  We investigate decoherence in quantum systems coupled via dephasing-type
interactions to an arbitrary environment with chaotic underlying classical
dynamics. The coherences of the reduced state of the central system written in
the preferential energy eigenbasis are quantum Loschmidt echoes, which in the
strong coupling regime are characterized at long times scales by fluctuations
around a constant mean value. We show that due to the chaotic dynamics of the
environment, the mean value and the width of the Loschmidt echo fluctuations
are inversely proportional to the quantity we define as the effective Hilbert
space dimension of the environment, which in general is smaller than the
dimension of the entire available Hilbert space. Nevertheless, in the
semiclassical regime this effective Hilbert space dimension is in general
large, in which case even a chaotic environment with few degrees of freedom
produces decoherence without revivals. Moreover we show that in this regime the
environment leads the central system to equilibrate to the time average of its
reduced density matrix, which corresponds to a diagonal state in the
preferential energy eigenbasis. For the case of two uncoupled, initially
entangled central systems that interact with identical local quantum
environments with chaotic underlying classical dynamics, we show that in the
semiclassical limit the equilibration state is arbitrarily close to a separable
state. We confirm our results with numerical simulations in which the
environment is modeled by the quantum kicked rotor in the chaotic regime.
