Skew-orthogonal polynomials in the complex plane and their Bergman-like kernels

Non-Hermitian random matrices with symplectic symmetry provide examples for Pfaffian point processes in the complex plane. These point processes are characterised by a matrix valued kernel of skew-orthogonal polynomials. We develop their theory in providing an explicit construction of skew-orthogonal polynomials in terms of orthogonal polynomials that satisfy a three-term recurrence relation, for general weight functions in the complex plane. New examples for symplectic ensembles are provided, based on recent developments in orthogonal polynomials on planar domains or curves in the complex plane. Furthermore, Bergman-like kernels of skew-orthogonal Hermite and Laguerre polynomials are derived, from which the conjectured universality of the elliptic symplectic Ginibre ensemble and its chiral partner follow in the limit of strong non-Hermiticity at the origin. A Christoffel perturbation of skew-orthogonal polynomials as it appears in applications to quantum field theory is provided.Comment: 33 pages; v2: uniqueness of odd polynomials clarified, minor correction

Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble

In this article, we compute and compare the statistics of the number of eigenvalues in a centred disc of radius $R$ in all three Ginibre ensembles. We determine the mean and variance as functions of $R$ in the vicinity of the origin, where the real and symplectic ensembles exhibit respectively an additional attraction to or repulsion from the real axis, leading to different results. In the large radius limit, all three ensembles coincide and display a universal bulk behaviour of $O(R^2)$ for the mean, and $O(R)$ for the variance. We present detailed conjectures for the bulk and edge scaling behaviours of the real Ginibre ensemble, having real and complex eigenvalues. For the symplectic ensemble we can go beyond the Gaussian case (corresponding to the Ginibre ensemble) and prove the universality of the full counting statistics both in the bulk and at the edge of the spectrum for rotationally invariant potentials, extending a recent work which considered the mean and the variance. This statistical behaviour coincides with the universality class of the complex Ginibre ensemble, which has been shown to be associated with the ground state of non-interacting fermions in a two-dimensional rotating harmonic trap. All our analytical results and conjectures are corroborated by numerical simulations.Comment: 47 pages, 6 figures; v2 48 pages, 6 figures, references and associated text adde

Structural and magnetic properties of Co-Mn-Sb thin films

Thin Co-Mn-Sb films of different compositions were investigated and utilized as electrodes in alumina based magnetic tunnel junctions with CoFe counter electrode. The preparation conditions were optimized with respect to magnetic and structural properties. The Co-Mn-Sb/Al-O interface was analyzed by X-ray absorption spectroscopy and magnetic circular dichroism with particular focus on the element-specific magnetic moments. Co-Mn-Sb crystallizes in different complex cubic structures depending on its composition. The magnetic moments of Co and Mn are ferromagnetically coupled in all cases. A tunnel magneto resistance ratio of up to 24 % at 13K was found and indicates that Co-Mn-Sb is not a ferromagnetic half-metal. These results are compared to recent works on the structure and predictions of the electronic properties.Comment: 8 pages, 9 figure

Insights into ultrafast demagnetization in pseudo-gap half metals

Interest in femtosecond demagnetization experiments was sparked by Bigot's discovery in 1995. These experiments unveil the elementary mechanisms coupling the electrons' temperature to their spin order. Even though first quantitative models describing ultrafast demagnetization have just been published within the past year, new calculations also suggest alternative mechanisms. Simultaneously, the application of fast demagnetization experiments has been demonstrated to provide key insight into technologically important systems such as high spin polarization metals, and consequently there is broad interest in further understanding the physics of these phenomena. To gain new and relevant insights, we perform ultrafast optical pump-probe experiments to characterize the demagnetization processes of highly spin-polarized magnetic thin films on a femtosecond time scale. Previous studies have suggested shifting the Fermi energy into the center of the gap by tuning the number of electrons and thereby to study its influence on spin-flip processes. Here we show that choosing isoelectronic Heusler compounds (Co2MnSi, Co2MnGe and Co2FeAl) allows us to vary the degree of spin polarization between 60% and 86%. We explain this behavior by considering the robustness of the gap against structural disorder. Moreover, we observe that Co-Fe-based pseudo gap materials, such as partially ordered Co-Fe-Ge alloys and also the well-known Co-Fe-B alloys, can reach similar values of the spin polarization. By using the unique features of these metals we vary the number of possible spin-flip channels, which allows us to pinpoint and control the half metals electronic structure and its influence onto the elementary mechanisms of ultrafast demagnetization.Comment: 17 pages, 4 figures, plus Supplementary Informatio

