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I show that the dynamics of the weakly interacting bose gas can be describedby a modified time dependent Bogoliubov theory. The novelty of the approach isto include decoherence steps that gradually transform the entanglement entropyof the pure state into the von Neumann entropy of a statistical mixture. Thisapproximation drastically reduces the entanglement that is needed in order torepresent the system's state while becoming exponentially accurate in the meanfield limit. I argue that this scheme can be extended to all quantum systemswhose ground state can be well approximated by a variational wave function. Theupshot is that the dynamics of almost all quantum systems can be reduced tostochastic classical motion supplemented with small quantum fluctuations.

Taming the entanglement in the dynamical theory of weakly interacting Bose gases