Adiabatic perturbation theory of energy transfer and charge transport in condensed matter

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.

Source: arXiv:2608.13066v1 - http://arxiv.org/abs/2608.13066v1 PDF: https://arxiv.org/pdf/2608.13066v1 Original Link: http://arxiv.org/abs/2608.13066v1