  We study the decoherence and thermalization dynamics of a nanoscale system
coupled nonperturbatively to a fully quantum-mechanical bath. The system is
prepared out of equilibrium in a pure state of the complete system. We propose
a random matrix model and show analytically that there are two robust temporal
regimes in the approach of the system to equilibrium --- an initial Gaussian
decay followed by an exponential tail, consistent with numerical results on
small interacting lattices [S. Genway, A.F. Ho and D.K.K. Lee, Phys. Rev. Lett.
105, 260402 (2010)]. Furthermore, the system decays towards a Gibbs ensemble in
accordance with the eigenstate thermalization hypothesis.
