Transversal Symmetry Research Articles

Approximate symmetries and quantum error correction

Quantum error correction (QEC) is a key concept in quantum computation as well as many areas of physics. There are fundamental tensions between continuous symmetries and QEC. One vital situation is unfolded by the Eastin–Knill theorem, which forbids the existence of QEC codes that admit transversal continuous symmetry actions (transformations). Here, we systematically study the competition between continuous symmetries and QEC in a quantitative manner. We first define a series of meaningful measures of approximate symmetries motivated from different perspectives, and then establish a series of trade-off bounds between them and QEC accuracy utilizing multiple different methods. Remarkably, the results allow us to derive general quantitative limitations of transversally implementable logical gates, an important topic in fault-tolerant quantum computation. As concrete examples, we showcase two explicit types of quantum codes, obtained from quantum Reed–Muller codes and thermodynamic codes, respectively, that nearly saturate our bounds. Finally, we discuss several potential applications of our results in physics.

A Novel Approach to Predict the Process-Induced Mechanical Behavior of Additively Manufactured Materials

The grain structure and texture of additively manufactured materials depend strongly on the local temperature gradients during the solidification of the material. These grain structures and textures influence the mechanical behavior, ranging from isotropy to transversal and orthotropic symmetry. In the present contribution, a cellular automaton is used to model the grain growth during selective electron beam melting. The resulting grain structures and textures serve as input for a mesoscopic mechanical model. The mechanical behavior on the mesoscale is modeled by means of gradient-enhanced crystal plasticity, applying the finite element method. Computational homogenization is applied to determine the resulting macroscopic elastic and plastic properties of the additively manufactured metals. A general orthotropic yield criterion is identified by means of the initial yield loci computed with mesoscopic simulations of representative volume elements. The numerical results are partly validated with experimental data.

The effect of the geometrical optical phase on the propagation of Hermite-Gaussian beams through transversal and parallel dielectric blocks

ABSTRACTWhen an optical beam propagates through dielectric blocks, its optical phase is responsible for the path of the beam. In particular, the first order Taylor expansion of the geometrical part reproduces the path predicted by the Snell and reflection laws whereas the first order expansion of the Fresnel phase leads to the Goos-Hänchen shift. In this paper, we analyze the effects of the second order Taylor expansion of the geometrical phase on the shape of the optical beam and show how it affects the transversal symmetry of Hermite-Gaussian beams. From the analytical expression of the transmitted beam, it is possible to determine in which transversal and parallel dielectric blocks configuration the transversal symmetry breaking is maximized or when the symmetry is recovered. We also discuss the axial spreading delay.

High‐Efficiency and Wide‐Angle Beam Steering Based on Catenary Optical Fields in Ultrathin Metalens

AbstractRecent advances in artificial subwavelength structures promise the realization of ultrathin, lightweight, and flat metalens, providing a potential candidate for traditional bulky and curved lens. Nevertheless, most metalenses are generally suffering from serious off‐axis aberration, resulting in a limited field‐of‐view (FOV). Here, a methodology to extend the FOV of metalens is presented by exploring the local catenary optical fields and symmetry transformation from rotational symmetry to transversal symmetry. As a proof of the concept, a high efficiency (>80% even when the incidence angle is titled by 60°) and ultrathin (≈0.127 λ) metalens consisting of bilayer geometric metasurface is designed, fabricated, and characterized. The wide FOV of metalens benefiting from local catenary fields and symmetry transformation is numerically demonstrated by full‐wave simulation and ray tracing method. Moreover, the wide‐angle beam steering ability beyond ± 60° is experimentally demonstrated, which exhibits obvious advantages compared with previous beam steering transmitarrays. The novelty of the proposed methodology lies at the fact that both transversal and longitudinal local catenary fields are excited in a single component: the transversal catenary field is utilized for high efficiency spin–orbit interaction and phase modulation, while the longitudinal catenary field and symmetry transformation ensure wide‐angle operation.

Assessment of an existing fully prestressed box-girder bridge

The N.S. da Guia Bridge is a 250 m-long post-tensioned box-girder bridge built in the late 1970s using the balanced cantilever method. During a routine inspection, a systematic cracking pattern that exhibited both longitudinal and transversal symmetry was detected in the webs and bottom slab, which raised concerns about the condition of the embedded post-tensioned cables. The working programme that was devised to perform the condition examination of the bridge is described. Besides a detailed visual inspection campaign and a short-term monitoring programme, non-destructive testing was also employed, most notably gamma-ray imaging of the internal tendons. Special attention is devoted to the numerical studies developed to explain the origin of the observed crack patterns. This information was crucial in order to decide on the best rehabilitation strategies. The crack pattern could be satisfactorily reproduced by taking into account the local stress conditions around the tendon anchorages, and the concerns related to the condition of the prestressed steel could be ruled out. The applied methodology constitutes an example of how detailed analysis techniques can be used in practice to help bridge owners evaluate the condition of special bridges and plan the rehabilitation intervention in a cost-effective way.

