Two-loop approximation in the Coulomb blockade problem

We study Coulomb blockade (CB) oscillations in the thermodynamics of a metallic grain connected to a lead by a tunneling contact with a large conductance g₀ in a wide temperature range, E_Cg₀⁴e^-g₀/2<T<E_C, where E_C is the charging energy. Using the instanton analysis and the renormalization-group approach we obtain our main result, the temperature dependence of the amplitude of CB oscillations, which differs from the previously obtained results. Assuming that at T<E_Cg₀⁴e^-g₀/2 the oscillation amplitude weakly depends on temperature we estimate the magnitude of CB oscillations in the ground-state energy as ∝E_Cg₀⁴e^-g₀/2.