Statistical properties of level widths and conductance peaks in a quantum dot

We study the statistics of level widths of a quantum dot with extended contacts in the absence of time-reversal symmetry. The widths are determined by the amplitude of the wave function averaged over the contact area. The distribution function of level widths for a two-point contact is evaluated exactly. The distribution resembles closely the result obtained when the wave function fluctuates independently at each point, but differs from the one-point contact case. Analytical calculations and numerical simulations show that the distribution for many-point contacts has a power-law behavior at small level widths. The exponent is given by the number of points in the contact and diverges in the continuous limit. The distribution of level widths is used to determine the distribution of conductance peaks in the resonance regime. At intermediate temperatures, we find that the distribution tends to normal and fluctuations in the height of the peaks are suppressed as the contact size is increased.