与原子核自由度并生成有效哈密顿量。在原子核被视为经典的特殊情形下，能量转移公式简化为经典粒子受力做功的常规公式，但粒子质量被因子M₀⁻¹(M₀+εM₁)增强，其中M₁是裸原子核质量张量M₀的非绝热修正项，更高阶还会出现额外的量子几何修正。绝热微扰理论还被用于按ε的阶次将非绝热跃迁纳入线性响应计算，本文计算了电子-离子体系的非绝热频率相关电导率与德鲁德权重。
英文摘要
Energy and charge transfer in condensed matter systems are often described in terms of quasiparticles. The order of accuracy of the results in terms of the electron-to-nucleus mass ratio $ε$, an adiabatic small parameter, is usually not known. To quantify energy transfer with controlled accuracy in $ε$, we use adiabatic perturbation theory to derive a formula for the rate of change of the nuclear kinetic energy. Applying a sequence of near-identity unitary transformations decouples the electronic and nuclear degrees of freedom to higher and higher order and produces an effective Hamiltonian. In the special case that the nuclei are treated classically, the energy transfer formula reduces to the usual formula for the rate of work done on a classical particle but the mass of the particle is enhanced by the factor $M_0^{-1}(M_0+εM_1)$, where $M_1$ is a nonadiabatic correction to the bare nuclear mass tensor $M_0$. Additional quantum geometric corrections appear at higher orders. Adiabatic perturbation theory is further used to incorporate, order-by-order in $ε$, nonadiabatic transitions into linear response calculations. The nonadiabatic frequency-dependent conductivity and Drude weight of an electron-ion system are calculated.
