  We revisit the dynamics of a Bose-Einstein condensate in a double-well
potential, from the regime of Josephson plasma oscillations to the
self-trapping regime, by means of the Bogoliubov quasiparticle projection
method. For very small imbalance between left and right wells only the lowest
Bogoliubov mode is significantly occupied. In this regime the system performs
plasma oscillations at the corresponding frequency, and the evolution of the
condensate is characterized by a periodic transfer of population between the
ground and the first excited state. As the initial imbalance is increased, more
excited modes -- though initially not macroscopically occupied -- get coupled
during the evolution of the system. Since their population also varies with
time, the frequency spectrum of the imbalance turns out to be still peaked
around a single frequency, which is continuously shifted towards lower values.
The nonlinear mixing between Bogoliubov modes eventually drives the system into
the the self-trapping regime, when the population of the ground state can be
transferred completely to the excited states at some time during the evolution.
For simplicity, here we consider a one-dimensional setup, but the results are
expected to hold also in higher dimensions.