Experimental confirmation of the transversal symmetry breaking in laser profiles

The Snell phase effects on the propagation of optical beams through dielectric blocks have been matter of recent theoretical studies. The effects of this phase on the laser profiles have been tested in our experiment. The data show an excellent agreement with the theoretical predictions confirming the axial spreading modification and the transversal symmetry breaking. The possibility to set, by rotating the dielectric blocks, different configurations allows to recover the transversal symmetry. Based on this experimental evidence, dielectric blocks can be used as alternative optical tools to control the beam profile.

Symmetry recovery for coupled photonic modes with transversal PT symmetry

Typical parity-time (PT) symmetric structures switch from the unbroken to the broken phase when gain increases through an exceptional point. In contrast, we report on systems with the unusual, reverse behavior, where the symmetric phase is recovered after a broken phase. We study this phenomenon analytically and numerically in the simplest possible system, consisting of four coupled modes, and we present potential dielectric and plasmonic implementations. The complex mode merging scheme, with two distinct unbroken PT phases encompassing a broken one, appears for a specific proportion range of the coupling constants. This regime with "inverse" exceptional points is interesting for the design of novel PT devices.

Vacancy Effects on Electric and Thermoelectric Properties of Zigzag Silicene Nanoribbons

We study the crystal reconstruction in the presence of monovacancies (MVs), divacancies (DVs) and linear vacancies (LVs) in a zigzag silicene nanoribbon (ZSiNR) with transversal symmetry. Their influence on the electric and thermoelectric properties is assessed by the density functional theory combined with the nonequilibrium Green's functions. In particular, we focus on the spin resolved conductance, magnetoresistance and current-voltage curves. A 5-atom-ring is formed in MVs, a 5-8-5 ring structure in DVs, and a 8-4-8-4 ring structure in LVs. The linear conductance becomes strongly spin dependent when the transversal symmetry is broken by vacancies especially if they are located on the ribbon's edges. The giant magnetoresistance can be smeared by asymmetric vacancies. Single spin negative differential resistance may appear in the presence of LVs and asymmetric MVs or DVs. A strong spin Seebeck effect is expected at room temperature in ZSiNRs with LVs.

Cytogenetic stability of chicken T-cell line transformed with Marek's disease virus: atomic force microscope, a new tool for investigation

The Marek's disease virus (MDV) integration may induce a novel organization of chromatin architecture with a modified genetic expression. In our opinion it is worthwhile trying to relate cytogenetic stability to functional modifications. Recently, atomic force microscopy technique was applied to study the structure of chromosomes at a nanoscale level. This high resolution allows to investigate the different structure of chromatin in order to study cytogenetic stability and chromosome aberrations due to MDV insertion. In this paper data are presented indicating a duplication [78,WZ,dup(1p)(p22-p23)] and a deletion [78,WZ cht del(3)(q2.10)] of Chromosomes 1 and 3 relatively. Relationships between GTG (G-bands by Trypsin using Giemsa) bands and the topography of chromosomes are also discussed, naming them Topographic Banding. The architecture of chromosomes observed by AFM can be related to the data obtained with classic banding techniques thus overcoming the optical resolution limits. The presence of chromatin bridges between sister chromatids at most of the heterochromatic regions is also evidenced. Besides, we present different studies of the longitudinal and transversal symmetry of the hetero and euchromatic regions to clearly demonstrate a different underlying architecture of these regions. It is indeed evident that the heterochromatic bands are more symmetrical than euchromatic bands.

Interchromatidal central ridge and transversal symmetry in early metaphasic human chromosome one

The topographic structure of Giemsa-banded (G-banded) early metaphase human chromosomes adsorbed on glass was analyzed by atomic force microscope using amplitude modulation mode (AM-AFM). Longitudinal height measurements for early metaphasic human chromosomes showed a central ridge that was further characterized by transversal height measurements. The heterochromatic regions displayed a high level of transversal symmetry, while the euchromatic ones presented several peaks across the transversal height measurements. We suggest that this central ridge and symmetry patterns point out a transitional arrangement of the early metaphase chromosome and support evidence for interchromatidal interactions prior to disjunction.

