Topological enhancement of non-normality in non-Hermitian skin effects

The non-Hermitian skin effects are representative phenomena intrinsic to non-Hermitian systems: the energy spectra and eigenstates under the open boundary condition (OBC) drastically differ from those under the periodic boundary condition (PBC). Whereas a non-trivial topology under the PBC characterizes the non-Hermitian skin effects, their proper measure under the OBC has not been clarified yet. This paper reveals that topological enhancement of non-normality under the OBC accurately quantifies the non-Hermitian skin effects. Correspondingly to spectrum and state changes of the skin effects, we introduce two scalar measures of non-normality and argue that the non-Hermitian skin effects enhance both macroscopically under the OBC. We also show that the enhanced non-normality correctly describes phase transitions causing the non-Hermitian skin effects and reveals the absence of non-Hermitian skin effects protected by average symmetry. The topological enhancement of non-normality governs the perturbation sensitivity of the OBC spectra and the anomalous time-evolution dynamics through the Bauer-Fike theorem.Comment: 33 pages, 14 figure

Microwave treatment of the cornea leads to localised disruption of the extracellular matrix

Microwave keratoplasty is a thermo-refractive surgical procedure that can correct myopia (short-sightedness) and pathologic corneal steepening by using microwave energy to cause localised shrinkage around an annulus of the cornea leading to its flattening and vision correction. The effects on the corneal extracellular matrix, however, have not yet been evaluated, thus the current study to assess post-procedure ultrastructural changes in an in-vivo rabbit model. To achieve this a series of small-angle x-ray scattering (SAXS) experiments were carried out across whole transects of treated and untreated rabbit corneas at 0.25 mm intervals, which indicated no significant change in collagen intra-fibrillar parameters (i.e. collagen fibril diameter or axial D-period), whereas inter-fibrillar measures (i.e. fibril spacing and the degree of spatial order) were markedly altered in microwave-treated regions of the cornea. These structural matrix alterations in microwave-treated corneas have predicted implications for corneal biomechanical strength and tissue transparency, and, we contend, potentially render microwave-treated corneas resistant to surgical stabilization using corneal cross-linking procedures currently employed to combat refractive error caused by corneal steepening

A 4% Geometric Distance to the Galaxy NGC4258 from Orbital Motions in a Nuclear Gas Disk

The water maser in the mildly active nucleus in the nearby galaxy NGC4258 traces a thin, nearly edge-on, subparsec-scale Keplerian disk. Using the technique of very long baseline interferometry, we have detected the proper motions of these masers as they sweep in front of the central black hole at an orbital velocity of about 1100 km/s. The average maser proper motion of 31.5 microarcseconds per year is used in conjunction with the observed acceleration of the masers to derive a purely geometric distance to the galaxy of 7.2 +- 0.3 Mpc. This is the most precise extragalactic distance measured to date, and, being independent of all other distance indicators, is likely to play an important role in calibrating the extragalactic distance scale.Comment: 11 pages, 3 figures. Accepted for publication in Natur

A multi-transition HCN and HCO+ study of 12 nearby active galaxies: AGN versus SB environments

Recent studies have indicated that the HCN-to-CO(J=1-0) and HCO+-to-HCN(J=1-0) ratios are significantly different between galaxies with AGN (active galactic nucleus) and SB (starburst) signatures. In order to study the molecular gas properties in active galaxies and search for differences between AGN and SB environments, we observed the HCN(J=1-0), (J=2-1), (J=3-2), HCO+(J=1-0) and HCO+(J=3-2), emission with the IRAM 30m in the centre of 12 nearby active galaxies which either exhibit nuclear SB and/or AGN signatures. Consistent with previous results, we find a significant difference of the HCN(J=2-1)-to-HCN(J=1-0), HCN(J=3-2)-to-HCN(J=1-0), HCO+(J=3-2)-to-HCO+(J=3-2), and HCO+-to-HCN intensity ratios between the sources dominated by an AGN and those with an additional or pure central SB: the HCN, HCO+ and HCO+-to-HCN intensity ratios tend to be higher in the galaxies of our sample with a central SB as opposed to the pure AGN cases which show rather low intensity ratios. Based on an LVG analysis of these data, i.e., assuming purely collisional excitation, the (average) molecular gas densities in the SB dominated sources of our sample seem to be systematically higher than in the AGN sources. The LVG analysis seems to further support systematically higher HCN and/or lower HCO+ abundances as well as similar or higher gas temperatures in AGN compared to the SB sources of our sample. Also, we find that the HCN-to-CO ratios decrease with increasing rotational number J for the AGN while they stay mostly constant for the SB sources.Comment: accepted for publication in ApJ; 20 pages, 7 figures; in emulateApJ forma

