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- W2951504515 abstract "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 $Z_0(omega) = R$, independent of the frequency ($omega$). 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 $Z_{n+1}(omega) = f(Z_n(omega))$, with the recursive function $f(z) = (iomega Lz/iomega L + z) + (z/1+iomega Cz)$. 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 $ntoinfty$ 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." @default.
- W2951504515 created "2019-06-27" @default.
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- W2951504515 date "2007-06-29" @default.
- W2951504515 modified "2023-09-27" @default.
- W2951504515 title "Resistance without resistors: An anomaly" @default.
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