Pointless Hyperelliptic Curves

In this paper we consider the question of whether there exists a hyperelliptic curve of genus g which is defined over but has no rational points over for various pairs . As an example of such a result, we show that if p is a prime such that is also prime then there will be pointless hyperelliptic curves over of every genus

Cyclic Critical Groups of Graphs

In this note, we describe a construction that leads to families of graphs whose critical groups are cyclic. For some of these families we are able to give a formula for the number of spanning trees of the graph, which then determines the group exactly

Pathways to double ionization of atoms in strong fields

We discuss the final stages of double ionization of atoms in a strong linearly polarized laser field within a classical model. We propose that all trajectories leading to non-sequential double ionization pass close to a saddle in phase space which we identify and characterize. The saddle lies in a two degree of freedom subspace of symmetrically escaping electrons. The distribution of longitudinal momenta of ions as calculated within the subspace shows the double hump structure observed in experiments. Including a symmetric bending mode of the electrons allows us to reproduce the transverse ion momenta. We discuss also a path to sequential ionization and show that it does not lead to the observed momentum distributions.Comment: 10 pages, 10 figures; fig.6 and 7 exchanged in the final version accepted for publication in Phys. Rev.

On Retardation Effects in Space Charge Calculations Of High Current Electron Beams

Laser-plasma accelerators are expected to deliver electron bunches with high space charge fields. Several recent publications have addressed the impact of space charge effects on such bunches after the extraction into vacuum. Artifacts due to the approximation of retardation effects are addressed, which are typically either neglected or approximated. We discuss a much more appropriate calculation for the case of laser wakefield acceleration with negligible retardation artifacts due to the calculation performed in the mean rest frame. This presented calculation approach also aims at a validation of other simulation approaches

Non-sequential triple ionization in strong fields

We consider the final stage of triple ionization of atoms in a strong linearly polarized laser field. We propose that for intensities below the saturation value for triple ionization the process is dominated by the simultaneous escape of three electrons from a highly excited intermediate complex. We identify within a classical model two pathways to triple ionization, one with a triangular configuration of electrons and one with a more linear one. Both are saddles in phase space. A stability analysis indicates that the triangular configuration has the larger cross sections and should be the dominant one. Trajectory simulations within the dominant symmetry subspace reproduce the experimentally observed distribution of ion momenta parallel to the polarization axis.Comment: 9 pages, 8 figures, accepted for publication in Phys. Rev.

Shear viscosity of a highly excited string and the black hole membrane paradigm

Black hole membrane paradigm states that a certain viscous membrane seems to be sitting on a stretched horizon of a black hole from the viewpoint of a distant observer. We show that the shear viscosity of the fictitious membrane can be reproduced by a highly excited string covering the stretched horizon except for a numerical coefficient.Comment: 22 pages, no figure, minor correction

Quantum bit detector

We propose and analyze an experimental scheme of quantum nondemolition detection of monophotonic and vacuum states in a superconductive toroidal cavity by means of Rydberg atoms.Comment: 4 pages, 3 figure

Non-dipole recollision-gated double ionization and observable effects

Using a three-dimensional semiclassical model, we study double ionization for strongly-driven He fully accounting for magnetic field effects. For linearly and slightly elliptically polarized laser fields, we show that recollisions and the magnetic field combined act as a gate. This gate favors more transverse - with respect to the electric field - initial momenta of the tunneling electron that are opposite to the propagation direction of the laser field. In the absence of non-dipole effects, the transverse initial momentum is symmetric with respect to zero. We find that this asymmetry in the transverse initial momentum gives rise to an asymmetry in a double ionization observable. Finally, we show that this asymmetry in the transverse initial momentum of the tunneling electron accounts for a recently-reported unexpectedly large average sum of the electron momenta parallel to the propagation direction of the laser field.Comment: Amended the focus of the paper and discussion. 9 pages, 7 figure

Non-thermalization in trapped atomic ion spin chains

Linear arrays of trapped and laser cooled atomic ions are a versatile platform for studying emergent phenomena in strongly-interacting many-body systems. Effective spins are encoded in long-lived electronic levels of each ion and made to interact through laser mediated optical dipole forces. The advantages of experiments with cold trapped ions, including high spatiotemporal resolution, decoupling from the external environment, and control over the system Hamiltonian, are used to measure quantum effects not always accessible in natural condensed matter samples. In this review we highlight recent work using trapped ions to explore a variety of non-ergodic phenomena in long-range interacting spin-models which are heralded by memory of out-of-equilibrium initial conditions. We observe long-lived memory in static magnetizations for quenched many-body localization and prethermalization, while memory is preserved in the periodic oscillations of a driven discrete time crystal state.Comment: 14 pages, 5 figures, submitted for edition of Phil. Trans. R. Soc. A on "Breakdown of ergodicity in quantum systems