On the spacing distribution of the Riemann zeros: corrections to the asymptotic result

It has been conjectured that the statistical properties of zeros of the Riemann zeta function near z = 1/2 + \ui E tend, as $E \to \infty$, to the distribution of eigenvalues of large random matrices from the Unitary Ensemble. At finite $E$ numerical results show that the nearest-neighbour spacing distribution presents deviations with respect to the conjectured asymptotic form. We give here arguments indicating that to leading order these deviations are the same as those of unitary random matrices of finite dimension $N_{\rm eff}=\log(E/2\pi)/\sqrt{12 \Lambda}$, where $\Lambda=1.57314 ...$ is a well defined constant.Comment: 9 pages, 3 figure

Multiplying unitary random matrices - universality and spectral properties

In this paper we calculate, in the large N limit, the eigenvalue density of an infinite product of random unitary matrices, each of them generated by a random hermitian matrix. This is equivalent to solving unitary diffusion generated by a hamiltonian random in time. We find that the result is universal and depends only on the second moment of the generator of the stochastic evolution. We find indications of critical behavior (eigenvalue spacing scaling like $1/N^{3/4}$) close to $\theta=\pi$ for a specific critical evolution time $t_c$.Comment: 12 pages, 2 figure

Quantum gray solitons in confining potentials

We define and study hole-like excitations (the Lieb II mode) in a weakly interacting Bose liquid subject to external confinement. These excitations are obtained by semiclassical quantization of gray solitons propagating on top of a Thomas-Fermi background. Radiation of phonons by an accelerated gray soliton leads to a finite life-time for the trapped Lieb II mode. It is shown that, for a large number of trapped atoms, most of the Lieb II levels can be experimentally resolved.Comment: 5 pages, 2 figure

Random polynomials, random matrices, and LL-functions

We show that the Circular Orthogonal Ensemble of random matrices arises naturally from a family of random polynomials. This sheds light on the appearance of random matrix statistics in the zeros of the Riemann zeta-function.Comment: Added background material. Final version. To appear in Nonlinearit

The lowest eigenvalue of Jacobi random matrix ensembles and Painlev\'e VI

We present two complementary methods, each applicable in a different range, to evaluate the distribution of the lowest eigenvalue of random matrices in a Jacobi ensemble. The first method solves an associated Painleve VI nonlinear differential equation numerically, with suitable initial conditions that we determine. The second method proceeds via constructing the power-series expansion of the Painleve VI function. Our results are applied in a forthcoming paper in which we model the distribution of the first zero above the central point of elliptic curve L-function families of finite conductor and of conjecturally orthogonal symmetry.Comment: 30 pages, 2 figure

Understanding Dark Current-Voltage Characteristics in Metal-Halide Perovskite Single Crystals

Hybrid halide perovskites have great potential for application in optoelectronic devices. However, an understanding of some basic properties, such as charge-carrier transport, remains inconclusive, mainly due to the mixed ionic and electronic nature of these materials. Here, we perform temperature-dependent pulsed-voltage space-charge-limited current measurements to provide a detailed look into the electronic properties of methylammonium lead tribromide (MAPbBr(3)) and methylammonium lead triiodide (MAPbI(3)) single crystals. We show that the background carrier density in these crystals is orders of magnitude higher than that expected from thermally excited carriers from the valence band. We highlight the complexity of the system via a combination of experiments and drift-diffusion simulations and show that different factors, such as thermal injection from the electrodes, temperature-dependent mobility, and trap and ion density, influence the free-carrier concentration. We experimentally determine effective activation energies for conductivity of (349 +/- 10) meV for MAPbBr3 and (193 +/- 12) meV for MAPbI(3), which includes the sum of all of these factors. We point out that fitting the dark current density-voltage curve with a drift-diffusion model allows for the extraction of intrinsic parameters, such as mobility and trap and ion density. From simulations, we determine a charge-carrier mobility of 12.9 cm(2)/Vs, a trap density of 1.52 x 10(13) cm(-3), and an ion density of 3.19 x 10(12) cm(-3) for MAPbBr(3) single crystals. Insights into charge-carrier transport in metal-halide perovskite single crystals will be beneficial for device optimization in various optoelectronic applications

Revealing Charge Carrier Mobility and Defect Densities in Metal Halide Perovskites via Space-Charge-Limited Current Measurements

Space-charge-limited current (SCLC) measurements have been widely used to study the charge carrier mobility and trap density in semiconductors. However, their applicability to metal halide perovskites is not straightforward, due to the mixed ionic and electronic nature of these materials. Here, we discuss the pitfalls of SCLC for perovskite semiconductors, and especially the effect of mobile ions. We show, using drift-diffusion (DD) simulations, that the ions strongly affect the measurement and that the usual analysis and interpretation of SCLC need to be refined. We highlight that the trap density and mobility cannot be directly quantified using classical methods. We discuss the advantages of pulsed SCLC for obtaining reliable data with minimal influence of the ionic motion. We then show that fitting the pulsed SCLC with DD modeling is a reliable method for extracting mobility, trap, and ion densities simultaneously. As a proof of concept, we obtain a trap density of 1.3 × 1013 cm-3, an ion density of 1.1 × 1013 cm-3, and a mobility of 13 cm2 V-1 s-1 for a MAPbBr3 single crystal

Painleve IV and degenerate Gaussian Unitary Ensembles

We consider those Gaussian Unitary Ensembles where the eigenvalues have prescribed multiplicities, and obtain joint probability density for the eigenvalues. In the simplest case where there is only one multiple eigenvalue t, this leads to orthogonal polynomials with the Hermite weight perturbed by a factor that has a multiple zero at t. We show through a pair of ladder operators, that the diagonal recurrence coefficients satisfy a particular Painleve IV equation for any real multiplicity. If the multiplicity is even they are expressed in terms of the generalized Hermite polynomials, with t as the independent variable.Comment: 17 page

Improving wrist imaging through a multicentre educational intervention: The challenge of orthogonal projections

YesIn relation to wrist imaging, the accepted requirement is two orthogonal projections obtained at 90°, each with the wrist in neutral position. However, the literature and anecdotal experience suggests that this principle is not universally applied. Method: This multiphase study was undertaken across eight different hospitals sites. Compliance with standard UK technique was confirmed if there was a change in ulna orientation between the dorsi-palmar (DP) and lateral wrist projections. A baseline evaluation for three days was randomly identified from the preceding three months. An educational intervention was implemented using a poster to demonstrate standard positioning. To measure the impact of the intervention, further evaluation took place at two weeks (early) and three months (late). Results: Across the study phases, only a minority of radiographs demonstrated compliance with the standard technique, with an identical anatomical appearance of the distal ulna across the projections. Initial compliance was 16.8% (n = 40/238), and this improved to 47.8% (n = 77/161) post-intervention, but declined to 32.8% (n = 41/125) within three months. The presence of pathology appeared to influence practice, with a greater proportion of those with an abnormal radiographic examination demonstrating a change in ulna appearances in the baseline cohort (

On the algebraic K-theory of the complex K-theory spectrum

Let p>3 be a prime, let ku be the connective complex K-theory spectrum, and let K(ku) be the algebraic K-theory spectrum of ku. We study the p-primary homotopy type of the spectrum K(ku) by computing its mod (p,v_1) homotopy groups. We show that up to a finite summand, these groups form a finitely generated free module over a polynomial algebra F_p[b], where b is a class of degree 2p+2 defined as a higher Bott element.Comment: Revised and expanded version, 42 pages