Invariants of Welded Virtual Knots Via Crossed Module Invariants of Knotted Surfaces

We define an invariant of welded virtual knots from each finite crossed module by considering crossed module invariants of ribbon knotted surfaces which are naturally associated with them. We elucidate that the invariants obtained are non trivial by calculating explicit examples. We define welded virtual graphs and consider invariants of them defined in a similar way.Comment: New results. A perfected version will appear in Compositio Mathematic

Reading to adults: Storytime is not just for children anymore

This program will focus on how to make poetry readings, readings from literary works both classic and contemporary, as well as from myths and folklore to adults and make it part of an overall program tied into major cultural holidays such as Halloween, Christmas, Valentine\u27s Day, summer reading programs; as well as stand alone programs, example reading from Edgar Allan Poe as part of a Halloween Program

The case of a southern European glacier disappearing under recent warming that survived Roman and Medieval warm periods

Mountain glaciers have generally experienced an accelerated retreat over the last three decades as a rapid response to current global warming. However, the response to previous warm periods in the Holocene is not well-described for glaciers of the of southern Europe mountain ranges, such as the Pyrenees. The situation during the Medieval Climate Anomaly (900-1300 CE) is particularly relevant since it is not certain whether the glaciers just experienced significant ice loss or whether they actually disappeared. We present here the first chronological study of a glacier located in the Central Pyrenees (N Spain), the Monte Perdido Glacier (MPG), carried out by ifferent radiochronological techniques and their comparison with geochemical proxies with neighboring paleoclimate records. The result of the chronological model proves that the glacier endured during the Roman Period and the Medieval Climate Anomaly. The lack of ice from last 600 years indicates that the ice formed during the Little Ice Age has melted away. The analyses of the content of several metals of anthropogenic origin, such as Zn, Se, Cd, Hg, Pb, appear in low amounts in MPG ice, which further supports our age model in which the record from the industrial period is lost. This study confirms the exceptional warming of the last decades in the context of last two millennia. We demonstrate that we are facing an unprecedented retreat of the Pyrenean glaciers which survival is compromised beyond a few decades.info:eu-repo/grantAgreement/MCIN/CGL2015-68993-R info:eu-repo/grantAgreement/MCIN/CGL2015-69160-R info:eu-repo/grantAgreement/MCIN/CTM2017-84441-R info:eu-repo/grantAgreement/MCIN/FJCI-2017-34235063753 info:eu-repo/grantAgreement/MCIN/CGL2015-72167-EXP info:eu-repo/grantAgreement/MCIN/CTM2017-84441-R info:eu-repo/grantAgreement/MINECO/MDM-2017-071

Influence of the Coulomb potential on above-threshold ionization: a quantum-orbit analysis beyond the strong-field approximation

We perform a detailed analysis of how the interplay between the residual binding potential and a strong laser field influences above-threshold ionization (ATI), employing a semi-analytical, Coulomb-corrected strong-field approximation (SFA) in which the Coulomb potential is incorporated in the electron propagation in the continuum. We find that the Coulomb interaction lifts the degeneracy of some SFA trajectories, and we identify a set of orbits which, for high enough photoelectron energies, may be associated with rescattering. Furthermore, by performing a direct comparison with the standard SFA, we show that several features in the ATI spectra can be traced back to the influence of the Coulomb potential on different electron trajectories. These features include a decrease in the contrast, a shift towards lower energies in the interference substructure, and an overall increase in the photoelectron yield. All features encountered exhibit a very good agreement with the \emph{ab initio} solution of the time-dependent Schr\"odinger equation.Comment: 12 pages, 10 figure

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

The quantum brachistochrone problem for non-Hermitian Hamiltonians

Recently Bender, Brody, Jones and Meister found that in the quantum brachistochrone problem the passage time needed for the evolution of certain initial states into specified final states can be made arbitrarily small, when the time-evolution operator is taken to be non-Hermitian but PT-symmetric. Here we demonstrate that such phenomena can also be obtained for non-Hermitian Hamiltonians for which PT-symmetry is completely broken, i.e. dissipative systems. We observe that the effect of a tunable passage time can be achieved by projecting between orthogonal eigenstates by means of a time-evolution operator associated with a non-Hermitian Hamiltonian. It is not essential that this Hamiltonian is PT-symmetric