Abstract
A Bose-Hubbard Hamiltonian, modeling cold bosons in an optical lattice, is used to simulate the dynamics of interacting open quantum systems as subsystems a larger closed system, avoiding complications like the introduction of baths, complex absorbing potentials or absorbing boundaries. The numerically exact unitary dynamics is compared with effective descriptions of the subsystems based on non-Hermitian Hamiltonians or Lindblad master equations. The validity of popular models with constant decay rates is explicitly analyzed for decaying single and double wells. In addition we present a discrete lattice version of the Siegert approximation method for calculating decay rates.
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