ABSOLUTE CONTINUITY OF BERNOULLI CONVOLUTIONS FOR ALGEBRAIC PARAMETERS

We prove that Bernoulli convolutions $\mu _\lambda$ are absolutely continuous provided the parameter $\lambda$ is an algebraic number sufficiently close to $1$ depending on the Mahler measure of $\lambda$

Temperature dependence of binary and ternary recombination of H3+ ions with electron

We study binary and the recently discovered process of ternary He-assisted recombination of H3+ ions with electrons in a low temperature afterglow plasma. The experiments are carried out over a broad range of pressures and temperatures of an afterglow plasma in a helium buffer gas. Binary and He-assisted ternary recombination are observed and the corresponding recombination rate coefficients are extracted for temperatures from 77 K to 330 K. We describe the observed ternary recombination as a two-step mechanism: First, a rotationally-excited long-lived neutral molecule H3* is formed in electron-H3+ collisions. Second, the H3* molecule collides with a helium atom that leads to the formation of a very long-lived Rydberg state with high orbital momentum. We present calculations of the lifetimes of H3* and of the ternary recombination rate coefficients for para and ortho-H3+. The calculations show a large difference between the ternary recombination rate coefficients of ortho- and para-H3+ at temperatures below 300 K. The measured binary and ternary rate coefficients are in reasonable agreement with the calculated values.Comment: 15 page

Recombination of H3+ Ions in the Afterglow of a He-Ar-H2 Plasma

Recombination of H3+ with electrons was studied in a low temperature plasma in helium. The plasma recombination rate is driven by two body, H3+ + e, and three-body, H3+ + e + He, processes with the rate coefficients 7.5x10^{-8}cm3/s and 2.8x10^{-25}cm6/s correspondingly at 260K. The two-body rate coefficient is in excellent agreement with results from storage ring experiments and theoretical calculations. We suggest that the three-body recombination involves formation of highly excited Rydberg neutral H3 followed by an l- or m- changing collision with He. Plasma electron spectroscopy indicates the presence of H3.Comment: 4 figure

Temperature dependence of binary and ternary recombination of H3+ ions with electron

We study binary and the recently discovered process of ternary He-assisted recombination of H3+ ions with electrons in a low temperature afterglow plasma. The experiments are carried out over a broad range of pressures and temperatures of an afterglow plasma in a helium buffer gas. Binary and He-assisted ternary recombination are observed and the corresponding recombination rate coefficients are extracted for temperatures from 77 K to 330 K. We describe the observed ternary recombination as a two-step mechanism: First, a rotationally-excited long-lived neutral molecule H3* is formed in electron-H3+ collisions. Second, the H3* molecule collides with a helium atom that leads to the formation of a very long-lived Rydberg state with high orbital momentum. We present calculations of the lifetimes of H3* and of the ternary recombination rate coefficients for para and ortho-H3+. The calculations show a large difference between the ternary recombination rate coefficients of ortho- and para-H3+ at temperatures below 300 K. The measured binary and ternary rate coefficients are in reasonable agreement with the calculated values.Comment: 15 page

Quantum repeated interactions and the chaos game

Inspired by the algorithm of Barnsley's chaos game, we construct an open quantum system model based on the repeated interaction process. We shown that the quantum dynamics of the appropriate fermionic/bosonic system (in interaction with an environment) provides a physical model of the chaos game. When considering fermionic operators, we follow the system's evolution by focusing on its reduced density matrix. The system is shown to be in a Gaussian state (at all time $t$) and the average number of particles is shown to obey the chaos game equation. Considering bosonic operators, with a system initially prepared in coherent states, the evolution of the system can be tracked by investigating the dynamics of the eigenvalues of the annihilation operator. This quantity is governed by a chaos game-like equation from which different scenarios emerge.Comment: 21 pages, 8 figue

Growth in solvable subgroups of GL_r(Z/pZ)

Let $K=Z/pZ$ and let $A$ be a subset of \GL_r(K) such that is solvable. We reduce the study of the growth of $A$ under the group operation to the nilpotent setting. Specifically we prove that either $A$ grows rapidly (meaning $|A\cdot A\cdot A|\gg |A|^{1+\delta}$), or else there are groups $U_R$ and $S$, with $S/U_R$ nilpotent such that $A_k\cap S$ is large and $U_R\subseteq A_k$, where $k$ is a bounded integer and $A_k = \{x_1 x_2...b x_k : x_i \in A \cup A^{-1} \cup {1}}$. The implied constants depend only on the rank $r$ of $\GL_r(K)$. When combined with recent work by Pyber and Szab\'o, the main result of this paper implies that it is possible to draw the same conclusions without supposing that is solvable.Comment: 46 pages. This version includes revisions recommended by an anonymous referee including, in particular, the statement of a new theorem, Theorem

Propagation-enhanced generation of intense high-harmonic continua in the 100-eV spectral region

The study of core electron dynamics through nonlinear spectroscopy requires intense isolated attosecond extreme ultraviolet or even X-ray pulses. A robust way to produce these pulses is high-harmonic generation (HHG) in a gas medium. However, the energy upscaling of the process depends on a very demanding next-generation laser technology that provides multi-terawatt (TW) laser pulses with few-optical-cycle duration and controlled electric field. Here, we revisit the HHG process driven by 16-TW sub-two-cycle laser pulses to reach high intensity in the 100-eV spectral region and beyond. We show that the combination of above barrier-suppression intensity with a long generation medium significantly enhances the isolation of attosecond pulses compared to lower intensities and/or shorter media and this way reduces the pulse duration as well as field-stability requirements on the laser driver. This novel regime facilitates the real-time observation of electron dynamics at the attosecond timescale in atoms, molecules, and solids

Meta-Analysis of the Long Term Success Rate of Different Interventions in Benign Biliary Strictures.

BACKGROUND: Benign biliary stricture is a rare condition and the majority of the cases are caused by operative trauma or chronic inflammation based on various etiology. Although the initial results of endoscopic, percutaneous and surgical treatment are impressive, no comparison about long term stricture resolution is available. AIMS: The goal of this study was to compare the long term disease free survival in benign biliary strictures with various etiology after surgery, percutaneous transhepatic-and endoscopic treatment. METHODS: PubMed, Embase, and Cochrane Library were searched by computer and manually for published studies. The investigators selected the publications according to the inclusion and exclusion criteria, processed the data and assessed the quality of the selected studies. Meta-analysis of data of 24 publications was performed to compare long term disease free survival of different treatment groups. RESULTS: Compared the subgroups surgery resulted in the highest long term stricture resolution rate, followed by the percutaneous transhepatic treatment, the multiple plastic stent insertion and covered self-expanding metal stents (SEMS), however the difference was not significant. All compared methods are significantly superior to the single plastic stent placement. Long term stricture resolution rate irrespectively of any therapy is still not more than 84%. CONCLUSIONS: In summary, the use of single plastic stent is not recommended. Further randomized studies and innovative technical development are required for improving the treatment of benign biliary strictures