Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2501.15209 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918060929056768 |
|---|---|
| author | Xu, Mingtao Gong, Zongping Yi, Wei |
| author_facet | Xu, Mingtao Gong, Zongping Yi, Wei |
| contents | The optimal transport problem seeks to minimize the total transportation cost between two distributions, thus providing a measure of distance between them. In this work, we study the optimal transport of the eigenspectrum of one-dimensional non-Hermitian models as the spectrum deforms on the complex plane under a varying imaginary gauge field. Notably, according to the non-Bloch band theory, the deforming spectrum continuously connects the eigenspectra of the original non-Hermitian model (with vanishing gauge field) under different boundary conditions. It follows that the optimal spectral transport should contain key information of the model. Characterizing the optimal spectral transport through the Wasserstein metric, we show that, indeed, important features of the non-Hermitian model, such as the (auxiliary) generalized Brillouin zone, the non-Bloch exceptional point, and topological phase transition, can be determined from the Wasserstein-metric calculation. We confirm our conclusions using concrete examples. Our work highlights the key role of spectral geometry in non-Hermitian physics, and offers a practical and convenient access to the properties of non-Hermitian models. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_15209 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal spectral transport of non-Hermitian systems Xu, Mingtao Gong, Zongping Yi, Wei Quantum Physics Mesoscale and Nanoscale Physics Quantum Gases The optimal transport problem seeks to minimize the total transportation cost between two distributions, thus providing a measure of distance between them. In this work, we study the optimal transport of the eigenspectrum of one-dimensional non-Hermitian models as the spectrum deforms on the complex plane under a varying imaginary gauge field. Notably, according to the non-Bloch band theory, the deforming spectrum continuously connects the eigenspectra of the original non-Hermitian model (with vanishing gauge field) under different boundary conditions. It follows that the optimal spectral transport should contain key information of the model. Characterizing the optimal spectral transport through the Wasserstein metric, we show that, indeed, important features of the non-Hermitian model, such as the (auxiliary) generalized Brillouin zone, the non-Bloch exceptional point, and topological phase transition, can be determined from the Wasserstein-metric calculation. We confirm our conclusions using concrete examples. Our work highlights the key role of spectral geometry in non-Hermitian physics, and offers a practical and convenient access to the properties of non-Hermitian models. |
| title | Optimal spectral transport of non-Hermitian systems |
| topic | Quantum Physics Mesoscale and Nanoscale Physics Quantum Gases |
| url | https://arxiv.org/abs/2501.15209 |