A Reciprocal-Space Formulation of Mixed Quantum-Classical Dynamics
arXiv:2103.06285 · doi:10.1063/5.0053177
Abstract
We derive a formulation of mixed quantum-classical dynamics for describing electronic carriers interacting with phonons in reciprocal space. For dispersionless phonons, we start by expressing the real-space classical coordinates in terms of complex variables. A Fourier series over these coordinates then yields the reciprocal-space coordinates. Evaluating the electron-phonon interaction term through Ehrenfest's theorem, we arrive at a reciprocal-space formalism that is equivalent to mean-field mixed quantum-classical dynamics in real space. This equivalence is numerically verified for the Holstein and Peierls models, for which we find the reciprocal-space Hellmann-Feynman forces to involve momentum derivative contributions in addition to the position derivative terms commonly seen in real space. We close by presenting a proof of concept for the inexpensive modeling of low-momentum carriers interacting with phonons by means of a truncated basis in reciprocal space, which is not possible within a real space formulation.
arXiv comment6 pages, 2 figures
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Cited by in corpus (5)
- Revealing Ultrafast Phonon Mediated Inter-Valley Scattering through Transient Absorption and High Harmonic Spectroscopies
- A Reciprocal-Space Formulation of Surface Hopping
- Overcoming positivity violations for density matrices in surface hopping
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