Noether's theorem and gauge transformations. Application to the bosonic string and CP(2,n-1) model

New results on the theory of constrained systems are applied to characterize the generators of Noethers symmetry transformations. As a byproduct, an algorithm to construct gauge transformations in Hamiltonian formalism is derived. This is illustrated with two relevant examples

Dynamical Hartree-Fock-Bogoliubov Theory of Vortices in Bose-Einstein Condensates at Finite Temperature

We present a method utilizing the continuity equation for the condensate density to make predictions of the precessional frequency of single off-axis vortices and of vortex arrays in Bose-Einstein condensates at finite temperature. We also present an orthogonalized Hartree-Fock-Bogoliubov (HFB) formalism. We solve the continuity equation for the condensate density self-consistently with the orthogonalized HFB equations, and find stationary solutions in the frame rotating at this frequency. As an example of the utility of this formalism we obtain time-independent solutions for quasi-two-dimensional rotating systems in the co-rotating frame. We compare these results with time-dependent predictions where we simulate stirring of the condensate.Comment: 13 pages, 11 figures, 1 tabl

An introduction to the spectrum, symmetries, and dynamics of spin-1/2 Heisenberg chains

Quantum spin chains are prototype quantum many-body systems. They are employed in the description of various complex physical phenomena. The goal of this paper is to provide an introduction to the subject by focusing on the time evolution of a Heisenberg spin-1/2 chain and interpreting the results based on the analysis of the eigenvalues, eigenstates, and symmetries of the system. We make available online all computer codes used to obtain our data.Comment: 8 pages, 3 figure

Lorenz integrable system moves \`a la Poinsot

A transformation is derived which takes Lorenz integrable system into the well-known Euler equations of a free-torque rigid body with a fixed point, i.e. the famous motion \`a la Poinsot. The proof is based on Lie group analysis applied to two third order ordinary differential equations admitting the same two-dimensional Lie symmetry algebra. Lie's classification of two-dimensional symmetry algebra in the plane is used. If the same transformation is applied to Lorenz system with any value of parameters, then one obtains Euler equations of a rigid body with a fixed point subjected to a torsion depending on time and angular velocity. The numerical solution of this system yields a three-dimensional picture which looks like a "tornado" whose cross-section has a butterfly-shape. Thus, Lorenz's {\em butterfly} has been transformed into a {\em tornado}.Comment: 14 pages, 6 figure

Symmetries of the Energy-Momentum Tensor: Some Basic Facts

It has been pointed by Hall et al. [1] that matter collinations can be defined by using three different methods. But there arises the question of whether one studies matter collineations by using the ${\cal L}_\xi T_{ab}=0$, or ${\cal L}_\xi T^{ab}=0$ or ${\cal L}_\xi T_a^b=0$. These alternative conditions are, of course, not generally equivalent. This problem has been explored by applying these three definitions to general static spherically symmetric spacetimes. We compare the results with each definition.Comment: 17 pages, accepted for publication in "Communications in Theoretical Physics

Nonlinear physics of the ionosphere and LOIS/LOFAR

The ionosphere is the only large-scale plasma laboratory without walls that we have direct access to. From results obtained in systematic, repeatable experiments in this natural laboratory, where we can vary the stimulus and observe its response in a controlled, repeatable manner, we can draw conclusions on similar physical processes occurring naturally in the Earth's plasma environment as well as in parts of the plasma universe that are not easily accessible to direct probing. Of particular interest is electromagnetic turbulence excited in the ionosphere by beams of particles (photons, electrons) and its manifestation in terms of secondary radiation (electrostatic and electromagnetic waves), structure formation (solitons, cavitons, alfveons, striations), and the associated exchange of energy, linear momentum, and angular momentum. We present a new diagnostic technique, based on vector radio allowing the utilization of EM angular momentum (vorticity), to study plasma turbulence remotely.Comment: Six pages, two figures. To appear in Plasma Physics and Controlled Fusio

On the classical central charge

In the canonical formulation of a classical field theory, symmetry properties are encoded in the Poisson bracket algebra, which may have a central term. Starting from this well understood canonical structure, we derive the related Lagrangian form of the central term.Comment: 23 pages, RevTeX, no figures; introduction improved, a few references adde

Confidence Intervals for the Area Under the Receiver Operating Characteristic Curve in the Presence of Ignorable Missing Data

Receiver operating characteristic curves are widely used as a measure of accuracy of diagnostic tests and can be summarised using the area under the receiver operating characteristic curve (AUC). Often, it is useful to construct a confidence interval for the AUC; however, because there are a number of different proposed methods to measure variance of the AUC, there are thus many different resulting methods for constructing these intervals. In this article, we compare different methods of constructing Wald‐type confidence interval in the presence of missing data where the missingness mechanism is ignorable. We find that constructing confidence intervals using multiple imputation based on logistic regression gives the most robust coverage probability and the choice of confidence interval method is less important. However, when missingness rate is less severe (e.g. less than 70%), we recommend using Newcombe\u27s Wald method for constructing confidence intervals along with multiple imputation using predictive mean matching

Lie point symmetries and first integrals: the Kowalevsky top

We show how the Lie group analysis method can be used in order to obtain first integrals of any system of ordinary differential equations. The method of reduction/increase of order developed by Nucci (J. Math. Phys. 37, 1772-1775 (1996)) is essential. Noether's theorem is neither necessary nor considered. The most striking example we present is the relationship between Lie group analysis and the famous first integral of the Kowalevski top.Comment: 23 page

On the generalized Davenport constant and the Noether number

Known results on the generalized Davenport constant related to zero-sum sequences over a finite abelian group are extended to the generalized Noether number related to the rings of polynomial invariants of an arbitrary finite group. An improved general upper bound is given on the degrees of polynomial invariants of a non-cyclic finite group which cut out the zero vector.Comment: 14 page