Constructing Berry-Maxwell equations with Lorentz invariance and Gauss' law of Weyl monopoles in 4D energy-momentum space
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2023
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866912054390030336 |
|---|---|
| author | Pan, Yiming Yin, Ruoyu |
| author_facet | Pan, Yiming Yin, Ruoyu |
| contents | We present the construction of a reciprocal electromagnetic field by extending the Berry curvatures into four-dimensional (4D) energy-momentum space. The resulting governing equations, termed Berry-Maxwell equations, are derived, by incorporating Lorentz invariance to constrain the parameter space of energy-momentum. Notably, these Berry-Maxwell equations exhibit dual and self-dual structures compared to the Maxwell equations. The very existence of Berry-Maxwell equations is independent of the geometrical phase of matter waves, implying that they cannot be directly derived from the time-dependent Schrödinger equation. Indeed, we find that the physical reality of this reciprocal electromagnetic field is rooted in the fundamental principles of special relativity and Gauss's law of Weyl monopoles. To validate our theory experimentally, we outline three effects for verification: (i) Lorentz boost of a Weyl monopole, (ii) reciprocal Thouless pumping, and (iii) plane-wave solutions of Berry-Maxwell's equations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2308_00612 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Constructing Berry-Maxwell equations with Lorentz invariance and Gauss' law of Weyl monopoles in 4D energy-momentum space Pan, Yiming Yin, Ruoyu Classical Physics Optics Quantum Physics We present the construction of a reciprocal electromagnetic field by extending the Berry curvatures into four-dimensional (4D) energy-momentum space. The resulting governing equations, termed Berry-Maxwell equations, are derived, by incorporating Lorentz invariance to constrain the parameter space of energy-momentum. Notably, these Berry-Maxwell equations exhibit dual and self-dual structures compared to the Maxwell equations. The very existence of Berry-Maxwell equations is independent of the geometrical phase of matter waves, implying that they cannot be directly derived from the time-dependent Schrödinger equation. Indeed, we find that the physical reality of this reciprocal electromagnetic field is rooted in the fundamental principles of special relativity and Gauss's law of Weyl monopoles. To validate our theory experimentally, we outline three effects for verification: (i) Lorentz boost of a Weyl monopole, (ii) reciprocal Thouless pumping, and (iii) plane-wave solutions of Berry-Maxwell's equations. |
| title | Constructing Berry-Maxwell equations with Lorentz invariance and Gauss' law of Weyl monopoles in 4D energy-momentum space |
| topic | Classical Physics Optics Quantum Physics |
| url | https://arxiv.org/abs/2308.00612 |