Tunneling time in non-Hermitian space fractional quantum mechanics
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915229530587136 |
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| author | Umar, Mohammad Singh, Vibhav Narayan Mandal, Bhabani Prasad |
| author_facet | Umar, Mohammad Singh, Vibhav Narayan Mandal, Bhabani Prasad |
| contents | We investigate the tunneling time of a wave packet propagating through a non-Hermitian potential $V_{r} - iV_{i}$ in space-fractional quantum mechanics. By applying the stationary phase method, we derive a closed-form expression for the tunneling time for this system. This study presents the first investigation of tunneling time at the interplay of non-Hermitian quantum mechanics and space-fractional quantum mechanics. The variation in tunneling time as the system transitions from a real to a complex potential is analyzed. We demonstrate that the tunneling time exhibits a dependence on the barrier width $d$ in the limit $d\rightarrow \infty$, showing the absence of the Hartman effect. A particularly striking feature of our findings is the potential manifestation of the Hartman effect for a specific combination of the absorption component $V_{i}$ and the Levy index $α$. This behavior arises from the fact that the presence of the absorption component $V_{i}$ leads to a monotonic increase in tunneling time with barrier thickness, whereas the Levy index $α$ reduces the tunneling time. The interplay of these contrasting influences facilitates the emergence of the Hartman effect under a specific combination of $V_{i}$ and the fractional parameter $α$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_04082 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Tunneling time in non-Hermitian space fractional quantum mechanics Umar, Mohammad Singh, Vibhav Narayan Mandal, Bhabani Prasad Quantum Physics High Energy Physics - Theory Mathematical Physics We investigate the tunneling time of a wave packet propagating through a non-Hermitian potential $V_{r} - iV_{i}$ in space-fractional quantum mechanics. By applying the stationary phase method, we derive a closed-form expression for the tunneling time for this system. This study presents the first investigation of tunneling time at the interplay of non-Hermitian quantum mechanics and space-fractional quantum mechanics. The variation in tunneling time as the system transitions from a real to a complex potential is analyzed. We demonstrate that the tunneling time exhibits a dependence on the barrier width $d$ in the limit $d\rightarrow \infty$, showing the absence of the Hartman effect. A particularly striking feature of our findings is the potential manifestation of the Hartman effect for a specific combination of the absorption component $V_{i}$ and the Levy index $α$. This behavior arises from the fact that the presence of the absorption component $V_{i}$ leads to a monotonic increase in tunneling time with barrier thickness, whereas the Levy index $α$ reduces the tunneling time. The interplay of these contrasting influences facilitates the emergence of the Hartman effect under a specific combination of $V_{i}$ and the fractional parameter $α$. |
| title | Tunneling time in non-Hermitian space fractional quantum mechanics |
| topic | Quantum Physics High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2504.04082 |