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

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

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

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

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

Charge transfer in dissociating iodomethane and fluoromethane molecules ionized by intense femtosecond X-ray pulses

Citation: Boll, R., Erk, B., Coffee, R., Trippel, S., Kierspel, T., Bomme, C., . . . Rudenko, A. (2016). Charge transfer in dissociating iodomethane and fluoromethane molecules ionized by intense femtosecond X-ray pulses. Structural Dynamics, 3(4). doi:10.1063/1.4944344Additional Authors: Marchenko, T.;Miron, C.;Patanen, M.;Osipov, T.;Schorb, S.;Simon, M.;Swiggers, M.;Techert, S.;Ueda, K.;Bostedt, C.;Rolles, D.;Rudenko, A.Ultrafast electron transfer in dissociating iodomethane and fluoromethane molecules was studied at the Linac Coherent Light Source free-electron laser using an ultraviolet-pump, X-ray-probe scheme. The results for both molecules are discussed with respect to the nature of their UV excitation and different chemical properties. Signatures of long-distance intramolecular charge transfer are observed for both species, and a quantitative analysis of its distance dependence in iodomethane is carried out for charge states up to I21+. The reconstructed critical distances for electron transfer are in good agreement with a classical over-the-barrier model and with an earlier experiment employing a near-infrared pump pulse. © 2016 Author(s)

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

Imaging Molecular Structure through Femtosecond Photoelectron Diffraction on Aligned and Oriented Gas-Phase Molecules

This paper gives an account of our progress towards performing femtosecond time-resolved photoelectron diffraction on gas-phase molecules in a pump-probe setup combining optical lasers and an X-ray Free-Electron Laser. We present results of two experiments aimed at measuring photoelectron angular distributions of laser-aligned 1-ethynyl-4-fluorobenzene (C8H5F) and dissociating, laseraligned 1,4-dibromobenzene (C6H4Br2) molecules and discuss them in the larger context of photoelectron diffraction on gas-phase molecules. We also show how the strong nanosecond laser pulse used for adiabatically laser-aligning the molecules influences the measured electron and ion spectra and angular distributions, and discuss how this may affect the outcome of future time-resolved photoelectron diffraction experiments.Comment: 24 pages, 10 figures, Faraday Discussions 17