Pierpaolo Vivo - ICTP Trieste	#	
Phase transitions in the quantum 
transport problem #
	Linear statistics on ensembles of 
random matrices occur frequently in many applications. I 
present a general method to compute probability distributions 
of linear statistics for large matrix size N. This is applied 
to the calculation of full probability distribution of 
conductance and shot noise for ballistic scattering in chaotic 
cavities, in the limit of large number of open electronic 
channels. The method is based on a mapping to a Coulomb gas 
problem in Laplace space, displaying phase transitions as the 
Laplace parameter is varied. As a consequence, the sought 
distributions generally display a central Gaussian region 
flanked on both sides by non-Gaussian tails, and weak 
non-analytic points at the junction of the two regimes. I also 
briefly discuss the case of Andreev reflection between a 
normal-superconductor interface in the random 
scattering-matrix approach.