Berlin 2014 – scientific programme

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A: Fachverband Atomphysik

A 15: Poster: Interaction with strong or short laser pulses

A 15.14: Poster

Monday, March 17, 2014, 16:30–18:30, Spree-Palais

Krylov subspace methods in relativistic quantum dynamics — •Randolf Beerwerth, Heiko Bauke, and Christoph H. Keitel — Max-Planck-Institut für Kernphysik Saupfercheckweg 1, 69117 Heidelberg

The theoretical investigation of relativistic quantum dynamics of electrons, atoms, or ions that interact with strong or short laser pulses often necessitates nonperturbative approaches which rely on numerical methods, e. g., the numerical solution of the time-dependent Dirac equation. Krylov subspace methods, e. g., the Lanczos algorithm, allow to calculate efficiently few approximate eigenvalues and eigenvectors of very large matrices and have become a standard method for solving the nonrelativistic Schrödinger equation. Here we transfer these methods into the domain of relativistic quantum dynamics. Since Krylov subspace methods usually converge to eigenstates with extremal eigenvalues and relativistic Hamiltonians are not bounded it is not self-evident that these methods are applicable in the relativistic domain.

We focus on bound states in relativistic systems and we demonstrate that Krylov subspace methods are well suited to calculate the bound states of the Dirac Hamiltonian. For this purpose, we combine the Lanczos algorithm with the pseudospectral method, where the wave function is expanded into harmonic oscillator eigenfunctions. Due to the exponential convergence of the pseudospectral approach this yields precise results using only a moderate number of basis functions. Time-dependent propagation of Dirac wave functions will also be demonstrated.