Two-center interference and ellipticity in high-order harmonic generation from H2+_2^+

We present a theoretical investigation into the two-center interference in aligned H$_2^+$. The influence of the laser field on the recombination step is investigated by comparing laser-induced harmonic generation with harmonic generation from field-free collisions of Gaussian wave packets with the core. We find that for different Gaussian wave packets colliding with the molecule, the interference minimum occurs at the same alignment angle. The same result is obtained for the laser-induced spectrum when only a single electronic trajectory per harmonic contributes. When multiple electronic trajectories contribute, we find an effect on the minimum position because the interference between short and long trajectories is alignment-dependent. The two-center interference and the influence of the Coulombic potential are clearly seen not only in the harmonic intensity and phase but also in the polarization direction and ellipticity. We observe significant ellipticity of the emitted radiation around the two-center interference minimum.Comment: 10 pages, 15 figures; v2: clearer figures and other small changes; v3: small correction

The wave equation as a port-Hamiltonian system and a finite-dimensional approximation

The problem of approximating a distributed parameter system with free boundary conditions is solved for the 2-dimensional wave equation. To this end we first model the wave equation as a distributed-parameter port-Hamiltonian system. Then we employ the idea that it is natural to use different finite elements for the approximation of di?erent geometric variables (forms) describing a distributed-parameter system, to spatially discretize the system and we show that we obtain a ?nite-dimensional port-Hamiltonian system, which also preserves the conservation laws

The exclusive (e,e′'p) reaction at high missing momenta

The reduced (e,e$'$p) cross section is calculated for kinematics that probe high missing momenta. The final-state interaction is handled within a non-relativistic many-body framework. One- and two-body nuclear currents are included. Electron distortion effects are treated in an exact distorted wave calculation. It is shown that at high missing momenta the calculated (e,e$'$p) cross sections exhibit a pronounced sensitivity to ground-state correlations of the RPA type and two-body currents. The role of these mechanisms is found to be relatively small at low missing momenta.Comment: 15 pages in REVtex with embedded psfigure

Control of recollision wave packets for molecular orbital tomography using short laser pulses

The tomographic imaging of arbitrary molecular orbitals via high-order harmonic generation requires that electrons recollide from one direction only. Within a semi-classical model, we show that extremely short phase-stabilized laser pulses offer control over the momentum distribution of the returning electrons. By adjusting the carrier-envelope phase, recollisions can be forced to occur from mainly one side, while retaining a broad energy spectrum. The signatures of the semi-classical distributions are observed in harmonic spectra obtained by numerical solution of the time-dependent Schr\"{o}dinger equation.Comment: 8 pages, 4 figures; v2: Added some extra clarifications; v3: minor grammatical change

The group of automorphisms of the first weyl algebra in prime characteristic and the restriction map

Let K be a perfect field of characteristic p > 0; A(1) := K be the first Weyl algebra; and Z := K[X := x(p), Y := partial derivative(p)] be its centre. It is proved that (1) the restriction map res : Aut(K)(A(1)) -> Aut(K)(Z), sigma bar right arrow sigma vertical bar(Z) is a monomorphism with im(res) = Gamma := (tau is an element of Aut(K)(Z) vertical bar J(tau) = 1), where J(tau) is the Jacobian of tau, (Note that Aut(K)(Z) = K* (sic) Gamma, and if K is not perfect then im(res) not equal Gamma.); (ii) the bijection res : Aut(K)(A(1)) -> Gamma is a monomorphism of infinite dimensional algebraic groups which is not an isomorphism (even if K is algebraically closed); (iii) an explicit formula for res(-1) is found via differential operators D(Z) on Z and negative powers of the Fronenius map F. Proofs are based on the following (non-obvious) equality proved in the paper: (d/dx + f)(p) = (d/dx)(p) + d(p-1)f/dx(p-1) + f(p), f is an element of K[x]

First Detection of Molecular Gas in the Shells of CenA

Shells are faint arc-like stellar structures, which have been observed around early type galaxies and are thought to be the result of an interaction. HI gas has recently been detected in shells, a surprising result in view of the theoretical predictions that most of the gas should decouple from stars and fall into the nucleus in such interactions. Here we report the first detection of molecular gas (CO) in shells, found 15kpc away from the center of NGC5128 (CenA), a giant elliptical galaxy that harbors an active nucleus (AGN). The ratio between CO and HI emission in the shells is the same as that found in the central regions, which is unexpected given the metallicity gradient usually observed in galaxies. We propose that the dynamics of the gas can be understood within the standard picture of shell formation if one takes into account that the interstellar medium is clumpy and hence not highly dissipative. The observed metal enrichment could be due to star formation induced by the AGN jet in the shells. Furthermore our observations provide evidence that molecular gas in mergers may be spread out far from the nuclear regions.Comment: Accepted for publication in Astronomy & Astrophysics Letters, (Vol. 356), 4 pages + 1 color figur

Hamiltonian mechanics on discrete manifolds

The mathematical/geometric structure of discrete models of systems, whether these models are obtained after discretization of a smooth system or as a direct result of modeling at the discrete level, have not been studied much. Mostly one is concerned regarding the nature of the solutions, but not much has been done regarding the structure of these discrete models. In this paper we provide a framework for the study of discrete models, speci?cally we present a Hamiltonian point of view. To this end we introduce the concept of a discrete calculus

Interconnection structures in physical systems: a mathematical formulation

The power-conserving structure of a physical system is known as interconnection structure. This paper presents a mathematical formulation of the interconnection structure in Hilbert spaces. Some properties of interconnection structures are pointed out and their three natural representations are treated. The developed theory is illustrated on two examples: electrical circuit and one-dimensional transmission lin