7,420 research outputs found
Categorical Groups, Knots and Knotted Surfaces
We define a knot invariant and a 2-knot invariant from any finite categorical
group. We calculate an explicit example for the Spun Trefoil.Comment: 40 pages, lots of figures. Second version: Added example and
discussion, clarification of the fact that the maps associated with
Reidemeister Moves are well define
Influence of asymmetry and nodal planes on high-harmonic generation in heteronuclear molecules
The relation between high-harmonic spectra and the geometry of the molecular
orbitals in position and momentum space is investigated. In particular we
choose two isoelectronic pairs of homonuclear and heteronuclear molecules, such
that the highest occupied molecular orbital of the former exhibit at least one
nodal plane. The imprint of such planes is a strong suppression in the harmonic
spectra, for particular alignment angles. We are able to identify two distinct
types of nodal planes. If the nodal planes are determined by the atomic
wavefunctions only, the angle for which the yield is suppressed will remain the
same for both types of molecules. In contrast, if they are determined by the
linear combination of atomic orbitals at different centers in the molecule,
there will be a shift in the angle at which the suppression occurs for the
heteronuclear molecules, with regard to their homonuclear counterpart. This
shows that, in principle, molecular imaging, which uses the homonuclear
molecule as a reference and enables one to observe the wavefunction distortions
in its heteronuclear counterpart, is possible.Comment: 14 pages, 7 figures. Figs. 3, 5 and 6 have been simplified in order
to comply with the arXiv size requirement
Low redshift constraints on energy-momentum-powered gravity models
There has been recent interest in the cosmological consequences of
energy-momentum-powered gravity models, in which the matter side of Einstein's
equations is modified by the addition of a term proportional to some power,
, of the energy-momentum tensor, in addition to the canonical linear term.
In this work we treat these models as phenomenological extensions of the
standard CDM, containing both matter and a cosmological constant. We
also quantitatively constrain the additional model parameters using low
redshift background cosmology data that are specifically from Type Ia
supernovas and Hubble parameter measurements. We start by studying specific
cases of these models with fixed values of which lead to an analytic
expression for the Friedmann equation; we discuss both their current
constraints and how the models may be further constrained by future
observations of Type Ia supernovas for WFIRST complemented by measurements of
the redshift drift by the ELT. We then consider and constrain a more extended
parameter space, allowing to be a free parameter and considering scenarios
with and without a cosmological constant. These models do not solve the
cosmological constant problem per se. Nonetheless these models can
phenomenologically lead to a recent accelerating universe without a
cosmological constant at the cost of having a preferred matter density of
around instead of the usual . Finally we
also briefly constrain scenarios without a cosmological constant, where the
single component has a constant equation of state which needs not be that of
matter; we provide an illustrative comparison of this model with a more
standard dynamical dark energy model with a constant equation of state.Comment: 13+2 pages, 12+1 figures; A&A (in press
Existence criteria for stabilization from the scaling behaviour of ionization probabilities
We provide a systematic derivation of the scaling behaviour of various
quantities and establish in particular the scale invariance of the ionization
probability. We discuss the gauge invariance of the scaling properties and the
manner in which they can be exploited as consistency check in explicit
analytical expressions, in perturbation theory, in the Kramers-Henneberger and
Floquet approximation, in upper and lower bound estimates and fully numerical
solutions of the time dependent Schroedinger equation. The scaling invariance
leads to a differential equation which has to be satisfied by the ionization
probability and which yields an alternative criterium for the existence of
atomic bound state stabilization.Comment: 12 pages of Latex, one figur
Coulomb-corrected quantum interference in above-threshold ionization: Working towards multi-trajectory electron holography
Using the recently developed Coulomb Quantum Orbit Strong-Field Approximation
(CQSFA), we perform a systematic analysis of several features encountered in
above-threshold ionization (ATI) photoelectron angle-resolved distributions
(PADs), such as side lobes, and intra- and intercycle interference patterns.
The latter include not only the well-known intra-cycle rings and the
near-threshold fan-shaped structure, but also previously overlooked patterns.
We provide a direct account of how the Coulomb potential distorts different
types of interfering trajectories and changes the corresponding phase
differences, and show that these patterns may be viewed as generalized
holographic structures formed by up to three types of trajectories. We also
derive analytical interference conditions and estimates valid in the presence
or absence of the residual potential, and assess the range of validity of
Coulomb-corrected interference conditions provided in the literature.Comment: 17 pages, 11 figures. Some figures have been compressed in order to
comply with the arXiv requirement
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