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This paper surveys the magnetic flux effects in multiply connected conductors, both normal metals and superconductors. Discussion of these effects for hopping conduction on the dielectric side of the metalinsulator transition is presented also. The main emphasis in the review is on the modern theoretical picture of these phenomena and comparison of theoretical results with experimental data.

We demonstrate the level statistics in the vicinity of the Anderson transition in d ) 2 dimensions to be universal and drastically difFerent from both Wigner-Dyson in the metallic regime and Poisson in the insulator regime. 'The variance of the number of levels N in a given energy interval with (N) » 1 is proved to behave as (N)» where p = 1 -(vd) ' and v is the correlation length exponent.The inequality p & 1, shown to be required by an exact sum rule, results from nontrivial cancellations (due to the causality and scaling requirements) in calculating the two-level correlation function. PACS numbers: 71.30.+h, 05.60.+w, 72.15.Rn The problem of level statistics in random quantum systems is attracting considerable interest even now, four decades after the pioneer works of Wigner and Dyson [1]. This is because of the universality of the Wigner-Dyson statistics which makes it relevant for a large variety of quantum systems [2].

The quasi-particle lifetime is calculated for electrons in a quantum dot as a function of energy, disorder, and dot size. As a result of electron-electron interaction, the spectrum is discrete only in close vicinity of the Fermi level. In the strongly diffusive case, levels farther than the Thouless energy (inverse diffusion time across the dot) from the Fermi level are broadened by the interaction beyond the average level spacing and merge to form a continuous spectrum. The number of discrete levels is hence of the order of 5-20 in typical experiments though such dots may contain thousands of electrons. For less disordered and ballistics dots, the number of discrete levels is of the order of the square root of the number of electrons in the dot.