Tunneling time in non-Hermitian space fractional quantum mechanics

• URL: http://arxiv.org/abs/2504.04082v1
• Date: Sat, 05 Apr 2025 07:08:37 GMT
• Title: Tunneling time in non-Hermitian space fractional quantum mechanics
• Authors: Mohammad Umar, Vibhav Narayan Singh, Bhabani Prasad Mandal,
• Abstract summary: This study presents the first investigation of tunneling time at the interplay of non-Hermitian quantum mechanics and space-fractional quantum mechanics.<n>A particular 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 $alpha$.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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 $\alpha$. 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 $\alpha$ 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 $\alpha$.

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