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The Kondo effect is a condensed matter version of asymptotic freedom: the spin-exchange interaction between a localized magnetic impurity and itinerant electrons binds them into a spin-singlet resonance state at low temperatures. Instead of increasing temperature, introducing competing quantum effects can also destroy the Kondo resonance. I will examine two such examples in the Bose-Fermi Kondo model and the two-impurity Kondo model, with an emphysis on their quantum ciritical properties. These models are not only directly realizable in quantum-dot systems, but also provide solutions to the Kondo lattice model for heavy fermion materials with the dynamical mean-field approach. Applications to these areas are also addressed. Host: Jian-Xin Zhu |