Absorbing boundary conditions for the time-dependent Schrödinger-type equations in R^{3}.

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ID: 101677
2020
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Abstract
Absorbing boundary conditions are presented for three-dimensional time-dependent Schrödinger-type of equations as a means to reduce the cost of the quantum-mechanical calculations. The boundary condition is first derived from a semidiscrete approximation of the Schrödinger equation with the advantage that the resulting formulas are automatically compatible with the finite-difference scheme and no further discretization is needed in space. The absorbing boundary condition is expressed as a discrete Dirichlet-to-Neumann map, which can be further approximated in time by using rational approximations of the Laplace transform to enable a more efficient implementation. This approach can be applied to domains with arbitrary geometry. The stability of the zeroth-order and first-order absorbing boundary conditions is proved. We tested the boundary conditions on benchmark problems. The effectiveness is further verified by a time-dependent Hartree-Fock model with Skyrme interactions. The accuracy in terms of energy and nucleon density is examined as well.
Reference Key
wu2020absorbingphysical Use this key to autocite in the manuscript while using SciMatic Manuscript Manager or Thesis Manager
Authors Wu, Xiaojie;Li, Xiantao;
Journal physical review e
Year 2020
DOI
10.1103/PhysRevE.101.013304
URL
Keywords
high pressure feps3 first principles calculations insulator-to-metal transition layered compound

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