Fig. 2: Experimental observations of continuum Landau modes.
From: Observation of continuum Landau modes in non-Hermitian electric circuits
a Photograph of part of the circuit board, with numbers labeling the main circuit components: (i) the position-dependent capacitor \(n{C}_{0}\) (\({C}_{0}=10{{{{{\rm{nF}}}}}}\)) built of parallel surface mounted device (SMD) capacitors; (ii) grounding for each node with an SMD inductor (\({L}_{0}=12.4{{{{{\rm{\mu }}}}}}{{{{{\rm{H}}}}}}\)) and parallel SMD resistors yielding position-dependent resistor \({R}_{0}/m\) (\({R}_{0}=100\Omega\)); (iii) INIC made of an SMD capacitor (\({C}_{2}=10{{{{{\rm{nF}}}}}}\)), the operational amplifier LT1363 with supply voltages, and an equal pair of SMD resistor (\({R}_{a}=1{{{{{\rm{k}}}}}}\Omega\)); (iv) the reciprocal coupling built of SMD a capacitor (\({C}_{1}=10{{{{{\rm{nF}}}}}}\)). b Measured admittance spectrum for the frequency \(f=162{{{{{\rm{kHz}}}}}}\). The color of each point indicates the participation ratio of the corresponding eigenstate. c Measured distribution of the eigenstate marked by star in b. d Experimental observations of \({{{{\mathrm{Re}}}}}[j/(i\omega )]\) (Left Panel) and Im[j/(iω)] (Right Panel) versus the eigenstate’s position expectation values \(\left\langle y\right\rangle\) and \(\left\langle x\right\rangle\), respectively. The gray-dashed lines are the corrected bounding lines by introducing loss offset and modified inductor. e Experimental observations of Im[j/(iω)] versus \(\left\langle x\right\rangle\) for the different frequencies \(f=140\) and \(180{{{{{\rm{kHz}}}}}}\). The dashed lines denote the corrected central trend lines (\({{{{{{\mathcal{E}}}}}}}_{{{{{{\rm{k}}}}}}+{{{{{\rm{q}}}}}}}^{0}\to 0\)) obtained from Eq. (2). f Measured voltage responses |V| by separately exciting three positions \((2,2)\), \((5,5)\), and \((9,9)\) at their resonance frequencies \({f}_{{{{{{\rm{r}}}}}}}=197\), \(179\), and \(151{{{{{\rm{kHz}}}}}}\), respectively.
