On the reduced dynamics of a subset of interacting bosonic particles
Highlights: Discusses open quantum systems where system and environment are indistinguishable. Perturbative, microscopic treatment of interacting bosonic many-body systems. First-order approximation: BBGKY-hierarchy and, as a special case, Gross–Pitaevskii equation. Second-order approximation: Nonlinear master equation with interaction-induced decoherence. - Abstract: The quantum dynamics of a subset of interacting bosons in a subspace of fixed particle number is described in terms of symmetrized many-particle states. A suitable partial trace operation over the von Neumann equation of an N-particle system produces a hierarchical expansion for the subdynamics of M≤N particles. Truncating this hierarchy with a pure product state ansatz yields the general, nonlinear coherent mean-field equation of motion. In the special case of a contact interaction potential, this reproduces the Gross–Pitaevskii equation. To account for incoherent effects on top of the mean-field evolution, we discuss possible extensions towards a second-order perturbation theory that accounts for interaction-induced decoherence in form of a nonlinear Lindblad-type master equation.