Zeromphonons inMoS2nanotubes

Phonon dispersions of single-wall $\mathrm{Mo}{\mathrm{S}}_{2}$ nanotubes are calculated within a full symmetry implemented valence force-field model. For transversal, twisting, and breathing modes symmetry assignation, chirality, and diameter dependence of their frequencies and displacements are discussed. Tubular structure is found to be characterized by two Raman active modes: by the in-phase breathing mode (in full analogy to carbon nanotubes) with frequency approaching Brillouin scattering domain (as diameter approaches nm), and by the high-energy breathing mode with sulfur shells breathing in phase, but out of phase relative to the molybdenum atoms. Likewise, the longitudinal rigid-shell mode, where sulfur shells vibrate out of phase whilst molybdenum atoms barely move, is predicted to be a fingerprint of the cylindrical configuration in infrared spectra. It is also found that twisting rigid-layer modes characterize chirality of the tubes. Finally, the large diameter limit is discussed and related to the measured Raman and infrared spectra of the layered structure.

DYNAMICAL PROPERTIES OF THE INTERFACE BETWEEN TWO THIN FILMS

The effect on the vibrational properties of nanostructures at the interface between two thin films is presented. The model used consists of the coupling of two semi-infinite plans A and B having three and two atomic layers, respectively. Theoretical calculations of localized phonon modes and vibrational field were carried out using the matching procedure. Close to the interface, the transversal translational symmetry is broken down inducing Raleigh-like branches. The polarization degeneracy of the ordered surface Raleigh mode in the longitudinal direction is lifted. The presence of acoustic and optical-like phonons is discussed in terms of the elastic constant forces. The density of states and the spectral densities are presented for sample atomic sites. A hyperfine resonance structure is obtained. It allows the analysis of the dynamical evolution from thin film A to thin film B.

Isotropic discrete orientation distributions on the 3D special orthogonal group

In modeling the linear elastic behavior of a polycrystalline material on the microscopic level, a special problem is to determine a so-called discrete orientation distributions (DODs) which satisfy the isotropy condition. A DOD is a probability measure with finite support on SO(3), the special orthogonal group in three dimensions. Isotropy of a DOD can be viewed as an invariance property of a certain moment matrix of the DOD. So the problem of finding isotropic DODs resembles that of finding weakly invariant linear regression designs. In fact, methods from matrix and group theory which have been successfully applied in linear regression design can also be utilized here to construct various isotropic DODs. Of particular interest are isotropic DODs with small support. Crystal classes with additional symmetry properties are modeled by stiffness tensors having a non-trivial symmetry group. There are six possible non-trivial symmetry groups, up to conjugation. In either cases we find isotropic DODs with fairly small support, in particular for the cubic and the transversal symmetry groups.

A POSTERIORI ERROR ESTIMATES FOR THE FOKKER–PLANCK AND FERMI PENCIL BEAM EQUATIONS

We prove a posteriori error estimates for a finite element method for steady-state, energy dependent, Fokker–Planck and Fermi pencil beam equations in two space dimensions and with a forward-peaked scattering (i.e. with velocities varying within the right unit semi-circle). Our estimates are based on a transversal symmetry assumption, together with a strong stability estimate for an associated dual problem combined with the Galerkin orthogonality of the finite element method.

A laser-acoustic method for testing and classifying hard surface layers

The laser-acoustic method is accepted to be an interesting method of testing thin films. It is based on measuring the dispersion of surface acoustic waves which are generated by short laser pulses. A reliable test equipment was developed that allows a user-friendly operation. The method is non-destructive, the test takes little time and special sample preparation is not required. It is mainly applied to measure the Young’s modulus of thin films with thickness down to less than 50 nm. Recent studies showed these results to correlate with important microstructural and mechanical properties of hard and superhard films. The laser-acoustic technique was improved to test multilayer films consisting of two components. The approach of an effective medium of transversal symmetry is used to describe the elastic behavior of multilayer films. It enables the elastic anisotropy of the multilayer film to be evaluated. Applications are presented, performed at multilayers of diamond-like carbon and aluminum deposited by laser-arc on steel and silicon. The films consisted of four and twenty single layers, respectively. The Young’s modulus of the diamond-like carbon in the multilayer was determined with the laser-acoustic technique. The results reveal the reproducibility of the deposition technique and demonstrate the potential of the laser-acoustic technique to test multilayer films. The laser-acoustic method is shown to be sensitive to machining layers. The effect of grinding and polishing steel surfaces was studied. Studies were performed to compare the results of the laser-acoustic technique with those of membrane deflection and micro-indentation. TiN, CrN and TiCN films (thickness: 0.8–2.3 μm) were tested with laser-acoustics and micro-indentation, polysilicon films (thickness: 0.46 μm) with laser-acoustics and the membrane deflection technique.

