Low-energy local density of states of the 1D Hubbard model

We examine the local density of states (DOS) at low energies numerically and analytically for the Hubbard model in one dimension. The eigenstates represent separate spin and charge excitations with a remarkably rich structure of the local DOS in space and energy. The results predict signatures of strongly correlated excitations in the tunneling probability along finite quantum wires, such as carbon nanotubes, atomic chains or semiconductor wires in scanning tunneling spectroscopy (STS) experiments. However, the detailed signatures can only be partly explained by standard Luttinger liquid theory. In particular, we find that the effective boundary exponent can be negative in finite wires, which leads to an increase of the local DOS near the edges in contrast to the established behavior in the thermodynamic limit.Comment: 6 pages, 4 figures, more information can be found at http://www.physik.uni-kl.de/eggert/papers/index.htm

Universal features in sequential and nonsequential two-photon double ionization of helium

We analyze two-photon double ionization of helium in both the nonsequential and sequential regime. We show that the energy spacing between the two emitted electrons provides the key parameter that controls both the energy and the angular distribution and reveals the universal features present in both the nonsequential and sequential regime. This universality, i.e., independence of photon energy, is a manifestation of the continuity across the threshold for sequential double ionization. For all photon energies, the energy distribution can be described by a universal shape function that contains only the spectral and temporal information entering second-order time-dependent perturbation theory. Angular correlations and distributions are found to be more sensitive to the photon energy. In particular, shake-up interferences have a large effect on the angular distribution. Energy spectra, angular distributions parameterized by the anisotropy parameters, and total cross sections presented in this paper are obtained by fully correlated time-dependent ab initio calculations.Comment: 12 pages, 8 figure

On the Integrability of Classical Ruijsenaars-Schneider Model of BC2BC_{2} Type

The problem of finding most general form of the classical integrable relativistic models of many-body interaction of the $BC_{n}$ type is considered. In the simplest nontrivial case of $n=2$,the extra integral of motion is presented in explicit form within the ansatz similar to the nonrelativistic Calogero-Moser models. The resulting Hamiltonian has been found by solving the set of two functional equations.Comment: 10 pages, LaTeX2e, no figure

Two-photon Double Ionization of H2_2 in Intense Femtosecond Laser Pulses

Triple-differential cross sections for two-photon double ionization of molecular hydrogen are presented for a central photon energy of 30 eV. The calculations are based on a fully {\it ab initio}, nonperturbative, approach to the time-dependent Schroedinger equation in prolate spheroidal coordinates, discretized by a finite-element discrete-variable-representation. The wave function is propagated in time for a few femtoseconds using the short, iterative Lanczos method to study the correlated response of the two photoelectrons to short, intense laser radiation. The current results often lie in between those of Colgan {\it et al} [J. Phys. B {\bf 41} (2008) 121002] and Morales {\it et al} [J. Phys. B {\bf 41} (2009) 134013]. However, we argue that these individual predictions should not be compared directly to each other, but preferably to experimental data generated under well-defined conditions.Comment: 4 pages, 4 figure