Analytical approximations for the higher energy structure in strong field ionization with inhomogeneous electric fields

Recently, the emergence of a higher energy structure (HES) due to a spatial inhomogeneity in the laser electric field, as is typically found close to a nano tip, was reported in Phys.~Rev. Letter {\bf 119}, 053204 (2017). For practical applications, such as the characterization of near-fields or the creation of localized sources of monoenergetic electron beams with tunable energies, further insight into the nature of this higher energy structure is needed. Here, we give a closed form analytical approximation to describe the movement of the electron in the inhomogeneous electric field. In particular, we derive a simple scaling law for the location of the HES peak and give a scheme to analytically tune the width of the peak, both of which will prove useful in optimizing the nanostructure size or geometry for creating the HES in experimental settings

Massless particles, electromagnetism, and Rieffel induction

The connection between space-time covariant representations (obtained by inducing from the Lorentz group) and irreducible unitary representations (induced from Wigner's little group) of the Poincar\'{e} group is re-examined in the massless case. In the situation relevant to physics, it is found that these are related by Marsden-Weinstein reduction with respect to a gauge group. An analogous phenomenon is observed for classical massless relativistic particles. This symplectic reduction procedure can be (`second') quantized using a generalization of the Rieffel induction technique in operator algebra theory, which is carried through in detail for electro- magnetism. Starting from the so-called Fermi representation of the field algebra generated by the free abelian gauge field, we construct a new (`rigged') sesquilinear form on the representation space, which is positive semi-definite, and given in terms of a Gaussian weak distribution (promeasure) on the gauge group (taken to be a Hilbert Lie group). This eventually constructs the algebra of observables of quantum electro- magnetism (directly in its vacuum representation) as a representation of the so-called algebra of weak observables induced by the trivial representation of the gauge group.Comment: LaTeX, 52 page

Intensity dependence of Rydberg states

We investigate numerically and analytically the intensity dependence of the fraction of electrons that end up in a Rydberg state after strong-field ionization with linearly polarized light. We find that including the intensity dependent distribution of ionization times and non-adiabatic effects leads to a better understanding of experimental results. Furthermore, we observe using Classical Trajectory Monte Carlo simulations that the intensity dependence of the Rydberg yield changes with wavelength and that the previously observed power-law dependence breaks down at longer wavelengths. Our work suggests that Rydberg yield measurements can be used as an independent test for non-adiabaticity in strong field ionization

The effect of electron-electron correlation on the attoclock experiment

We investigate multi-electron effects in strong-field ionization of Helium using a semi-classical model that, unlike other commonly used theoretical approaches, takes into account electron-electron correlation. Our approach has an additional advantage of allowing to selectively switch off different contributions from the parent ion (such as the remaining electron or the nuclear charge) and thereby investigate in detail how the final electron angle in the attoclock experiment is influenced by these contributions. We find that the bound electron exerts a significant effect on the final electron momenta distribution that can, however, be accounted for by an appropriately selected mean field. Our results show excellent agreement with other widely used theoretical models done within a single active electron approximation

Controlling the quantum number distribution and yield of Rydberg states via the duration of the laser pulse

We show that the distribution of quantum numbers of Rydberg states does not only depend on the field strength and wavelength of the laser which the atom is exposed to, but that it also changes significantly with the duration of the laser pulse. We provide an intuitive explanation for the underlying mechanism and derive a scaling law for the position of the peak in the quantum number distribution on the pulse duration. The new analytic description for the electron's movement in the superposed laser and Coulomb field (applied in the study of quantum numbers) is then used to explain the decrease of the Rydberg yield with longer pulse durations. This description stands in contrast to the concepts that explained the decrease so far and also reveals that approximations which neglect Coulomb effects during propagation are not sufficient in cases such as this.Comment: 8 pages, 8 figure

Helium-rich EHB Stars in Globular Clusters

Recent UV observations of the most massive Galactic globular clusters show a significant population of hot stars below the zero-age HB (``blue hook'' stars), which cannot be explained by canonical stellar evolution. Stars which suffer unusually large mass loss on the red giant branch and thus experience the helium-core flash while descending the white dwarf cooling curve could populate this region. They should show higher temperatures than the hottest canonical HB stars and their atmospheres should be helium-rich and probably C/N-rich. We have obtained spectra of blue hook stars in omega Cen and NGC 2808 to test this possibility. Our analysis shows that the blue hook stars in these clusters reach effective temperatures well beyond the hot end of the canonical EHB and have higher helium abundances than canonical EHB stars. These results support the hypothesis that the blue hook stars arise from stars which ignite helium on the white dwarf cooling curve.Comment: LaTeX, 8 pages, 3 figures, uses Kluwer style files (included), to appear in "Extreme Horizontal Branch Stars and Related Objects", Astrophysics and Space Science, Kluwer Academic Publishers, proceedings of the meeting held in Keele, UK, June 16-20, 200

Parameter Uncertainty in Exponential Family Tail Estimation

Actuaries are often faced with the task of estimating tails of loss distributions from just a few observations. Thus estimates of tail probabilities (reinsurance prices) and percentiles (solvency capital requirements) are typically subject to substantial parameter uncertainty. We study the bias and MSE of estimators of tail probabilities and percentiles, with focus on 1-parameter exponential families. Using asymptotic arguments it is shown that tail estimates are subject to significant positive bias. Moreover, the use of bootstrap predictive distributions, which has been proposed in the actuarial literature as a way of addressing parameter uncertainty, is seen to double the estimation bias. A bias corrected estimator is thus proposed. It is then shown that the MSE of the MLE, the parametric bootstrap and the bias corrected estimators only differ in terms of order O(n −2), which provides decision-makers with some flexibility as to which estimator to use. The accuracy of asymptotic methods, even for small samples, is demonstrated exactly for the exponential and related distributions, while other 1-parameter distributions are considered in a simulation study. We argue that the presence of positive bias may be desirable in solvency capital calculations, though not necessarily in pricing problems