Is the Multichannel Kondo Model Appropriate to Describe the Single Electron Transistor?

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We investigate the low-temperature dynamics of single electron boxes and transistors close to their degeneracy point using renormalization group methods. We show that intermode scattering is a relevant perturbation and always drives the system to the two-channel Kondo fixed point, where the two channels correspond to the real spins of the conduction electrons. However, the crossover temperature T*, below which Matveev's two-channel Kondo scenario [K.A. Matveev, Phys. Rev. B 51, 1743 (1995)] develops decreases exponentially with the number of conduction modes in the tunneling junctions and is extremely small in most cases. Above T* the 'infinite channel model' of Ref.onlineciteSchoen turns out to be a rather good approximation. We discuss the experimental limitations and suggest a new experimental setup to observe the multichannel Kondo behavior.