The reduction of quantum scattering leads to the suppression of shot noise [1], and to the breakdown of the universality in quantum transport  [2]. I will discuss three different scenarios of the crossover from quantum to classical transport regime in mesoscopic billiards.  The results of the numerical simulation [2] indicate that the crossover in chaotic billiards is determined by the separation of the quantum phase space into a stochastic and a deterministic phase.  Interestingly, in disordered billiards such a separation does not always take place [3].  I will present the theory of crossover which is based on the recently introduced stochastic path integral formalism [4].

[1] S. Oberholzer, E.S., and C. Schonenberger, Nature 415, 765 (2002).
[2]Ph. Jacquod, and E.S., Phys. Rev. Lett. 92, 116801 (2004).
[3] E.S., and O. Bulashenko, cond-mat/0408075.
[4] A. Jordan, E.S., and S. Pilgram, J. Math. Phys. 45, 4386 (2004).