Seebeck Effect in Magnetic Tunnel Junctions

Creating temperature gradients in magnetic nanostructures has resulted in a new research direction, i.e., the combination of magneto- and thermoelectric effects. Here, we demonstrate the observation of one important effect of this class: the magneto-Seebeck effect. It is observed when a magnetic configuration changes the charge based Seebeck coefficient. In particular, the Seebeck coefficient changes during the transition from a parallel to an antiparallel magnetic configuration in a tunnel junction. In that respect, it is the analog to the tunneling magnetoresistance. The Seebeck coefficients in parallel and antiparallel configuration are in the order of the voltages known from the charge-Seebeck effect. The size and sign of the effect can be controlled by the composition of the electrodes' atomic layers adjacent to the barrier and the temperature. Experimentally, we realized 8.8 % magneto-Seebeck effect, which results from a voltage change of about -8.7 {\mu}V/K from the antiparallel to the parallel direction close to the predicted value of -12.1 {\mu}V/K.Comment: 16 pages, 7 figures, 2 table

Congruence between NOTCH3 mutations and GOM in 131 CADASIL patients

Cerebral autosomal dominant arteriopathy with subcortical infarcts and leukoencephalopathy (CADASIL) is the most common hereditary subcortical vascular dementia. It is caused by mutations in NOTCH3 gene, which encodes a large transmembrane receptor Notch3. The key pathological finding is the accumulation of granular osmiophilic material (GOM), which contains extracellular domains of Notch3, on degenerating vascular smooth muscle cells (VSMCs). GOM has been considered specifically diagnostic for CADASIL, but the reports on the sensitivity of detecting GOM in patients’ skin biopsy have been contradictory. To solve this contradiction, we performed a retrospective investigation of 131 Finnish, Swedish and French CADASIL patients, who had been adequately examined for both NOTCH3 mutation and presence of GOM. The patients were examined according to the diagnostic practice in each country. NOTCH3 mutations were assessed by restriction enzyme analysis of specific mutations or by sequence analysis. Presence of GOM was examined by electron microscopy (EM) in skin biopsies. Biopsies of 26 mutation-negative relatives from CADASIL families served as the controls. GOM was detected in all 131 mutation positive patients. Altogether our patients had 34 different pathogenic mutations which included three novel point mutations (p.Cys67Ser, p.Cys251Tyr and p.Tyr1069Cys) and a novel duplication (p.Glu434_Leu436dup). The detection of GOM by EM in skin biopsies was a highly reliable diagnostic method: in this cohort the congruence between NOTCH3 mutations and presence of GOM was 100%. However, due to the retrospective nature of this study, exact figure for sensitivity cannot be determined, but it would require a prospective study to exclude possible selection bias. The identification of a pathogenic NOTCH3 mutation is an indisputable evidence for CADASIL, but demonstration of GOM provides a cost-effective guide for estimating how far one should proceed with the extensive search for a new or an uncommon mutations among the presently known over 170 different NOTCH3 gene defects. The diagnostic skin biopsy should include the border zone between deep dermis and upper subcutis, where small arterial vessels of correct size are located. Detection of GOM requires technically adequate biopsies and distinction of true GOM from fallacious deposits. If GOM is not found in the first vessel or biopsy, other vessels or additional biopsies should be examined

Cerebral Autosomal Dominant Arteriopathy with Subcortical Infarcts and Leukoencephalopathy: A Genetic Cause of Cerebral Small Vessel Disease

