Unitarity limit

Figure 3.15 (Heeger 1969, p. 306) shows the added resistivity due to iron-group impurities in gold. The low-temperature values, for which scattering cross-sections of order a2 occur (the unitarity limit ), include Kondo scattering. At room temperature, kBT is too great for most of the electrons near E to resonate...

Fig. 16.48 This residual density of states was pointed out theoretically to appear in the unitarity limit scattering by non-magnetic impurities in p- or d-wave superconductors in a heavy fermion study.49 From this result it became possible to explain the BCS-like temperature dependence of the penetration depth, A,50 which supported strongly the. 9-wave pairing model in high-7 , superconductors at an early stage, in terms of the d-wave + impurity model.51 53...

Fig. 16. Knight shift of Cu in the CuC>2 plane in YBa2(Cui vZnx)0748 Inset shows the density of states in the 2-D d-wave model with the pair-breaking effect due to impurity scattering in the unitarity limit.

The R ions form a periodic lattice, which leads for the 4f electrons together with the conduction electrons to the formation of quasi-particle bands, i.e. the electrons are in a coherent state. Since the magnetic moments either vanish (in the non-magnetic Kondo state) or form themselves a periodic magnetic structure (Kondo systems with magnetic order) there is no elastic scattering of the conduction electrons and therefore Pn,(0) = 0. This is different at high temperatures, where even in a periodic lattice one has disordered moments, which scatter elastically. The coefficient Ai can be calculated analytically. One finds A = j j + with the resistivity in the unitarity limit... 

Newton, the limit h —> 0 is singular. The symmetries underlying quantum and classical dynamics - unitarity and symplecticity, respectively - are fundamentally incompatible with the opposing theory s notion of a physical state quantum-mechanically, a positive semi-definite density matrix classically, a positive phase-space distribution function. 

The United Nations Institute for Training and Reseach (UNITAR) organized several International Conferences on Heavy Crudes and Tar Sands. The 1st was in Edmonton, Canada (1979), the 2nd in Caracas, Venezuela (1982), the 3rd in Long Beach, USA (1985), the 4th in Edmonton (1988), the 5th in Caracas (1991), the 6th in Houston, USA (1995), and the 7th in Beijing (1998). Although the proceedings of these symposia contain about 100 technical papers with an enormous amoimt of information on heavy crudes, tar sand oils, and bitumens, they carry rather limited information on extraheavy crude oil emulsions. 

Analogous equations hold for the creation operators. The operators Cpq B) and drPQ S) are defined trough their Taylor expansions and are limited through the unitarity conditions... 

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