Kondo Effect from the TGD perspective

Abstract

Kondo effect is due to a scattering of conduction electrons from valence electrons of magnetic impurity atoms and implies logarithmic increase of the resistance of the conductor at the zero temperature limit. Anderson's impurity model combined with the renormalization group explains the logarithmic increase of the quadratic coupling between conduction electron and valence electron. The Kondo effect occurs in the non-perturbative regime of the Anderson model and this implies several analogies with QCD and hadron physics. With a motivation coming from the QCD analogy and TGD view of hadrons, the Kondo effect is discussed from the TGD view point by introducing notion of the magnetic body carrying dark matter as h_eff > h phase, assignable to the impurity spin. The conduction electrons forming the electron cloud around the impurity spin and neutralizing would be actually dark valence electrons. It is assumed that Nature is theoretician friendly. As the perturbation series ceases to converge, either the quantum coherence is lost or the value of Planck constant h increases to h_eff > h to guarantee its convergence. Also the generalization of Nottale's hypothesis from gravitational to electromagnetic situation is assumed. In the recent situation the relevant coupling parameter would be Q²e², where Q is the total charge of the valence electron cloud around the impurity: after the transition the coupling parameter would be universally β/4π; β₀ = v₀/c < 1. This transition would happen in the Kondo effect and lead to the formation of spin singlets as analogs of hadrons in color confinement. The dark valence electrons would be analogs of sea partons and the impurity electrons would be counterparts of valence quarks in this picture. This picture also allows us to understand heavy fermions as analogs of constituent quarks and Kondo insulators. This picture also provides new insights to hadron physics.