Development of a general time-dependent absorbing potential for the constrained adiabatic trajectory method.

The constrained adiabatic trajectory method (CATM) allows us to compute solutions of the time-dependent Schrödinger equation using the Floquet formalism and Fourier decomposition, using matrix manipulation within a non-orthogonal basis set, provided that suitable constraints can be applied to the initial conditions for the Floquet eigenstate. A general form is derived for the inherent absorbing potential, which can reproduce any dispersed boundary conditions. This new artificial potential acting over an additional time interval transforms any wavefunction into a desired state, with an error involving exponentially decreasing factors.

Iterative eigenvalue method using the Bloch wave operator formalism with Padé approximants and absorbing boundaries.

We present an iterative method for calculating eigenvalues and eigenvectors of large non-Hermitian matrices. The method uses an iterative procedure to solve the basic Bloch equation HOmega=OmegaHOmega of wave operator theory. It involves nonlinear transformations such as the translation of diagonal matrix elements in the complex plane and the use of Padé approximants to treat the strongly coupled states which constitute an intermediate space around the model space.