  We consider a distribution of conductance fluctuations in quantum dots with
single channel leads and continuous level spectra and we demonstrate that it
has a distinctly non-Gaussian shape and strong dependence on time-reversal
symmetry, in contrast to an almost Gaussian distribution of conductances in a
disordered metallic sample connected to a reservoir by broad multi-channel
leads. In the absence of time-reversal symmetry, our results obtained within
the diagrammatic approach coincide with those derived within non-perturbative
techniques. In addition, we show that the distribution has lognormal tails for
weak disorder, similar to the case of broad leads, and that it becomes almost
lognormal as the amount of disorder is increased towards the Anderson
transition.