Cerebral autosomal dominant arteriopathy with subcortical infarcts and leukoencephalopathy (CADASIL) is a single-gene disorder of the cerebral small blood vessels caused by mutations in the Notch3 gene. The exact prevalence of this disorder was unknown currently, and the number of reported CADASIL families is steadily increasing as the clinical picture and diagnostic examinations are becoming more widely known. The main clinical manifestations are recurrent stroke, migraine, psychiatric symptoms, and progressive cognitive impairment. The clinical course of CADASIL is highly variable, even within families. The involvement of the anterior temporal lobe and the external capsule on brain magnetic resonance imaging was found to have high sensitivity and specificity in differentiating CADASIL from the much more common sporadic cerebral small-vessel disease (SVD). The pathologic hallmark of the disease is the presence of granular osmiophilic material in the walls of affected vessels. CADASIL is a prototype single-gene disorder that has evolved as a unique model for studying the mechanisms underlying cerebral SVD. At present, the incidence and prevalence of CADASIL seem to be underestimated due to limitations in clinical, neuroradiological, and genetic diagnoses of this disorder

Universal Scaling Limits of the Symplectic Elliptic Ginibre Ensemble

Ebke M. Universal Scaling Limits of the Symplectic Elliptic Ginibre Ensemble. Bielefeld: Universität Bielefeld; 2022.This thesis is concerned with eigenvalue statistics of non-Hermitian random matrices in the symplectic symmetry class. It contributes to the questions of how to compute the microscopic scaling limit and whether it is universal

Universality of the Number Variance in Rotational Invariant Two-Dimensional Coulomb Gases

Akemann G, Byun S-S, Ebke M. Universality of the Number Variance in Rotational Invariant Two-Dimensional Coulomb Gases. Journal of Statistical Physics . 2023;190(1): 9.An exact map was established by Lacroix-A-Chez-Toine et al. in (Phys Rev A 99(2):021602, 2019) between the N complex eigenvalues of complex non-Hermitian random matrices from the Ginibre ensemble, and the positions of N non-interacting Fermions in a rotating trap in the ground state. An important quantity is the statistics of the number of Fermions N-a in a disc of radius a. Extending the work (Lacroix-A-Chez-Toine et al., in Phys Rev A 99(2):021602, 2019) covering Gaussian and rotationally invariant potentials Q, we present a rigorous analysis in planar complex and symplectic ensembles, which both represent 2D Coulomb gases. We show that the variance of N-a is universal in the large-N limit, when measured in units of the mean density proportional to Delta Q, which itself is non-universal. This holds in the large-N limit in the bulk and at the edge, when a finite fraction or almost all Fermions are inside the disc. In contrast, at the origin, when few eigenvalues are contained, it is the singularity of the potential that determines the universality class. We present three explicit examples from the Mittag-Leffler ensemble, products of Ginibre matrices, and truncated unitary random matrices. Our proofs exploit the integrable structure of the underlying determinantal respectively Pfaffian point processes and a simple representation of the variance in terms of truncated moments at finite-N

Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble

Akemann G, Byun S-S, Ebke M, Schehr G. Universality in the number variance and counting statistics of the real and symplectic Ginibre ensemble. arXiv:2308.05519. 2023.In this article, we compute and compare the statistics of the number of eigenvalues in a centred disc of radius R in all three Ginibre ensembles. We determine the mean and variance as functions of R in the vicinity of the origin, where the real and symplectic ensembles exhibit respectively an additional attraction to or repulsion from the real axis, leading to different results. In the large radius limit, all three ensembles coincide and display a universal bulk behaviour of O(R2) for the mean, and O(R) for the variance. We present detailed conjectures for the bulk and edge scaling behaviours of the real Ginibre ensemble, having real and complex eigenvalues. For the symplectic ensemble we can go beyond the Gaussian case (corresponding to the Ginibre ensemble) and prove the universality of the full counting statistics both in the bulk and at the edge of the spectrum for rotationally invariant potentials, extending a recent work which considered the mean and the variance. This statistical behaviour coincides with the universality class of the complex Ginibre ensemble, which has been shown to be associated with the ground state of non-interacting fermions in a two-dimensional rotating harmonic trap. All our analytical results and conjectures are corroborated by numerical simulations