Investigation of a non-Hermitian edge burst with time-dependent perturbation theory
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arXiv
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| Natura: | Preprint |
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2023
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| _version_ | 1866913242489552896 |
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| author | Wen, Pengyu Pi, Jinghui Long, Guilu |
| author_facet | Wen, Pengyu Pi, Jinghui Long, Guilu |
| contents | Edge burst is a phenomenon in non-Hermitian quantum dynamics discovered by a recent numerical study [W.-T. Xue, et al, Phys. Rev. Lett 2, 128.120401(2022)]. It finds that a large proportion of particle loss occurs at the system boundary in a class of non-Hermitian quantum walk. In this paper, we investigate the evolution of real-space wave functions for this lattice system. We find the wave function of the edge site is distinct from the bulk sites. Using time-dependent perturbation theory, we derive the analytical expression of the real-space wave functions and find that the different evolution behaviors between the edge and bulk sites are due to their different nearest-neighbor site configurations. We also find the edge wave function primarily results from the transition of the two nearest-neighbor non-decay sites. Besides, the numerical diagonalization shows the edge wave function is mainly propagated by a group of eigen-modes with a relatively large imaginary part. Our work provides an analytical method for studying non-Hermitian quantum dynamical problems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_17219 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Investigation of a non-Hermitian edge burst with time-dependent perturbation theory Wen, Pengyu Pi, Jinghui Long, Guilu Quantum Physics Edge burst is a phenomenon in non-Hermitian quantum dynamics discovered by a recent numerical study [W.-T. Xue, et al, Phys. Rev. Lett 2, 128.120401(2022)]. It finds that a large proportion of particle loss occurs at the system boundary in a class of non-Hermitian quantum walk. In this paper, we investigate the evolution of real-space wave functions for this lattice system. We find the wave function of the edge site is distinct from the bulk sites. Using time-dependent perturbation theory, we derive the analytical expression of the real-space wave functions and find that the different evolution behaviors between the edge and bulk sites are due to their different nearest-neighbor site configurations. We also find the edge wave function primarily results from the transition of the two nearest-neighbor non-decay sites. Besides, the numerical diagonalization shows the edge wave function is mainly propagated by a group of eigen-modes with a relatively large imaginary part. Our work provides an analytical method for studying non-Hermitian quantum dynamical problems. |
| title | Investigation of a non-Hermitian edge burst with time-dependent perturbation theory |
| topic | Quantum Physics |
| url | https://arxiv.org/abs/2303.17219 |