Absorbing Boundary Conditions for Time-dependent Schrödinger equations: A Density-matrix Formulation
This work provides a practical boundary condition method for quantum simulations, but it is an incremental improvement over existing ABC techniques applied to a specific domain (TDDFT).
The paper develops absorbing boundary conditions for time-dependent density-functional theory simulations, expressed in terms of density-matrix elements, with efficient approximations for the convolution integral that guarantee stability. Numerical tests demonstrate effectiveness.
This paper presents some absorbing boundary conditions (ABC) for simulations based on the time-dependent density-functional theory (TDDFT). The boundary conditions are expressed in terms of the elements of the density-matrix, and it is derived from the full model over a much larger domain. To make the implementation much more efficient, several approximations for the convolution integral will be constructed with guaranteed stability. These approximations lead to modified density-matrix equations at the boundary. The effectiveness is examined via numerical tests.