Multiconfigurational time-dependent Hartree method to describe particle loss due to absorbing boundary conditions

Absorbing boundary conditions in the form of a complex absorbing potential are routinely introduced in the Schroedinger equation to limit the computational domain or to study reactive scattering events using the multiconfigurational time-dependent Hartree (MCTDH) method. However, it is known that a pure wave-function description does not allow the modeling and propagation of the remnants of a system of which some parts are removed by the absorbing boundary. It was recently shown [S. Selstoe and S. Kvaal, J. Phys. B: At. Mol. Opt. Phys. 43, 065004 (2010)] that a master equation of Lindblad form was necessary for such a description. We formulate a MCTDH method for this master equation, usable for any quantum system composed of any mixture of species. The formulation is a strict generalization of pure-state propagation using standard MCTDH for identical particles and mixtures. We demonstrate the formulation with a numerical experiment.