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Absorbing boundary conditions for time-dependent Schrödinger equations: A density-matrix formulation
1Department of Mathematics, The Pennsylvania State University, University Park, Pennsylvania 16802-6400, USA.
Abstract:
This paper presents some absorbing boundary conditions for simulations based on the time-dependent Schrödinger equations. 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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