[en] It is shown that at zero temperature the magnetic field μH >> T_K does not move the system from the strong coupling to the weak coupling regime. As a result, the average of the impurity spin approaches its saturation value as a power of the small parameter (2T_K/μH)². The study of the high-temperature expansion of the free energy shows that the Kondo problem contains at least two energy scales and that these scales are separated by the coupling constant. The Hamiltonian of the Kondo problem is not renormalizable. (methodological notes)

[en] Many novel superconducting compounds such as the high T_c oxides are intrinsically inhomogeneous systems by virtue of the superconductivity being closely related to the carrier density which is in turn provided in most cases by doping. An inhomogeneous structure is thus created by the statistical nature of the distribution of dopants. At the same time doping also leads to pair-breaking and, consequently, to a local depression of T_c. This is a major factor leading to inhomogeneity. As a result, the critical temperature is spatially dependent: T_c=T_c(r). The 'pseudogap' state is characterized by several energy scales: T*, T_c*, and T_c . The highest energy scale (T*) corresponds to phase separation (at T< T*) into a mixed metallic-insulating structure. Especially interesting is the region T_c*>T>T_c where the compound contains superconducting 'islands' embedded in a normal metallic matrix. As a result, the system is characterized by a normal conductance along with an energy gap structure, anomalous diamagnetism, unusual a.c. properties, an isotope effect, and a 'giant' Josephson proximity effect. An energy gap may persist to temperatures above T_c* caused by the presence of a charge density wave (CDW) or spin density wave (SDW) in the region T>T_c* but less than T*, whereas below T_c* superconducting pairing also makes a contribution to the energy gap (T_c* is an 'intrinsic' critical temperature). The values of T*, T_c*, T_c depend on the compound and the doping level. The transition at T_c into the dissipationless (R=0) macroscopically coherent state is of a percolation nature