  We investigate the longstanding problem of thermalization of quantum systems
coupled to an environment by focusing on a bistable quartic oscillator
interacting with a finite number of harmonic oscillators. In order to overcome
the exponential wall that one usually encounters in grid based approaches to
solve the time-dependent Schr\"odinger equation of the extended system, methods
based on the time-dependent variational principle are best suited. Here we will
apply the method of coupled coherent states [D. V. Shalashilin and M. S. Child,
J. Chem. Phys. {\bf 113}, 10028 (2000)]. By investigating the dynamics of an
initial wavefunction on top of the barrier of the double well, it will be shown
that only a handful of oscillators with suitably chosen frequencies, starting
in their ground states, is enough to drive the bistable system close to its
uncoupled ground state. The long-time average of the double-well energy is
found to be a monotonously decaying function of the number of environmental
oscillators in the parameter range that was numerically accessible.
