由一般Smith-Volterra-Cantor势导出的Tunnel
Tunneling from general Smith-Volterra-Cantor potential
摘要：
研究了有限长$L$的一般Smith-Volterra-Cantor（SVC）势的隧穿问题，该势由标度参数$ρ$和阶段$G$表征.我们证明了$G$阶的SVC（$ρ$）势是$G$阶超周期势的特例.利用我们以前发展的SPP形式，借助于$q$ -Pochhammer符号，给出了隧道概率$T_{G}(k)$的封闭形式表达式.发现具有波矢量$k$的$T_{G}(k)$的分布随着阶段$G$的增加而饱和。非常尖锐的传输谐振被发现发生从这个系统，这可能会发现在尖锐的传输滤波器的设计中的应用。
英文摘要：
We study the tunneling problem from general Smith-Volterra-Cantor (SVC) potential of finite length $L$ characterized by the scaling parameter $ρ$ and stage $G$. We show that the SVC($ρ$) potential of stage $G$ is the special case of super periodic potential (SPP) of order $G$. By using SPP formalism developed by us earlier, we provide the close form expression of tunneling probability $T_{G}(k)$ with the help of $q$-Pochhammer symbol. The profile of $T_{G}(k)$ with wave vector $k$ is found to saturate with increasing stage $G$. Very sharp transmission resonances are found to occur from this system which may find applications in the design of sharp transmission filters.
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