Self-adjoint symmetry operators connected with the magnetic Heisenberg ring

We consider symmetry operators a from the group ring C[S_N] which act on the Hilbert space H of the 1D spin-1/2 Heisenberg magnetic ring with N sites. We investigate such symmetry operators a which are self-adjoint (in a sence defined in the paper) and which yield consequently observables of the Heisenberg model. We prove the following results: (i) One can construct a self-adjoint idempotent symmetry operator from every irreducible character of every subgroup of S_N. This leads to a big manifold of observables. In particular every commutation symmetry yields such an idempotent. (ii) The set of all generating idempotents of a minimal right ideal R of C[S_N] contains one and only one idempotent which ist self-adjoint. (iii) Every self-adjoint idempotent e can be decomposed into primitive idempotents e = f_1 + ... + f_k which are also self-adjoint and pairwise orthogonal. We give a computer algorithm for the calculation of such decompositions. Furthermore we present 3 additional algorithms which are helpful for the calculation of self-adjoint operators by means of discrete Fourier transforms of S_N. In our investigations we use computer calculations by means of our Mathematica packages PERMS and HRing.Comment: 13 page

Reexamination of the nonperturbative renormalization-group approach to the Kosterlitz-Thouless transition

We reexamine the two-dimensional linear O(2) model ($\varphi^4$ theory) in the framework of the nonperturbative renormalization-group. From the flow equations obtained in the derivative expansion to second order and with optimization of the infrared regulator, we find a transition between a high-temperature (disordered) phase and a low-temperature phase displaying a line of fixed points and algebraic order. We obtain a picture in agreement with the standard theory of the Kosterlitz-Thouless (KT) transition and reproduce the universal features of the transition. In particular, we find the anomalous dimension \eta(\Tkt)\simeq 0.24 and the stiffness jump \rho_s(\Tkt^-)\simeq 0.64 at the transition temperature \Tkt, in very good agreement with the exact results \eta(\Tkt)=1/4 and \rho_s(\Tkt^-)=2/\pi, as well as an essential singularity of the correlation length in the high-temperature phase as T\to \Tkt.Comment: v2) Final version as published (with revised title): 10 pages, 10 figure

On local linearization of control systems

We consider the problem of topological linearization of smooth (C infinity or real analytic) control systems, i.e. of their local equivalence to a linear controllable system via point-wise transformations on the state and the control (static feedback transformations) that are topological but not necessarily differentiable. We prove that local topological linearization implies local smooth linearization, at generic points. At arbitrary points, it implies local conjugation to a linear system via a homeomorphism that induces a smooth diffeomorphism on the state variables, and, except at "strongly" singular points, this homeomorphism can be chosen to be a smooth mapping (the inverse map needs not be smooth). Deciding whether the same is true at "strongly" singular points is tantamount to solve an intriguing open question in differential topology

Proximity of Iron Pnictide Superconductors to a Quantum Tricritical Point

We determine the nature of the magnetic quantum critical point in the doped LaFeAsO using a set of constrained density functional calculations that provide ab initio coefficients for a Landau order parameter analysis. The system turns out to be remarkably close to a quantum tricritical point, where the nature of the phase transition changes from first to second order. We compare with the effective field theory and discuss the experimental consequences.Comment: 4 pages, 4 figure

Fermi surface instabilities at finite Temperature

We present a new method to detect Fermi surface instabilities for interacting systems at finite temperature. We first apply it to a list of cases studied previously, recovering already known results in a very economic way, and obtaining most of the information on the phase diagram analytically. As an example, in the continuum limit we obtain the critical temperature as an implicit function of the magnetic field and the chemical potential $T_c(\mu,h)$. By applying the method to a model proposed to describe reentrant behavior in $Sr_3Ru_2O_7$, we reproduce the phase diagram obtained experimentally and show the presence of a non-Fermi Liquid region at temperatures above the nematic phase.Comment: 10 pages, 10 figure

Drying of a Microdroplet of Water Suspension of Nanoparticles: from Surface Aggregates to Microcrystal

The method of formation of nanoparticle aggregates such as high-coverage spherical shells of microspheres or 3-D micro crystals grown in the geometry unaffected by a substrate is described. In the reported experiment, the evaporation of single levitated water droplet containing 200 nm diameter polystyrene spheres was studied. Successive stages of the drying process were discussed by analyzing the intensity of light elastically scattered by the evaporating droplet. The numerically simulated self-assembly coincides nicely with the observed morphologies resulting from transformation of a droplet of suspension into a solid microcrystal via kinetically driven self-assembly of nanostructures.Comment: 5 pages, 6 figure

Scaling laws near the conformal window of many-flavor QCD

We derive universal scaling laws for physical observables such as the critical temperature, the chiral condensate, and the pion decay constant as a function of the flavor number near the conformal window of many-flavor QCD in the chiral limit. We argue on general grounds that the associated critical exponents are all interrelated and can be determined from the critical exponent of the running gauge coupling at the Caswell-Banks-Zaks infrared fixed point. We illustrate our findings with the aid of nonperturbative functional Renormalization Group (RG) calculations and low-energy QCD models.Comment: 18 pages, 4 figures, references added and discussion expanded (matches JHEP version

Central statistical monitoring in clinical trial management: A scoping review

BACKGROUND: Clinical trials handle a huge amount of data which can be used during the trial to improve the ongoing study conduct. It is suggested by regulators to implement the remote approach to evaluate clinical trials by analysing collected data. Central statistical monitoring helps to achieve that by employing quantitative methods, the results of which are a basis for decision-making on quality issues. METHODS: This article presents a scoping review which is based on a systematic and iterative approach to identify and synthesise literature on central statistical monitoring methodology. In particular, we investigated the decision-making processes (with emphasis on quality issues) of central statistical monitoring methodology and its place in the clinical trial workflow. We reviewed papers published over the last 10 years in two databases (Scopus and Web of Science) with a focus on data mining algorithms of central statistical monitoring and its benefit to the quality of trials. RESULTS: As a result, 24 scientific papers were selected for this review, and they consider central statistical monitoring at two levels. First, the perspective of the central statistical monitoring process and its location in the study conduct in terms of quality issues. Second, central statistical monitoring methods categorised into practices applied in the industry, and innovative methods in development. The established methods are discussed through the prism of categories of their usage. In turn, the innovations refer to either research on new methods or extensions to existing ones. DISCUSSION: Our review suggests directions for further research into central statistical monitoring methodology - including increased application of multivariate analysis and using advanced distance metrics - and guidance on how central statistical monitoring operates in response to regulators' requirements