Spectral modeling and propagation schemes for time-dependent quantum systems

In this paper, we propose effective modeling and novel spectral-based propagation schemes to address the general problems of time-dependent quantum simulations. The integral solution of the time-ordered evolution operator is obtained accurately via direct Hamiltonian diagonalizations performed using the new eigenvalue solver FEAST. In addition, we have designed a new highly efficient basis transformed propagation scheme (BTPS) which reduces considerably the simulation times needed by time intervals. These numerical schemes are applied to study the AC response of a (5,5) carbon nanotube within a 3D real-space mesh framework, and obtaining the kinetic inductance.