  We numerically investigate decoherence of a two-spin system (central system)
by a bath of many spins 1/2. By carefully adjusting parameters, the dynamical
regime of the bath has been varied from quantum chaos to regular, while all
other dynamical characteristics have been kept practically intact. We
explicitly demonstrate that for a many-body quantum bath, the onset of quantum
chaos leads to significantly faster and stronger decoherence compared to an
equivalent non-chaotic bath. Moreover, the non-diagonal elements of the
system's density matrix decay differently for chaotic and non-chaotic baths.
Therefore, knowledge of the basic parameters of the bath (strength of the
system-bath interaction, bath's spectral density of states) is not always
sufficient, and much finer details of the bath's dynamics can strongly affect
the decoherence process.
