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Mirror symmetry

About: Mirror symmetry is a research topic. Over the lifetime, 2422 publications have been published within this topic receiving 90786 citations.


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TL;DR: In this article, an analysis of weakly coupled two-dimensional spatial optical solitons in a large-aperture class A laser with a saturable absorber is developed.
Abstract: An analysis of clusters of weakly coupled two-dimensional spatial optical solitons in a large-aperture class A laser with a saturable absorber is developed. The symmetries that control the transverse motion of the clusters are described. Numerical solutions of the governing generalized complex Ginzburg-Landau equation demonstrate the existence of four types of clusters of weakly coupled cavity solitons that correspond to symmetries of transverse intensity distributions and energy flows: (1) stationary (with two mirror symmetry axes), (2) rotating about a stationary center of mass (invariant under rotation), (3) translating without rotation (with a single mirror symmetry axis), and (4) asymmetric ones rotating about a center of mass that moves around a circle (with equal periods of rotation and circular motion).

17 citations

Journal ArticleDOI
TL;DR: In this article, the authors study the inequivalent quantizations of the N = 3 Calogero model by separation of variables, in which the model decomposes into the angular and the radial parts.
Abstract: We study the inequivalent quantizations of the N=3 Calogero model by separation of variables, in which the model decomposes into the angular and the radial parts. Our inequivalent quantizations respect the “mirror-S3” invariance (which realizes the symmetry under the cyclic permutations of the particles) and the scale invariance in the limit of vanishing harmonic potential. We find a two-parameter family of novel quantizations in the angular part and classify the eigenstates in terms of the irreducible representations of the S3 group. The scale invariance restricts the quantization in the radial part uniquely, except for the eigenstates coupled to the lowest two angular levels for which two types of boundary conditions are allowed independently from all upper levels. It is also found that the eigenvalues corresponding to the singlet representations of the S3 are universal (parameter-independent) in the family, whereas those corresponding to the doublets of the S3 are dependent on one of the parameters. Th...

17 citations

Journal ArticleDOI
TL;DR: In this paper, a detailed investigation of the contribution from Coulomb effects to the observed mirror energy difference diagrams in nuclei in the lower part of the upper fp shell is presented by means of large-scale shell-model calculations.
Abstract: A detailed investigation of the contribution from Coulomb effects to the observed mirror energy difference diagrams in nuclei in the lower part of the upper fp shell is presented by means of large-scale shell-model calculations.

17 citations

Journal ArticleDOI
TL;DR: In this paper, angle-resolved photoemission was used to discover a metal state with the dispersion of a Dirac cone at a low-symmetry point of W(110).
Abstract: Topologically nontrivial states reveal themselves in strongly spin-orbit coupled systems by Dirac cones. However, their appearance is not a sufficient criterion for a topological phase. In topological insulators, where these states protect surface metallicity, they are straightforwardly assigned based on bulk-boundary correspondence. On metals, where these states are suspected to have tremendous impact as well, e.g., in catalysis, their topological protection is difficult to assess due to the lacking band gap and the frequent assignment to topological properties appears unjustified. Here, we discover by angle-resolved photoemission a state with the dispersion of a Dirac cone at a low-symmetry point of W(110). Our ab initio calculations predict this feature with a linear band crossing and high spin polarization. However, instead of being born by topology, the states arise from Rashba split bands and do not fundamentally depend on the opening of a spin-orbit gap. On the other hand, we find that the [001] mirror plane protects the band crossing point and renormalizes the dispersion towards a Dirac-cone shape. In this sense, the discovered state is the metal counterpart of the surface state of a topological crystalline insulator. The Dirac cone is tilted due to its origin in an accidental band crossing away from high symmetry points. Tilted Dirac cones have recently been predicted for two- and three-dimensional materials and were observed in three-dimensional Weyl semimetals. Accordingly, the protection and renormalization by mirror symmetry uncovered here are a potentially much wider spread phenomenon which does not require topological properties. Our results also indicate why the massive gapless crossing predicted for topological crystalline insulators has never been observed.

17 citations

Journal ArticleDOI
TL;DR: In this paper, the authors search for hidden mirror symmetries at large angular scales in the WMAP 7 year Internal Linear Combination map of CMB temperature anisotropies using global pixel based estimators introduced for this aim.
Abstract: We search for hidden mirror symmetries at large angular scales in the WMAP 7 year Internal Linear Combination map of CMB temperature anisotropies using global pixel based estimators introduced for this aim. Two different axes are found for which the CMB intensity pattern is anomalously symmetric (or anti-symmetric) under reflection with respect to orthogonal planes at the 99.84(99.96)% CL (confidence level), if compared to a result for an arbitrary axis in simulations without the symmetry. We have verified that our results are robust to the introduction of the galactic mask. The direction of such axes is close to the CMB kinematic dipole and nearly orthogonal to the ecliptic plane, respectively. If instead the real data are compared to those in simulations taken with respect to planes for which the maximal mirror symmetry is generated by chance, the confidence level decreases to 92.39 (76.65)%. But when the effect in question translates into the anomalous alignment between normals to planes of maximal mirror (anti)-symmetry and these natural axes mentioned. We also introduce the representation of the above estimators in the harmonic domain, confirming the results obtained in the pixel one. The symmetry anomaly is shown to be almost entirely due to low multipoles, so it may have a cosmological and even primordial origin. Contrary, the anti-symmetry one is mainly due to intermediate multipoles that probably suggests its non-fundamental nature. We have demonstrated that these anomalies are not connected to the known issue of the low variance in WMAP observations and we have checked that axially symmetric parts of these anomalies are small, so that the axes are not the symmetry ones.

17 citations


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Performance
Metrics
No. of papers in the topic in previous years
YearPapers
202351
2022116
2021138
2020130
2019139
2018125