Abstract
A Bose–Hubbard Hamiltonian, modelling cold bosons in an optical lattice, is used to simulate the dynamics of interacting open quantum systems as subsystems of 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 the 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 analysed for decaying single and double wells. For simplicity, we concentrate on simulations with very small particle numbers (mostly N = 2, 3) and neglect the interaction in parts of the system where this is appropriate. We furthermore present a discrete lattice version of the Siegert approximation method for calculating decay rates.
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