Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Discretization of Time-Dependent Quantum Systems: Real-Time Propagation
  of The Evolution Operator   We discuss time dependent quantum systems on bounded domains. Our work may be
viewed as a framework for several models, including linear iterations involved
in time dependent density functional theory (TDDFT), the Hartree-Fock model, or
other quantum models. A key aspect of the analysis of the algorithms is the use
of time-ordered evolution operators, which allow for both a well-posed problem
and its approximation. The approximation theorems obtained for the time-ordered
evolution operators complement those in the current literature. We discuss the
available theory at the outset, and proceed to apply the theory systematically
in later sections via approximations and a global existence theorem for a
nonlinear system, obtained via a fixed point theorem for the evolution
operator. Our work is consistent with first-principle real time propagation of
electronic states, aimed at finding the electronic responses of quantum
molecular systems and nanostructures. We present two full 3D quantum atomistic
simulations using the finite element method for discretizing the real-space,
and the FEAST eigenvalue algorithm for solving the evolution operator at each
time step. These numerical experiments are representative of the theoretical
results.

32
The categories of this paper are: atom-ph
14
The categories of this paper are: math-ph
23
The categories of this paper are: solv-int
0
The categories of this paper are: hep-ph
7
The categories of this paper are: hep-th
8
The categories of this paper are: hep-ex
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
28
The categories of this paper are: alg-geom
10
The categories of this paper are: q-bio
33
The categories of this paper are: plasm-ph
26
The categories of this paper are: bayes-an
15
The categories of this paper are: nucl-ex
24
The categories of this paper are: dg-ga
36
The categories of this paper are: cmp-lg
1
The categories of this paper are: cs