  This paper concerns with the time-reversal characteristics of intrinsic
normal diffusion in quantum systems. Time-reversible properties are quantified
by the time-reversal test; the system evolved in the forward direction for a
certain period is time-reversed for the same period after applying a small
perturbation at the reversal time, and the separation between the time-reversed
perturbed and unperturbed states is measured as a function of perturbation
strength, which characterizes sensitivity of the time reversed system to the
perturbation and is called the time-reversal characteristic.
  Time-reversal characteristics are investigated for various quantum systems,
namely, classically chaotic quantum systems and disordered systems including
various stochastic diffusion systems. When the system is normally diffusive,
there exists a fundamental quantum unit of perturbation, and all the models
exhibit a universal scaling behavior in the time-reversal dynamics as well as
in the time-reversal characteristics, which leads us to a basic understanding
on the nature of quantum irreversibility.
