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

TL;DR

This paper extends the multiconfigurational time-dependent Hartree method to include particle loss via absorbing boundary conditions, using a Lindblad master equation approach, enabling accurate modeling of open quantum systems.

Contribution

It introduces a generalized MCTDH framework for Lindblad master equations, allowing for the simulation of systems with particle loss due to absorbing boundaries.

Findings

Successfully formulated a multiconfigurational approach for Lindblad equations.

Demonstrated the method with a numerical experiment.

Enables modeling of open quantum systems with particle loss.

Abstract

Absorbing boundary conditions in the form of a complex absorbing potential are routinely introduced in the Schr\"odinger equation to limit the computational domain or to study reactive scattering events using the multi-configurational time-dependent Hartree method (MCTDH). 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. Selst{\o} and S. Kvaal, J. Phys. B: At. Mol. Opt. Phys. {\bfseries 43} (2010), 065004] that a master equation of Lindblad form was necessary for such a description. We formulate a multiconfigurational time-dependent Hartree 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. We demonstrate the formulation with a numerical experiment.