509 research outputs found
On multiplicative functions which are small on average
Let be a completely multiplicative function that assumes values inside
the unit disc. We show that if \sum_{n2, for
some , then either is small on average or pretends to be
for some .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 (). This means that the electron mean free
path is much smaller than the normalized spiral length which in
turn is much smaller than (with 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 . 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 . 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
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