412 research outputs found
Large deviations for solutions to stochastic recurrence equations under Kesten's condition
In this paper we prove large deviations results for partial sums constructed
from the solution to a stochastic recurrence equation. We assume Kesten's
condition [Acta Math. 131 (1973) 207-248] under which the solution of the
stochastic recurrence equation has a marginal distribution with power law
tails, while the noise sequence of the equations can have light tails. The
results of the paper are analogs to those obtained by A. V. Nagaev [Theory
Probab. Appl. 14 (1969) 51-64; 193-208] and S. V. Nagaev [Ann. Probab. 7 (1979)
745-789] in the case of partial sums of i.i.d. random variables. In the latter
case, the large deviation probabilities of the partial sums are essentially
determined by the largest step size of the partial sum. For the solution to a
stochastic recurrence equation, the magnitude of the large deviation
probabilities is again given by the tail of the maximum summand, but the exact
asymptotic tail behavior is also influenced by clusters of extreme values, due
to dependencies in the sequence. We apply the large deviation results to study
the asymptotic behavior of the ruin probabilities in the model.Comment: Published in at http://dx.doi.org/10.1214/12-AOP782 the Annals of
Probability (http://www.imstat.org/aop/) by the Institute of Mathematical
Statistics (http://www.imstat.org
Attosecond transient absorption spectroscopy without inversion symmetry
Transient absorption is a very powerful observable in attosecond experiments on atoms, molecules and solids and is frequently used in experiments employing phase-locked few-cycle infrared and XUV laser pulses derived from high harmonic generation. We show numerically and analytically that in non-centrosymmetric systems, such as many polyatomic molecules, which-way interference enabled by the lack of parity conservation leads to new spectral absorption features, which directly reveal the laser electric field. The extension of attosecond transient absorption spectroscopy (ATAS) to such targets hence becomes sensitive to global and local inversion symmetry. We anticipate that ATAS will find new applications in non-centrosymmetric systems, in which the carrier-to-envelope phase of the infrared pulse becomes a relevant parameter and in which the orientation of the sample and the electronic symmetry of the molecule can be addressed
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Attosecond transient absorption spectroscopy without inversion symmetry
Transient absorption is a very powerful observable in attosecond experiments on atoms, molecules and solids and is frequently used in experiments employing phase-locked few-cycle infrared and XUV laser pulses derived from high harmonic generation. We show numerically and analytically that in non-centrosymmetric systems, such as many polyatomic molecules, which-way interference enabled by the lack of parity conservation leads to new spectral absorption features, which directly reveal the laser electric field. The extension of attosecond transient absorption spectroscopy (ATAS) to such targets hence becomes sensitive to global and local inversion symmetry. We anticipate that ATAS will find new applications in non-centrosymmetric systems, in which the carrier-to-envelope phase of the infrared pulse becomes a relevant parameter and in which the orientation of the sample and the electronic symmetry of the molecule can be addressed. © 2020 The Author(s). Published by IOP Publishing Ltd
Evaporation of buffer gas-thermalized anions out of a multipole rf ion trap
We identify plain evaporation of ions as the fundamental loss mechanism out
of a multipole ion trap. Using thermalized negative Cl- ions we find that the
evaporative loss rate is proportional to a Boltzmann factor. This thermodynamic
description sheds new light on the dynamics of particles in time-varying
confining potentials. It specifically allows us to extract the effective depth
of the ion trap as the activation energy for evaporation. As a function of the
rf amplitude we find two distinct regimes related to the stability of motion of
the trapped ions. For low amplitudes the entire trap allows for stable motion
and the trap depth increases with the rf field. For larger rf amplitudes,
however, rapid energy transfer from the field to the ion motion can occur at
large trap radii, which leads to a reduction of the effective trapping volume.
