Universal departure from Johnson-Nyquist relation caused by limited resolution

Exploiting the two-point measurement statistics, we propose a quantum measurement scheme of current with limited resolution of electron counting. Our scheme is equivalent to the full counting statistics in the long-time measurement with the ideal resolution, but is theoretically extended to take into account the resolution limit of actual measurement devices. Applying our scheme to a resonant level model, we show that the limited resolution of current measurement gives rise to a positive excess noise, which leads to a deviation from the Johnson-Nyquist relation. The deviation exhibits universal single-parameter scaling with the scaling variable Q≡SM/S0, which represents the degree of the insufficiency of the resolution. Here, S0 is the intrinsic noise, and SM is the positive quantity that has the same dimension as S0 and is defined solely by the measurement scheme. For the lack of the ideal resolution, the deviation emerges for Q<1 as 2exp[-(2π)2/Q] having an essential singularity at Q=0, which followed by the square root dependence Q/4π for Q≫1. Our findings offer an explanation for the anomalous enhancement of noise temperature observed in Johnson noise thermometry.