50 research outputs found
Spectral-based Propagation Schemes for Time-Dependent Quantum Systems with Application to Carbon Nanotubes
Effective modeling and numerical spectral-based propagation schemes are
proposed for addressing the challenges in time-dependent quantum simulations of
systems ranging from atoms, molecules, and nanostructures to emerging
nanoelectronic devices. While time-dependent Hamiltonian problems can be
formally solved by propagating the solutions along tiny simulation time steps,
a direct numerical treatment is often considered too computationally demanding.
In this paper, however, we propose to go beyond these limitations by
introducing high-performance numerical propagation schemes to compute the
solution of the time-ordered evolution operator. In addition to the direct
Hamiltonian diagonalizations that can be efficiently performed using the new
eigenvalue solver FEAST, we have designed a Gaussian propagation scheme and a
basis transformed propagation scheme (BTPS) which allow to reduce considerably
the simulation times needed by time intervals. It is outlined that BTPS offers
the best computational efficiency allowing new perspectives in time-dependent
simulations. Finally, these numerical schemes are applied to study the AC
response of a (5,5) carbon nanotube within a 3D real-space mesh framework