We study the equilibrium properties of a quantum dot connected to a bulk lead by a single-mode quantum point contact. The ground state energy and other thermodynamic characteristics of the grain show periodic dependence on the gate voltage (Coulomb blockade). We consider the case of almost perfect transmission, and show that the oscillations exist as long as the transmission coefficient of the contact is less than unity. Near the points where the dot charge is half-integer the thermodynamic characteristics show a non-analytic behavior identical to that of the two-channel spin-1/2 Kondo model. In particular, at any transmission coefficient the capacitance measured between the gate and the lead shows periodic logarithmic singularities as a function of the gate voltage.

16 pages, Revtex 3.0