Absorbing Boundary Conditions for Time-dependent Schrödinger equations: A Density-matrix Formulation

Abstract

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.

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Cited by in corpus (4)

• Absorbing boundary conditions for the time-dependent Schrödinger-type equations in ${\mathbb{R}}^3$
• A Projection-based Reduced-order Method for Electron Transport Problems with Long-range Interactions
• Time-parallel simulation of the Schrödinger Equation
• A reduced-order modeling approach for electron transport in molecular junctions