Zero Thermal Noise in Resistors at Zero Temperature
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abstract
The bandwidth of transistors in logic devices approaches the quantum limit, where Johnson noise and associated error rates are supposed to be strongly enhanced. However, the related theory asserting a temperature-independent quantum zero-point (ZP) contribution to Johnson noise, which dominates the quantum regime is controversial and resolution of the controversy is essential to determine the real error rate and fundamental energy dissipation limits of logic gates in the quantum limit. The CallenWelton formula (fluctuationdissipation theorem) of voltage and current noise for a resistance is the sum of Nyquists classical Johnson noise equation and a quantum ZP term with a power density spectrum proportional to frequency and independent of temperature. The classical JohnsonNyquist formula vanishes at the approach of zero temperature, but the quantum ZP term still predicts non-zero noise voltage and current. Here, we show that this noise cannot be reconciled with the FermiDirac distribution, which defines the thermodynamics of electrons according to quantum-statistical physics. Consequently, Johnson noise must be nil at zero temperature, and non-zero noise found for certain experimental arrangements may be a measurement artifact, such as the one mentioned in Kleens uncertainty relation argument.
