Fig. 5: Circuit realization and simulated measurements of scale-free state accumulation.
a The circuit of Eq. (8), whose asymmetric couplings are implemented through a negative impedance converter with current inversion (INICs) and capacitors. The extra variable inductor l gives rise to a coupling "impurity’’. Suitably designed grounding elements (see the “Methods” section) enable desired eigenstates to be isolated at appropriate driving voltage frequency ω. b Simulated impedance measurements across the impurity at various impurity strength μ, with position ω and height of impedance peaks loosely corresponding to the real and imaginary parts of the spectrum ϵ/(iωC) (inset). Here the capacities of C1 and C2 are parameterized as \({C}_{1}=C\sinh \alpha\), \({C}_{2}=C\cosh \alpha\). Parameters used are L = 9, C1 = 1 and C2 = 3, so that \(C=\sqrt{8}\) and α = 0.364. c Simulated electrical potential measurements vs. the profile of the bulk eigenstate with largest ϵ/(iωC), tuned close to resonance via Eq. (2). Not only is Eq. (7) accurate, the nature of eigenstate accumulation also agrees perfectly with the regimes of Fig. 1d. Parameters are L = 20, C1 = 2.9, C2 = 3, such that 2α ≈ 4.
