Resolution effects on the current measurement in a resonant level model

Current measurements have attracted much attention in studies on understanding the intrinsic information of nanoscale systems. Here, we theoretically study the influence of the smallest detectable change in the measurement, i.e. resolution, on the outcomes of the measurements, using an extension of the full counting statistics for a resonant level model. It is shown that the limited resolution of current measurement gives rise to a positive excess noise, which leads to a violation of the Johnson-Nyquist relation naively expected between the measured conductance and the measured current noise. The deviation from the Johnson-Nyquist relation exhibits universal single-parameter scaling with the nondimensional scaling variable $S_0/S_M$ where $S_0$ is the intrinsic noise and $S_M$ represents the characteristic noise determined from the measurement process. In addition, our findings offer an explanation for anomalous enhancement of noise temperature observed in Johnson noise thermometry. [1] Y. Yamada and M. Imada, arXiv:1307.7535.