Abstract
In this paper we consider various methods for measuring current fluctuations. Our aim is to reveal a quantity which can be measured in treating fluctuations and transfer statistics on the whole. The answer is known for an average current where the quantity sought for is the averaged current operator hIi Tr frIg in view of the validity of the ergodic hypothesis. The situation with current±current correlators is far less clear, since the operators should be arranged in time (in general, current operators at different times are not commutative). In fact, this problem is reduced to the measurement of vacuum current fluctuations, and similar to the one of recording photons in optics and the measurement of vacuum electromagnetic fluctuations, although there is a significant difference. Considerable recent attention has been focussed on the measurement of zero-point current and voltage oscillations including the very possibility of such measurements. Current fluctuations have been studied both theoretically and experimentally [1 ± 5]. In Refs [6, 7] measurements were performed at frequencies at which zero-point oscillations can arise at practically attainable temperatures ho > kBT. On the other hand, paper [8] attracted considerable interest to the possible breaking of the phase of conducting electrons by vacuum fluctuations of an electric field, which can significantly modify the localization behaviour at zero temperature. To begin, let us consider the spectral density of fluctuations. 1. Measurement of spectral density of noise with a resonance circuit. Current fluctuations of finite frequency are usually measured by one of two main methods. In the first, the current is measured as a time-dependent function I t, for example, with a normal ammeter, and then the spectral density S o is calculated numerically using a Fourier transformation. The classical equation ofmotion for an ammeter coincides with the equation for an oscillator with friction and external force / I t
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