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arXiv 1504.00115quant-ph
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一维新形状共振

New shape resonances in one dimension

Zafar Ahmed, Shashin Pavaskar, Lakshmi Prakash

摘要:

最近,在阱或刚性壁旁边的1/4厚的势垒被认为是在一维中引起共振(亚稳态)的最简单形状的势:$x \in(-\infty, \infty)$。在这样的势中,在势垒以下的能量处有三个真正的转折点。共振是伽莫夫的(按时间)衰减状态,具有离散的复能量$({\cal E}_n = E_n -iΓ_n/2)$。这些也是空间灾难性的状态,表现为在$E = ε_n \approx E_n$的维格纳反射时间延迟的峰值/摆动。在这里,我们探索的潜力与更简单的形状引起共振-两件上升的潜力只有一个转折点。我们证明了我们的观点,通过使用各种方式的指数上升曲线。

英文摘要:

Hitherto, a finitely thick barrier next to a well or a rigid wall has been considered the potential of simplest shape giving rise to resonances (metastable states) in one dimension: $x \in(-\infty, \infty)$. In such a potential, there are three real turning points at an energy below the barrier. Resonances are Gamow's (time-wise) decaying states with discrete complex energies $({\cal E}_n = E_n -iΓ_n/2)$. These are also spatially catastrophic states that manifest as peaks/wiggles in Wigner's reflection time-delay at $E = ε_n \approx E_n$. Here we explore potentials with simpler shapes giving rise to resonances - two-piece rising potentials having just one-turning point. We demonstrate our point by using rising exponential profile in various ways.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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