In this regime the trap depth decreases again with increasing rf amplitude. We
give an analytical parameterization of the trap depth for various multipole
traps that allows predictions of the most favorable trapping conditions.Comment: Phys. Rev. Lett., in pres
Photodetachment of cold OH- in a multipole ion trap
The absolute photodetachment cross section of OH- anions at a rotational and
translational temperature of 170K is determined by measuring the
detachment-induced decay rate of the anions in a multipole radio-frequency ion
trap. In comparison with previous results, the obtained cross section shows the
importance of the initial rotational state distribution. Using a tomography
scan of the photodetachment laser through the trapped ion cloud, the derived
cross section is model-independent and thus features a small systematic
uncertainty. The tomography also yields the column density of the OH- anions in
the 22-pole ion trap in good agreement with the expected trapping potential of
a large field free region bound by steep potential walls.Comment: Phys. Rev. Lett., in pres
Sequential and direct ionic excitation in the strong-field ionization of 1-butene molecules
We study the Strong-Field Ionization (SFI) of the hydrocarbon 1-butene as a function of wavelength using photoion-photoelectron covariance and coincidence spectroscopy. We observe a striking transition in the fragment-associated photoelectron spectra: from a single Above Threshold Ionization (ATI) progression for photon energies less than the cation D0–D1 gap to two ATI progressions for a photon energy greater than this gap. For the first case, electronically excited cations are created by SFI populating the ground cationic state D0, followed by sequential post-ionization excitation. For the second case, direct sub-cycle SFI to the D1 excited cation state contributes significantly. Our experiments access ionization dynamics in a regime where strong-field and resonance-enhanced processes can interplay
Structural phase transitions in multipole traps
A small number of laser-cooled ions trapped in a linear radiofrequency
multipole trap forms a hollow tube structure. We have studied, by means of
molecular dynamics simulations, the structural transition from a double ring to
a single ring of ions. We show that the single-ring configuration has the
advantage to inhibit the thermal transfer from the rf-excited radial components
of the motion to the axial component, allowing to reach the Doppler limit
temperature along the direction of the trap axis. Once cooled in this
particular configuration, the ions experience an angular dependency of the
confinement if the local adiabaticity parameter exceeds the empirical limit.
Bunching of the ion structures can then be observed and an analytic expression
is proposed to take into account for this behaviour
How can a 22-pole ion trap exhibit 10 local minima in the effective potential?
The column density distribution of trapped OH ions in a 22-pole ion trap
is measured for different trap parameters. The density is obtained from
position-dependent photodetachment rate measurements. Overall, agreement is
found with the effective potential of an ideal 22-pole. However, in addition we
observe 10 distinct minima in the trapping potential, which indicate a breaking
of the 22-fold symmetry. Numerical simulations show that a displacement of a
subset of the radiofrequency electrodes can serve as an explanation for this
symmetry breaking
The Visibility Graph: a new method for estimating the Hurst exponent of fractional Brownian motion
Fractional Brownian motion (fBm) has been used as a theoretical framework to
study real time series appearing in diverse scientific fields. Because its
intrinsic non-stationarity and long range dependence, its characterization via
the Hurst parameter H requires sophisticated techniques that often yield
ambiguous results. In this work we show that fBm series map into a scale free
visibility graph whose degree distribution is a function of H. Concretely, it
is shown that the exponent of the power law degree distribution depends
linearly on H. This also applies to fractional Gaussian noises (fGn) and
generic f^(-b) noises. Taking advantage of these facts, we propose a brand new
methodology to quantify long range dependence in these series. Its reliability
is confirmed with extensive numerical simulations and analytical developments.
Finally, we illustrate this method quantifying the persistent behavior of human
gait dynamics.Comment: 5 pages, submitted for publicatio
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Molecular orbital imprint in laser-driven electron recollision
Electrons released by strong-field ionization from atoms and molecules or in solids can be accelerated in the oscillating laser field and driven back to their ion core. The ensuing interaction, phase-locked to the optical cycle, initiates the central processes underlying attosecond science. A common assumption assigns a single, welldefined return direction to the recolliding electron. We study laser-induced electron rescattering associated with two different ionization continua in the same, spatially aligned, polyatomic molecule. We show by experiment and theory that the electron return probability is molecular frame-dependent and carries structural information on the ionized orbital. The returning wave packet structure has to be accounted for in analyzing strong-field spectroscopy experiments that critically depend on the interaction of the laser-driven continuum electron, such as laser-induced electron diffraction
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