A quantum model for Johnson noise

Abstract

Johnson noise is a small random voltage that appears between terminals of any resistor interacting with its thermal bath at temperature T. It looks like continuous, but the discreteness of the electrical charge suggests its discrete origin coming from the charge noise due to random translocations of individual electrons between terminals. The capacitance allowing these translocations would quantize the energy entering the resistor in this way, thus acting as the antenna of the resistor to pick up thermal energy in the form of charge unbalances (fluctuations of energy) between its terminals. The subsequent relaxations of these fluctuations by the conductance G=1/R of the resistor (the collective reaction of all its carriers) would give rise to its Johnson noise. This collective reaction to dissipate fluctuations of energy caused by individual electrons, agrees with the Fluctuation-Dissipation framework that Callen and Welton proposed in 1951 for noisy processes.