Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Absorbing Boundary Conditions for Time-dependent Schr\"{o}dinger
  equations: A Density-matrix Formulation   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.

22
The categories of this paper are: chao-dyn
15
The categories of this paper are: nucl-ex
8
The categories of this paper are: hep-ex
16
The categories of this paper are: stat
19
The categories of this paper are: eess
20
The categories of this paper are: acc-phys
26
The categories of this paper are: bayes-an
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
29
The categories of this paper are: funct-an
21
The categories of this paper are: adap-org
17
The categories of this paper are: q-fin
23
The categories of this paper are: solv-int
36
The categories of this paper are: cmp-lg
0
The categories of this paper are: hep-ph