32,695 research outputs found
General moments of the inverse real Wishart distribution and orthogonal Weingarten functions
Let be a random positive definite symmetric matrix distributed according
to a real Wishart distribution and let be its inverse
matrix. We compute general moments explicitly. To do so, we employ the orthogonal Weingarten
function, which was recently introduced in the study for Haar-distributed
orthogonal matrices. As applications, we give formulas for moments of traces of
a Wishart matrix and its inverse.Comment: 29 pages. The last version differs from the published version, but it
includes Appendi
Attosecond two-photon interferometry for doubly excited states of helium
We show that the correlation dynamics in coherently excited doubly excited
resonances of helium can be followed in real time by two-photon interferometry.
This approach promises to map the evolution of the two-electron wave packet
onto experimentally easily accessible non-coincident single electron spectra.
We analyze the interferometric signal in terms of a semi-analytical model which
is validated by a numerical solution of the time-dependent two-electron
Schr\"odinger equation in its full dimensionality.Comment: 5 pages, 4 figure
Nonlinearity of vacuum reggeons and exclusive diffractive production of vector mesons at HERA
The processes of exclusive photo- and electroproduction of vector mesons
(770), (1020) and (3096) at collision energies and transferred momenta squared are considered in
the framework of a phenomenological Regge-eikonal scheme with nonlinear Regge
trajectories in which their QCD asymptotic behavior is taken into account
explicitly. By comparison of available experimental data from ZEUS and H1
Collaborations with the model predictions it is demonstrated that corresponding
angular distributions and integrated cross-sections in the above-mentioned
kinematical range can be quantitatively described with use of two -even
vacuum Regge trajectories. These are the "soft" pomeron dominating the high
energy reactions without a hard scale and the "hard" pomeron giving an
essential contribution to photo- and electroproduction of heavy vector mesons
and deeply virtual electroproduction of light vector mesons.Comment: 25 pages, 12 figure
Angular momentum exchange between coherent light and matter fields
Full, three dimensional, time-dependent simulations are presented
demonstrating the quantized transfer of angular momentum to a Bose-Einstein
condensate from a laser carrying orbital angular momentum in a
Laguerre-Gaussian mode. The process is described in terms of coherent Bragg
scattering of atoms from a chiral optical lattice. The transfer efficiency and
the angular momentum content of the output coupled vortex state are analyzed
and compared with a recent experiment.Comment: 4 pages, 4 figure
Non-Markovian Stochastic Resonance
The phenomenological linear response theory of non-Markovian Stochastic
Resonance (SR) is put forward for stationary two-state renewal processes. In
terms of a derivation of a non-Markov regression theorem we evaluate the
characteristic SR-quantifiers; i.e. the spectral power amplification (SPA) and
the signal-to-noise ratio (SNR), respectively. In clear contrast to Markovian
SR, a characteristic benchmark of genuine non-Markovian SR is its distinctive
dependence of the SPA and SNR on small (adiabatic) driving frequencies;
particularly, the adiabatic SNR becomes strongly suppressed over its Markovian
counterpart. This non-Markovian SR theory is elucidated for a fractal gating
dynamics of a potassium ion channel possessing an infinite variance of closed
sojourn times.Comment: 4 pages, 1 figur
A Method to Tackle First Order Differential Equations with Liouvillian Functions in the Solution - II
We present a semi-decision procedure to tackle first order differential
equations, with Liouvillian functions in the solution (LFOODEs). As in the case
of the Prelle-Singer procedure, this method is based on the knowledge of the
integrating factor structure.Comment: 11 pages, late
Spin Dependence of Massive Lepton Pair Production in Proton-Proton Collisions
We calculate the transverse momentum distribution for the production of
massive lepton-pairs in longitudinally polarized proton-proton reactions at
collider energies within the context of perturbative quantum chromodynamics.
For values of the transverse momentum Q_T greater than roughly half the pair
mass Q, Q_T > Q/2, we show that the differential cross section is dominated by
subprocesses initiated by incident gluons, provided that the polarized gluon
density is not too small. Massive lepton-pair differential cross sections
should be a good source of independent constraints on the polarized gluon
density, free from the experimental and theoretical complications of photon
isolation that beset studies of prompt photon production. We provide
predictions for the spin-averaged and spin-dependent differential cross
sections as a function of Q_T at energies relevant for the Relativistic Heavy
Ion Collider (RHIC) at Brookhaven, and we compare these with predictions for
real prompt photon production.Comment: 34 pages, RevTeX including 17 figures in .ps file
Probing Electron Correlation via Attosecond XUV Pulses in the Two-Photon Double Ionization of Helium
Recent experimental developments of high-intensity, short-pulse XUV light
sources are enhancing our ability to study electron-electron correlations. We
perform time-dependent calculations to investigate the so-called "sequential"
regime (photon energy above 54.4 eV) in the two-photon double ionization of
helium. We show that attosecond pulses allow to induce and probe angular and
energy correlations of the emitted electrons. The final momentum distribution
reveals regions dominated by the Wannier ridge break-up scenario and by
post-collision interaction.Comment: 4 pages, 5 figure
Universal features in sequential and nonsequential two-photon double ionization of helium
We analyze two-photon double ionization of helium in both the nonsequential
and sequential regime. We show that the energy spacing between the two emitted
electrons provides the key parameter that controls both the energy and the
angular distribution and reveals the universal features present in both the
nonsequential and sequential regime. This universality, i.e., independence of
photon energy, is a manifestation of the continuity across the threshold for
sequential double ionization. For all photon energies, the energy distribution
can be described by a universal shape function that contains only the spectral
and temporal information entering second-order time-dependent perturbation
theory. Angular correlations and distributions are found to be more sensitive
to the photon energy. In particular, shake-up interferences have a large effect
on the angular distribution. Energy spectra, angular distributions
parameterized by the anisotropy parameters, and total cross sections presented
in this paper are obtained by fully correlated time-dependent ab initio
calculations.Comment: 12 pages, 8 figure
Entanglement and non-locality are different resources
Bell's theorem states that, to simulate the correlations created by
measurement on pure entangled quantum states, shared randomness is not enough:
some "non-local" resources are required. It has been demonstrated recently that
all projective measurements on the maximally entangled state of two qubits can
be simulated with a single use of a "non-local machine". We prove that a
strictly larger amount of this non-local resource is required for the
simulation of pure non-maximally entangled states of two qubits
with
.Comment: 8 pages, 3 figure
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