A Phase Space Electronic Structure View of The Solid State

Abstract

We develop a phase space electronic structure view of the solid state, where electronic bands are parameterized by both nuclear position Q and nuclear momentum Π (rather than the standard practice of only Q). Within this phase space, non-Born-Oppenheimer electronic structure context, we prove a nuclear wavevector (q)-dependent version of Nafie's equality relating the change in electronic momentum as a function of nuclear momentum, ∂ ⟨p⟩/∂ Π_q, to the change in electronic position as a function of nuclear position, ∂ ⟨r⟩/∂ Q_q. Furthermore, we show how information about electron-phonon interactions, specifically nuclear-induced electronic momentum, can be extracted from simple band structure calculations -- without Berry curvature calculations.

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BibTeX RIS

BibTeX

@misc{bradbury2026phase,
  title = {{A Phase Space Electronic Structure View of The Solid State}},
  author = {Nadine Bradbury and Linqing Peng and Joseph Subotnik},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2608.06260},
  eprint = {2608.06260},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.06260},
}

RIS

TY  - UNPB
TI  - A Phase Space Electronic Structure View of The Solid State
AU  - Nadine Bradbury
AU  - Linqing Peng
AU  - Joseph Subotnik
PY  - 2026
DA  - 2026/09/10
PB  - arXiv
DO  - 10.48550/arxiv.2608.06260
UR  - https://arxiv.org/abs/2608.06260
AB  - We develop a phase space electronic structure view of the solid state, where electronic bands are parameterized by both nuclear position Q and nuclear momentum Π (rather than the standard practice of only Q). Within this phase space, non-Born-Oppenheimer electronic structure context, we prove a nuclear wavevector (q)-dependent version of Nafie's equality relating the change in electronic momentum as a function of nuclear momentum, ∂ ⟨p⟩/∂ Π_q, to the change in electronic position as a function of nuclear position, ∂ ⟨r⟩/∂ Q_q. Furthermore, we show how information about electron-phonon interactions, specifically nuclear-induced electronic momentum, can be extracted from simple band structure calculations -- without Berry curvature calculations.
ER  -

Abstract

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