Random fluctuations of the electrical conductance are ubiquitous in small (typical dimension L ≲ 1 µm) metallic samples at low temperatures (typically T ≲ 1K ≃ 0.09 meV). The fluctuations result from the quantum-mechanical interference of the carrier wavefunctions. The superpositions of the wavefunctions depend randomly on the placement of impurities, on magnetic field, and on the current driven through the sample. At length scale Lφ (the average distance over which the carriers retain phase information), the fluctuations always have amplitude ΔG ≃ e2/h, and any observations at scale larger than the coherence length yield a decreased amplitude of the fluctuations. Since the carrier wavefunctions are not classical, local objects (they extend over regions of size Lφ), the conductance contains nonlocal terms. For instance, the conductance is not zero far from the classical current paths through the sample and is not symmetric under the reversal of the magnetic field. In this article, the physics of the fluctuations is reviewed, and some of the experiments which illuminate the physics are described.
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