On multiplicative functions which are small on average

Let $f$ be a completely multiplicative function that assumes values inside the unit disc. We show that if \sum_{n2, for some $A>2$, then either $f(p)$ is small on average or $f$ pretends to be $\mu(n)n^{it}$ for some $t$.Comment: 51 pages. Slightly strengthened Theorem 1.2 and simplified its statement. Removed Remark 1.3. Other minor changes and corrections. To appear in Geom. Funct. Ana

On the preservation of coherence in the electronic wavepacket of a neutral and rigid polyatomic molecule

We present various types of reduced models including five vibrational modes and three electronic states for the pyrazine molecule in order to investigate the lifetime of electronic coherence in a rigid and neutral system. Using an ultrafast optical pumping in the ground state (1 1 A g ), we prepare a coherent superposition of two bright excited states, 1 1 B 2u and 1 1 B 1u , and reveal the effect of the nuclear motion on the preservation of the electronic coherence induced by the laser pulse. More specifically, two aspects are considered: the anharmonicity of the potential energy surfaces and the dependence of the transition dipole moments (TDMs) with respect to the nuclear coordinates. To this end, we define an ideal model by making three approximations: (i) only the five totally symmetric modes move, (ii) which correspond to uncoupled harmonic oscillators, and (iii) the TDMs from the ground electronic state to the two bright states are constant (Franck-Condon approximation). We then lift the second and third approximations by considering, first, the effect of anharmonicity, second, the effect of coordinate-dependence of the TDMs (first-order Herzberg- Teller contribution), third, both. Our detailed numerical study with quantum dynamics confirms long-term revivals of the electronic coherence even for the most realistic model

Critical current of a Josephson junction containing a conical magnet

We calculate the critical current of a superconductor/ferromagnetic/superconductor (S/FM/S) Josephson junction in which the FM layer has a conical magnetic structure composed of an in-plane rotating antiferromagnetic phase and an out-of-plane ferromagnetic component. In view of the realistic electronic properties and magnetic structures that can be formed when conical magnets such as Ho are grown with a polycrystalline structure in thin-film form by methods such as direct current sputtering and evaporation, we have modeled this situation in the dirty limit with a large magnetic coherence length ($\xi_f$). This means that the electron mean free path is much smaller than the normalized spiral length $\lambda/2\pi$ which in turn is much smaller than $\xi_f$ (with $\lambda$ as the length a complete spiral makes along the growth direction of the FM). In this physically reasonable limit we have employed the linearized Usadel equations: we find that the triplet correlations are short ranged and manifested in the critical current as a rapid oscillation on the scale of $\lambda/2\pi$. These rapid oscillations in the critical current are superimposed on a slower oscillation which is related to the singlet correlations. Both oscillations decay on the scale of $\xi_f$. We derive an analytical solution and also describe a computational method for obtaining the critical current as a function of the conical magnetic layer thickness.Comment: Extended version of the published paper. Additional information about the computational method is included in the appendi

Attosecond electronic and nuclear quantum photodynamics of ozone: time-dependent Dyson orbitals and dipole

A nonadiabatic scheme for the description of the coupled electron and nuclear motions in the ozone molecule was proposed recently. An initial coherent nonstationary state was prepared as a superposition of the ground state and the excited Hartley band. In this situation neither the electrons nor the nuclei are in a stationary state. The multiconfiguration time dependent Hartree method was used to solve the coupled nuclear quantum dynamics in the framework of the adiabatic separation of the time-dependent Schr\"odinger equation. The resulting wave packet shows an oscillation of the electron density between the two chemical bonds. As a first step for probing the electronic motion we computed the time-dependent molecular dipole and the Dyson orbitals. The latter play an important role in the explanation of the photoelectron angular distribution. Calculations of the Dyson orbitals are presented both for the time-independent as well as the time-dependent situations. We limited our description of the electronic motion to the Franck-Condon region only due to the localization of the nuclear wave packets around this point during the first 5-6 fs

Coherence revival during the attosecond electronic and nuclear quantum photodynamics of the ozone molecule

A coherent superposition of two electronic states of ozone (ground and Hartley B) is prepared with a UV pump pulse. Using the multiconfiguration time-dependent Hartree approach, we calculate the subsequent time evolution of the two corresponding nuclear wave packets and the coherence between them. The resulting wave packet shows an oscillation between the two chemical bonds. Even more interesting, the coherence between the two electronics states reappears after the laser pulse is switched off, which could be observed experimentally with an attosecond probe pulse

Cross section measurement of the astrophysically important 17O(p,gamma)18F reaction in a wide energy range

The 17O(p,g)18F reaction plays an important role in hydrogen burning processes in different stages of stellar evolution. The rate of this reaction must therefore be known with high accuracy in order to provide the necessary input for astrophysical models. The cross section of 17O(p,g)18F is characterized by a complicated resonance structure at low energies. Experimental data, however, is scarce in a wide energy range which increases the uncertainty of the low energy extrapolations. The purpose of the present work is therefore to provide consistent and precise cross section values in a wide energy range. The cross section is measured using the activation method which provides directly the total cross section. With this technique some typical systematic uncertainties encountered in in-beam gamma-spectroscopy experiments can be avoided. The cross section was measured between 500 keV and 1.8 MeV proton energies with a total uncertainty of typically 10%. The results are compared with earlier measurements and it is found that the gross features of the 17O(p,g)18F excitation function is relatively well reproduced by the present data. Deviation of roughly a factor of 1.5 is found in the case of the total cross section when compared with the only one high energy dataset. At the lowest measured energy our result is in agreement with two recent datasets within one standard deviation and deviates by roughly two standard deviations from a third one. An R-matrix analysis of the present and previous data strengthen the reliability of the extrapolated zero energy astrophysical S-factor. Using an independent experimental technique, the literature cross section data of 17O(p,g)18F is confirmed in the energy region of the resonances while lower direct capture cross section is recommended at higher energies. The present dataset provides a constraint for the theoretical cross sections.Comment: Accepted for publication in Phys. Rev. C. Abstract shortened in order to comply with arxiv rule