Ab initio Derivation of Low-energy Model for Iron-Based Superconductors LaFeAsO and LaFePO

Effective Hamiltonians for LaFeAsO and LaFePO are derived from the downfolding scheme based on first-principles calculations and provide insights for newly discovered superconductivity in the family of LnFeAsO$_{1-x}$F$_x$, Ln = La, Ce, Pr, Nd, Sm, and Gd. Extended Hubbard Hamiltonians for five maximally localized Wannier orbitals per Fe are constructed dominantly from five-fold degenerate iron-3$d$ bands. They contain parameters for effective Coulomb and exchange interactions screened by the polarization of other electrons away from the Fermi level. The onsite Coulomb interaction estimated as 2.2-3.3 eV is compared with the transfer integrals between the nearest-neighbor Fe-3$d$ Wannier orbitals, 0.2-0.3 eV, indicating moderately strong electron correlation. The Hund's rule coupling is found to be 0.3-0.6 eV. The derived model offers a firm basis for further studies on physics of this family of materials. The effective models for As and P compounds turn out to have very similar screened interactions with slightly narrower bandwidth for the As compound.Comment: 5 pages, 3 figures, 1 table; to appear in J. Phys. Soc. Jpn. Vol. 77 No.9: Revised version contains corrected table values and discussions of quantitative accuracy of constrained random-phase approximatio

Borcherds symmetries in M-theory

It is well known but rather mysterious that root spaces of the $E_k$ Lie groups appear in the second integral cohomology of regular, complex, compact, del Pezzo surfaces. The corresponding groups act on the scalar fields (0-forms) of toroidal compactifications of M theory. Their Borel subgroups are actually subgroups of supergroups of finite dimension over the Grassmann algebra of differential forms on spacetime that have been shown to preserve the self-duality equation obeyed by all bosonic form-fields of the theory. We show here that the corresponding duality superalgebras are nothing but Borcherds superalgebras truncated by the above choice of Grassmann coefficients. The full Borcherds' root lattices are the second integral cohomology of the del Pezzo surfaces. Our choice of simple roots uses the anti-canonical form and its known orthogonal complement. Another result is the determination of del Pezzo surfaces associated to other string and field theory models. Dimensional reduction on $T^k$ corresponds to blow-up of $k$ points in general position with respect to each other. All theories of the Magic triangle that reduce to the $E_n$ sigma model in three dimensions correspond to singular del Pezzo surfaces with $A_{8-n}$ (normal) singularity at a point. The case of type I and heterotic theories if one drops their gauge sector corresponds to non-normal (singular along a curve) del Pezzo's. We comment on previous encounters with Borcherds algebras at the end of the paper.Comment: 30 pages. Besides expository improvements, we exclude by hand real fermionic simple roots when they would naively aris

Low-energy pions in nuclear matter and 2pi photoproduction within a BUU transport model

A description of low-energy scattering of pions and nuclei within a BUU transport model is presented. Implementing different scenarios of medium modifications, the mean free path of pions in nuclear matter at low momenta and pion absorption reactions on nuclei have been studied and compared to data and to results obtained via quantum mechanical scattering theory. We show that even in a regime of a long pionic wave length the semi-classical transport model is still a reliable framework for pion kinetic energies greater than ~20-30 MeV. Results are presented on pion-absorption cross sections in the regime of 10 MeV < E(kin) < 130 MeV and on photon-induced double-pion production at incident beam energies of 400-500 MeV.Comment: 22 pages, 20 figures Replaced with a revised version. Accepted for publication in EPJ A. Added a short section on pion reaction and charge exchange cross-section