Irreversibility and quantum macroscopic effects of classically chaotic systems

We show that in classically chaotic systems the quantum uncertainty, in spite of being assumed to be extremely small so as to make the classical approximation possible, increases very quickly thereby making these classical systems strongly quantum. It is argued that these systems also exhibit an irreversible-like behavior, albeit the phase correlations among different regions of the wavefunction make them reversible. From a statistical point of view it is difficult to distinguish the quantum behavior of these systems from the predictions of the classical approximation, unless the resulting transport process does not essentially rest either on tunneling or on localization processes (or on both). The dinstinctively quantum mechanical features of the transport process might be destroyed by the interaction between the system and environment. This possible role of environmental fluctuations, dealt within a fully quantum formalism, is discussed.