Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2509.00166 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908950002139136 |
|---|---|
| author | Ren, Yafei Barrero, M. E. Sanchez |
| author_facet | Ren, Yafei Barrero, M. E. Sanchez |
| contents | We develop a unified theory for the nonadiabatic wave-packet dynamics of Bloch electrons subject to slowly varying spatial and temporal perturbations. Extending the conventional wave-packet ansatz to include interband contributions, we derive equations for the interband coefficients using the time-dependent variational principle, referred to as the wave-packet coefficient equation. Solving these equations and integrating out interband contributions yields the leading-order nonadiabatic corrections to the wave-packet Lagrangian. These corrections appear in three forms: (i) a nonadiabatic metric in real and momentum space, which we identify with the energy-gap-renormalized quantum metric, (ii) modified Berry connections associated with the motion of the wave-packet center, and (iii) an energy correction arising from spatial and temporal variations of the Hamiltonian. This metric reformulates the wave-packet dynamics as geodesic motion in phase space, enabling an analogue-gravity perspective in condensed matter systems. As an application, we analyze one-dimensional Dirac electron systems under a slowly varying exchange field $\bm{m}$. Our results demonstrate that variations in the magnitude of $\bm{m}$ are important to nonadiabatic dynamics, in sharp contrast to the adiabatic regime where directional variations of $\bm{m}$ are crucial. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_00166 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonadiabatic Wave-Packet Dynamics: Nonadiabatic Metric, Quantum Geometry, and Gravitational Analogy Ren, Yafei Barrero, M. E. Sanchez Materials Science We develop a unified theory for the nonadiabatic wave-packet dynamics of Bloch electrons subject to slowly varying spatial and temporal perturbations. Extending the conventional wave-packet ansatz to include interband contributions, we derive equations for the interband coefficients using the time-dependent variational principle, referred to as the wave-packet coefficient equation. Solving these equations and integrating out interband contributions yields the leading-order nonadiabatic corrections to the wave-packet Lagrangian. These corrections appear in three forms: (i) a nonadiabatic metric in real and momentum space, which we identify with the energy-gap-renormalized quantum metric, (ii) modified Berry connections associated with the motion of the wave-packet center, and (iii) an energy correction arising from spatial and temporal variations of the Hamiltonian. This metric reformulates the wave-packet dynamics as geodesic motion in phase space, enabling an analogue-gravity perspective in condensed matter systems. As an application, we analyze one-dimensional Dirac electron systems under a slowly varying exchange field $\bm{m}$. Our results demonstrate that variations in the magnitude of $\bm{m}$ are important to nonadiabatic dynamics, in sharp contrast to the adiabatic regime where directional variations of $\bm{m}$ are crucial. |
| title | Nonadiabatic Wave-Packet Dynamics: Nonadiabatic Metric, Quantum Geometry, and Gravitational Analogy |
| topic | Materials Science |
| url | https://arxiv.org/abs/2509.00166 |