Gynoecium diversity and systematics of the Magnoliales and winteroids

Carpel and ovule structure was compared in representatives of all 11 families of the Magnoliales (Annonaceae, Canellaceae, Degeneriaceae, Eupomatiaceae, Himantandraceae, Magnoliaceae, Myristicaceae) and winteroids (Austrobaileyaceae, Illiciaceae, Schisandraceae, Winteraceae). Special attention was paid to features that are constant at family level. Bisexual flowers are always protogynous. In all representatives studied the carpels are closed at anthesis. Carpel closure is attained in three different ways: (1) postgenital fusion of inner surfaces (Degeneriaceae, Eupomatiaceae, Winteraceae), or (2) occlusion by secretion (Austrobaileyaceae, Schisandraceae), or (3) a combination of (1) and (2): in Annonaceae, Canellaceae, Myristicaceae there is a conspicuous secretory canal in the innermost part of the ventral slit; in Illiciaceae and Magnoliaceae there is a narrow canal in the innermost part of the ventral slit; and in Himantandraceae the ventral slit is postgenitally fused in the style but completely open in the ovary. In most families the carpels have a double stigmatic crest or they have two tips in the transversal symmetry plane (i.e. at right angles to the median plane). Stigmas are unicellular papillate in most families but the papillae are bi- to multicellular (uniseriate) in Degeneriaceae and Eupomatiaceae. An unusual cryptic extracarpellary compitum was found in Himantandraceae and Schisandraceae. Intrusive oil cells were found in the carpel epidermis of Illiciaceae and Schisandraceae. Mature ovules vary in length between 0.15 and 1.1 mm. The outer integument is fully annular (not semiannular) in Degeneriaceae, Himantandraceae, Canellaceae, Myristicaceae, and Illiciaceae. A rudimentary aril occurs in Canellaceae, and originates at the same site as in arillate Annonaceae and Myristicaceae. The results most strongly support an Annonaceae-Myristicaceae-Canellaceae alliance, to some degree also an Eupomatiaceae-Degeneriaceae-Himantandraceae-Magnoliaceae alliance, and an Illiciaceae-Schisandraceae-Winteraceae-Austrobaileyaceae alliance.

Gynoecium diversity and systematics of the Magnoliales and winteroids

Abstract Carpel and ovule structure was compared in representatives of all 11 families of the Magnoliales (Annonaceae, Canellaceae, Degeneriaceae, Eupomatiaceae, Himantandraceae, Magnoliaceae, Myristicaceae) and winteroids (Austrobaileyaceae, Illiciaceae, Schisandraceae, Winteraceae). Special attention was paid to features that are constant at family level. Bisexual flowers are always protogynous. In all representatives studied the carpels are closed at anthesis. Carpel closure is attained in three different ways: (1) postgenital fusion of inner surfaces (Degeneriaceae, Eupomatiaceae, Winteraceae), or (2) occlusion by secretion (Austrobaileyaceae, Schisandraceae), or (3) a combination of (1) and (2): in Annonaceae, Canellaceae, Myristicaceae there is a conspicuous secretory canal in the innermost part of the ventral slit; in Illiciaceae and Magnoliaceae there is a narrow canal in the innermost part of the ventral slit; and in Himantandraceae the ventral slit is postgenitally fused in the style but completely open in the ovary. In most families the carpels have a double stigmatic crest or they have two tips in the transversal symmetry plane (i.e. at right angles to the median plane). Stigmas are unicellular papillate in most families but the papillae are bi- to multicellular (uniseriate) in Degeneriaceae and Eupomatiaceae. An unusual cryptic extracarpellary compitum was found in Himantandraceae and Schisandraceae. Intrusive oil cells were found in the carpel epidermis of Illiciaceae and Schisandraceae. Mature ovules vary in length between 0.15 and 1.1 mm. The outer integument is fully annular (not semiannular) in Degeneriaceae, Himantandraceae, Canellaceae, Myristicaceae, and Illiciaceae. A rudimentary aril occurs in Canellaceae, and originates at the same site as in arillate Annonaceae and Myristicaceae. The results most strongly support an Annonaceae-Myristicaceae-Canellaceae alliance, to some degree also an Eupomatiaceae-Degeneriaceae-Himantandraceae-Magnoliaceae alliance, and an Illiciaceae-Schisandraceae-Winteraceae-Austrobaileyaceae alliance.

Conservation Laws for Distributed Four-Ports (Short Papers)

Condition of reciprocity, Iosslessness, bilateral symmetry, transversal symmetry, and semireciprocity is given for a four-port in terms of its impedance, admittance, scattering, and transfer representation. Corresponding conditions are also presented for the system coupling matrix of a uniform distributed circuit. The results are applied to an anisotropic stratified waveguide.

Transversal correlations and translational symmetry in quasi-low-dimensional anharmonic crystals

Transversal correlations and translational symmetry in quasi-low-dimensional anharmonic crystals