Observation of Three-dimensional Long-range Order in Smaller Ion Coulomb Crystals in an rf Trap

Three-dimensional long-range ordered structures in smaller and near-spherically symmetric Coulomb crystals of ^{40}Ca^+ ions confined in a linear rf Paul trap have been observed when the number of ions exceeds ~1000 ions. This result is unexpected from ground state molecular dynamics (MD) simulations, but found to be in agreement with MD simulations of metastable ion configurations. Previously, three-dimensional long-range ordered structures have only been reported in Penning traps in systems of ~50,000 ions or more.Comment: 5 pages; 4 figures; to appear in Phys. Rev. Lett.; changed content

Serre's "formule de masse" in prime degree

For a local field F with finite residue field of characteristic p, we describe completely the structure of the filtered F_p[G]-module K^*/K^*p in characteristic 0 and $K^+/\wp(K^+) in characteristic p, where K=F(\root{p-1}\of F^*) and G=\Gal(K|F). As an application, we give an elementary proof of Serre's mass formula in degree p. We also determine the compositum C of all degree p separable extensions with solvable galoisian closure over an arbitrary base field, and show that C is K(\root p\of K^*) or K(\wp^{-1}(K)) respectively, in the case of the local field F. Our method allows us to compute the contribution of each character G\to\F_p^* to the degree p mass formula, and, for any given group \Gamma, the contribution of those degree p separable extensions of F whose galoisian closure has group \Gamma.Comment: 36 pages; most of the new material has been moved to the new Section

Unitary relations in time-dependent harmonic oscillators

For a harmonic oscillator with time-dependent (positive) mass and frequency, an unitary operator is shown to transform the quantum states of the system to those of a harmonic oscillator system of unit mass and time-dependent frequency, as well as operators. For a driven harmonic oscillator, it is also shown that, there are unitary transformations which give the driven system from the system of same mass and frequency without driving force. The transformation for a driven oscillator depends on the solution of classical equation of motion of the driven system. These transformations, thus, give a simple way of finding exact wave functions of a driven harmonic oscillator system, provided the quantum states of the corresponding system of unit mass are given.Comment: Submitted to J. Phys.

Language contact: bridging the gap between individual interactions and areal patterns

Contact linguistics is the overarching term for a highly diversified field with branches that connect to such widely divergent areas as historical linguistics, typology, sociolinguistics, psycholinguistics, and grammatical theory. Because of this diversification, there is a risk of fragmentation and lack of interaction between the different subbranches of contact linguistics. Nevertheless, the different approaches share the general goal of accounting for the results of interacting linguistic systems. This common goal opens up possibilities for active communication, cooperation, and coordination between the different branches of contact linguistics. This book, therefore, explores the extent to which contact linguistics can be viewed as a coherent field, and whether the advances achieved in a particular subfield can be translated to others. In this way our aim is to encourage a boundary-free discussion between different types of specialists of contact linguistics, and to stimulate cross-pollination between them.Horizon 2020(H2020)818854Descriptive and Comparative Linguistic

Collisional Damping of Nuclear Collective Vibrations in a Non-Markovian Transport Approach

A detailed derivation of the collisional widths of collective vibrations is presented in both quantal and semi-classical frameworks by considering the linearized limits of the extended TDHF and the BUU model with a non-Markovian binary collision term. Damping widths of giant dipole and giant quadrupole excitations are calculated by employing an effective Skyrme force, and the results are compared with GDR measurements in Lead and Tin nuclei at finite temperature.Comment: 23 pages, 6 Figure

Inverting Time-Dependent Harmonic Oscillator Potential by a Unitary Transformation and a New Class of Exactly Solvable Oscillators

A time-dependent unitary (canonical) transformation is found which maps the Hamiltonian for a harmonic oscillator with time-dependent real mass and real frequency to that of a generalized harmonic oscillator with time-dependent real mass and imaginary frequency. The latter may be reduced to an ordinary harmonic oscillator by means of another unitary (canonical) transformation. A simple analysis of the resulting system leads to the identification of a previously unknown class of exactly solvable time-dependent oscillators. Furthermore, it is shown how one can apply these results to establish a canonical equivalence between some real and imaginary frequency oscillators. In particular it is shown that a harmonic oscillator whose frequency is constant and whose mass grows linearly in time is canonically equivalent with an oscillator whose frequency changes from being real to imaginary and vice versa repeatedly.Comment: 7 pages, 1 figure include

Continuum corrections to the level density and its dependence on excitation energy, n-p asymmetry, and deformation

In the independent-particle model, the nuclear level density is determined from the neutron and proton single-particle level densities. The single-particle level density for the positive-energy continuum levels is important at high excitation energies for stable nuclei and at all excitation energies for nuclei near the drip lines. This single-particle level density is subdivided into compound-nucleus and gas components. Two methods were considered for this subdivision. First in the subtraction method, the single-particle level density is determined from the scattering phase shifts. In the Gamov method, only the narrow Gamov states or resonances are included. The level densities calculated with these two methods are similar, both can be approximated by the backshifted Fermi-gas expression with level-density parameters that are dependent on A, but with very little dependence on the neutron or proton richness of the nucleus. However, a small decrease in the level-density parameter was predicted for some nuclei very close to the drip lines. The largest difference between the calculations using the two methods was the deformation dependence on the level density. The Gamov method predicts a very strong peaking of the level density at sphericity for high excitation energies. This leads to a suppression of deformed configurations and, consequently, the fission rate predicted by the statistical model is reduced in the Gamov method.Comment: 18 pages 24 figure

Canonical quantization of so-called non-Lagrangian systems

We present an approach to the canonical quantization of systems with equations of motion that are historically called non-Lagrangian equations. Our viewpoint of this problem is the following: despite the fact that a set of differential equations cannot be directly identified with a set of Euler-Lagrange equations, one can reformulate such a set in an equivalent first-order form which can always be treated as the Euler-Lagrange equations of a certain action. We construct such an action explicitly. It turns out that in the general case the hamiltonization and canonical quantization of such an action are non-trivial problems, since the theory involves time-dependent constraints. We adopt the general approach of hamiltonization and canonical quantization for such theories (Gitman, Tyutin, 1990) to the case under consideration. There exists an ambiguity (not reduced to a total time derivative) in associating a Lagrange function with a given set of equations. We present a complete description of this ambiguity. The proposed scheme is applied to the quantization of a general quadratic theory. In addition, we consider the quantization of a damped oscillator and of a radiating point-like charge.Comment: 13 page

Phases in Strongly Coupled Electronic Bilayer Liquids

The strongly correlated liquid state of a bilayer of charged particles has been studied via the HNC calculation of the two-body functions. We report the first time emergence of a series of structural phases, identified through the behavior of the two-body functions.Comment: 5 pages, RevTEX 3.0, 4 ps figures; Submitted to Phys. Rev. Let

Diagnostic criterion for crystallized beams

Small ion crystals in a Paul trap are stable even in the absence of laser cooling. Based on this theoretically and experimentally well-established fact we propose the following diagnostic criterion for establishing the presence of a crystallized beam: Absence of heating following the shut-down of all cooling devices. The validity of the criterion is checked with the help of detailed numerical simulations.Comment: REVTeX, 11 pages, 4 figures; submitted to PR