In this chapter we derive an expression for the spectrum of thermal agitations of electrons in an electric RC circuit [18.1] (the spectral function of the current-current correlation function) as a measure of the “noise” in the system. These results were first derived, including quantum effects, by Nyquist [18.2]. The system is another version of the Brownian relaxator considered earlier Chap. 5. Let us use linear response theory and consider the RC circuit under the influence of an external voltage V e (Fig. 18.1). The total current j in the circuit then consists of the average Ohmic current J = V/R and the noise component Δj, where V is the voltage drop at the resistor with resistance R, which is in thermal contact with a heat bath of temperature T.
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