Linearly edge-reinforced random walks

We review results on linearly edge-reinforced random walks. On finite graphs, the process has the same distribution as a mixture of reversible Markov chains. This has applications in Bayesian statistics and it has been used in studying the random walk on infinite graphs. On trees, one has a representation as a random walk in an independent random environment. We review recent results for the random walk on ladders: recurrence, a representation as a random walk in a random environment, and estimates for the position of the random walker.Comment: Published at http://dx.doi.org/10.1214/074921706000000103 in the IMS Lecture Notes--Monograph Series (http://www.imstat.org/publications/lecnotes.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Femtosecond photoelectron diffraction: A new approach to image molecular structure during photochemical reactions.

Continuing technical advances in the creation of (sub-) femtosecond VUV and X-ray pulses with Free-Electron Lasers and laser-based high-harmonic-generation sources have created new opportunities for studying ultrafast dynamics during chemical reactions. Here, we present an approach to image the geometric structure of gas-phase molecules with fewfemtosecond temporal and sub-Ångström spatial resolution using femtosecond photoelectron diffraction. This technique allows imaging the molecules “from within” by analyzing the diffraction of inner-shell photoelectrons that are created by femtosecond VUV and X-ray pulses. Using pump-probe schemes, ultrafast structural changes during photochemical reactions can thus be directly visualized with a temporal resolution that is only limited by the pulse durations of the pump and the probe pulse and the synchronization of the two light pulses. Here, we illustrate the principle of photoelectron diffraction using a simple, geometric scattering model and present results from photoelectron diffraction experiments on laser-aligned molecules using X-ray pulses from a Free-Electron Laser

Imaging Molecules from Within: Ultra-fast, {\AA}ngstr\"om Scale Structure Determination of Molecules via Photoelectron Holography using Free Electron Lasers

A new scheme based on (i) upcoming brilliant X-ray Free Electron Laser (FEL) sources, (ii) novel energy and angular dispersive, large-area electron imagers and (iii) the well-known photoelectron holography is elaborated that provides time-dependent three-dimensional structure determination of small to medium sized molecules with {\AA}ngstr\"om spatial and femtosecond time resolution. Inducing molecular dynamics, wave-packet motion, dissociation, passage through conical intersections or isomerization by a pump pulse this motion is visualized by the X-ray FEL probe pulse launching keV photoelectrons within few femtoseconds from specific and well-defined sites, deep core levels of individual atoms, inside the molecule. On their way out the photoelectrons are diffracted generating a hologram on the detector that encodes the molecular structure at the instant of photoionization, thus providing 'femtosecond snapshot images of the molecule from within'. Detailed calculations in various approximations of increasing sophistication are presented and three-dimensional retrieval of the spatial structure of the molecule with {\AA}ngstr\"om spatial resolution is demonstrated. Due to the large photo-absorption cross sections the method extends X-ray diffraction based, time-dependent structure investigations envisioned at FELs to new classes of samples that are not accessible by any other method. Among them are dilute samples in the gas phase such as aligned, oriented or conformer selected molecules, ultra-cold ensembles and/or molecular or cluster objects containing mainly light atoms that do not scatter X-rays efficiently.Comment: 18 pages, 11 figure

Low-Energy Nondipole Effects in Molecular Nitrogen Valence-Shell Photoionization

Observations are reported for the first time of significant nondipole effects in the photoionization of the outer-valence orbitals of diatomic molecules. Measured nondipole angular-distribution parameters for the 3sigmag, 1piu, and 2sigmau shells of N2 exhibit spectral variations with incident photon energies from thresholds to ~200 eV which are attributed via concomitant calculations to particular final-state symmetry waves arising from (E1)[direct-product](M1,E2) radiation-matter interactions first-order in photon momentum. Comparisons with previously reported K-edge studies in N2 verify linear scaling with photon momentum, accounting in part for the significantly enhanced nondipole behavior observed in inner-shell ionization at correspondingly higher momentum values in this molecule

Diffraction effects in the Recoil-Frame Photoelectron Angular Distributions of Halomethanes

Citation: Bomme, C., Anielski, D., Savelyev, E., Boll, R., Erk, B., Bari, S., . . . Rolles, D. (2015). Diffraction effects in the Recoil-Frame Photoelectron Angular Distributions of Halomethanes. 635(11). doi:10.1088/1742-6596/635/11/112020We have measured the Recoil Frame-Photoelectron Angular Distributions (RF-PADs) for inner-shell photoionization of CH3F, CH3I and CF3I halomethane molecules for photoelectron energies up to 300 eV detected within a 4? solid angle in the gas-phase. For high kinetic energies, the RF-PADs are dominated by diffraction effects that encode information on the molecular geometry. © Published under licence by IOP Publishing Ltd

Nearest-Neighbor-Atom Core-Hole Transfer in Isolated Molecules

A new phenomenon sensitive only to next-door-neighbor atoms in isolated molecules is demonstrated using angle-resolved photoemission of site-selective core electrons. Evidence for this interatomic core-to-core electron interaction is observable only by measuring nondipolar angular distributions of photoelectrons. In essence, the phenomenon acts as a very fine atomic-scale sensor of nearest-neighbor elemental identity

Time-Resolved Measurement of Interatomic Coulombic Decay in Ne_2

The lifetime of interatomic Coulombic decay (ICD) [L. S. Cederbaum et al., Phys. Rev. Lett. 79, 4778 (1997)] in Ne_2 is determined via an extreme ultraviolet pump-probe experiment at the Free-Electron Laser in Hamburg. The pump pulse creates a 2s inner-shell vacancy in one of the two Ne atoms, whereupon the ionized dimer undergoes ICD resulting in a repulsive Ne^{+}(2p^{-1}) - Ne^{+}(2p^{-1}) state, which is probed with a second pulse, removing a further electron. The yield of coincident Ne^{+} - Ne^{2+} pairs is recorded as a function of the pump-probe delay, allowing us to deduce the ICD lifetime of the Ne_{2}^{+}(2s^{-1}) state to be (150 +/- 50) fs in agreement with quantum calculations.Comment: 5 pages, 3 figures, accepted by PRL on July 11th, 201

Nondipole Effects in the Photoionization of Xe 4d5/2 and 4d3/2: Evidence for Quadrupole Satellites

Measurements of nondipole parameters in spin-orbit-resolved Xe 4d photoionization demonstrate dynamical differences arising from relativistic effects. The experimental data do not agree with relativistic random-phase approximation calculations of single ionization dipole and quadrupole channels. It is suggested that the discrepancy is due to the omission of multiple-excitation quadrupole channels, i.e., quadrupole satellite transitions