无电阻的电阻：异常
Resistance without resistors: An anomaly
摘要：
基本2端网络由串联的电容器（$R-$）分流电感（$L$）和电容器（$C-$）分流电阻（$R$）以及$R = \sqrt{L/C}$组成，已知其非色散耗散响应$i.e.,$，输入阻抗为$Z_0(ω) = R$，与频率无关（$ω$）。在这篇文章中，我们研究了一种新的等效网络的性质，该等效网络是通过用整个2端网络替换所有的电阻部分$R$来迭代地从2端网络导出的。这种替换建议使用递归函数$f(z) = (iωLz/iωL + z) + (z/1+iωCz)$的递归$Z_{n+1}(ω) = f(Z_n(ω))$。递归映射有两个不动点--不稳定不动点$Z_u^\star = 0$和稳定不动点$Z_s^\star = R$。因此，在不改变输入阻抗$Z_\infty (= R)$的情况下，可以使无限迭代网络的边界端接电阻任意小。因此，这导致在极限$n\to\infty$中实现仅包括基本上非耗散电抗元件（$L$和$C$）的有效耗散网络。因此，矛盾修饰法--没有电阻的电阻!最好把这看作是一种类似于湍流中所遇到的典型反常现象。作为一个正式的退相干设备-{\it假通道}-可能的应用进行了简要讨论，其量子模拟。
英文摘要：
The elementary 2-terminal network consisting of a resistively ($R-$) shunted inductance ($L$) in series with a capacitatively ($C-$) shunted resistance ($R$) with $R = \sqrt{L/C}$, is known for its non-dispersive dissipative response, $i.e.,$ with the input impedance $Z_0(ω) = R$, independent of the frequency ($ω$). In this communication we examine the properties of a novel equivalent network derived iteratively from this 2-terminal network by replacing everywhere the elemental resistive part $R$ with the whole 2-terminal network. This replacement suggests a recursion $Z_{n+1}(ω) = f(Z_n(ω))$, with the recursive function $f(z) = (iωLz/iωL + z) + (z/1+iωCz)$. The recursive map has two fixed points -- an unstable fixed point $Z_u^\star = 0$, and a stable fixed point $Z_s^\star = R$. Thus, resistances at the boundary terminating the infinitely iterated network can now be made arbitrarily small without changing the input impedance $Z_\infty (= R)$. This, therefore, leads to realizing in the limit $n\to\infty$ an effectively dissipative network comprising essentially non-dissipative reactive elements ($L$ and $C$) only. Hence the oxymoron -- resistance without resistors! This is best viewed as a classical anomaly akin to the one encountered in turbulence. Possible application as a formal decoherence device -- the {\it fake channel} -- is briefly discussed for its quantum analogue.
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