Symmetry Restrictions Research Articles

Incommensurate atomic and magnetic modulations in the spin-frustrated β−NaMnO2 triangular lattice

The layered {\beta}-NaMnO2, a promising Na-ion energy-storage material has been investigated for its triangular lattice capability to promote complex magnetic configurations that may release symmetry restrictions for the coexistence of ferroelectric and magnetic orders. The complexity of the neutron powder diffraction patterns underlines that the routinely adopted commensurate structural models are inadequate. Instead, a single-phase superspace symmetry description is necessary, demonstrating that the material crystallizes in a compositionally modulated q= (0.077(1), 0, 0) structure. Here, Mn3+ Jahn-Teller distorted MnO6 octahedra form corrugated layer stacking sequences of the {\beta}-NaMnO2 type, which are interrupted by flat sheets of the {\alpha}-like oxygen topology. Spontaneous long-range collinear antiferromagnetic order, defined by the propagation vector k= (1/2, 1/2, 1/2), appears below TN1= 200 K. Moreover, a second transition into a spatially modulated proper-screw magnetic state (k+-q) is established at TN2= 95 K, with an antiferromagnetic order parameter resembling that of a two-dimensional (2D) system. The evolution of 23Na NMR spin-lattice relaxation identifies a magnetically inhomogene-ous state in the intermediate T-region (TN2 <T< TN1), while its strong suppression below TN2 indicates that a spin-gap opens in the excitation spectrum. High-resolution neutron inelastic scattering confirms that the magnetic dynamics are indeed gapped ({\Delta}~5 meV) in the low-temperature magnetic phase, while simulations on the basis of the single-mode approximation suggest that Mn-spins residing on ad-jacent antiferromagnetic chains, establish sizable 2D correlations. Our analysis points that novel struc-tural degrees of freedom promote, cooperative magnetism and emerging dielectric properties in this non-perovskite-type of manganite.

The TDHF code Sky3D version 1.1

The nuclear mean-field model based on Skyrme forces or related density functionals has found widespread application to the description of nuclear ground states, collective vibrational excitations, and heavy-ion collisions. The code Sky3D solves the static or dynamic equations on a three-dimensional Cartesian mesh with isolated or periodic boundary conditions and no further symmetry assumptions. Pairing can be included in the BCS approximation for the static case. The code is implemented with a view to allow easy modifications for including additional physics or special analysis of the results.

Lattice dynamics of ASb2O6 ( A=Cu , Co) with trirutile structure

Raman spectroscopy experiments on single crystals of CuSb2O6 and CoSb2O6 quasi-one-dimensional antiferromagnets with trirutile crystal structure were performed, with a focus on the first material. The observed Raman-active phonon modes and previously reported infrared-active modes were identified with the aid of ab-initio lattice dynamics calculations. The structural transition between monoclinic beta-CuSb2O6 and tetragonal alpha-CuSb2O6 phases at Ts=400 K is manifested in our spectra by a "repulsion" of two accidentally quasi-degenerate symmetric modes below Ts, caused by a phonon mixing effect that is only operative in the monoclinic beta-CuSb2O6 phase due to symmetry restrictions. Also, two specific phonons, associated with CuO6 octahedra rotation and with a Jahn-Teller elongation mode, soften and broaden appreciably as T -> Ts. A crossover from a displacive to an order-disorder transition at Ts is inferred.

Thermoelectrics of Interacting Nanosystems—Exploiting Superselection Instead of Time-Reversal Symmetry

Thermoelectric transport is traditionally analyzed using relations imposed by time-reversal symmetry, ranging from Onsager's results to fluctuation relations in counting statistics. In this paper, we show that a recently discovered duality relation for fermionic systems -- deriving from the fundamental fermion-parity superselection principle of quantum many-particle systems -- provides new insights into thermoelectric transport. Using a master equation, we analyze the stationary charge and heat currents through a weakly coupled, but strongly interacting single-level quantum dot subject to electrical and thermal bias. In linear transport, the fermion-parity duality shows that features of thermoelectric response coefficients are actually dominated by the average and fluctuations of the charge in a dual quantum dot system, governed by attractive instead of repulsive electron-electron interaction. In the nonlinear regime, the duality furthermore relates most transport coefficients to much better understood equilibrium quantities. Finally, we naturally identify the fermion-parity as the part of the Coulomb interaction relevant for both the linear and nonlinear Fourier heat. Altogether, our findings hence reveal that next to time-reversal, the duality imposes equally important symmetry restrictions on thermoelectric transport. As such, it is also expected to simplify computations and clarify the physical understanding for more complex systems than the simplest relevant interacting nanostructure model studied here.

Nonlinear Dirac cones

Physics arising from two-dimensional~(2D) Dirac cones has been a topic of great theoretical and experimental interest to studies of gapless topological phases and to simulations of relativistic systems. Such $2$D Dirac cones are often characterized by a $\pi$ Berry phase and are destroyed by a perturbative mass term. By considering mean-field nonlinearity in a minimal two-band Chern insulator model, we obtain a novel type of Dirac cones that are robust to local perturbations without symmetry restrictions. Due to a different pseudo-spin texture, the Berry phase of the Dirac cone is no longer quantized in $\pi$, and can be continuously tuned as an order parameter. Furthermore, in an Aharonov-Bohm~(AB) interference setup to detect such Dirac cones, the adiabatic AB phase is found to be $\pi$ both theoretically and computationally, offering an observable topological invariant and a fascinating example where the Berry phase and AB phase are fundamentally different. We hence discover a nonlinearity-induced quantum phase transition from a known topological insulating phase to an unusual gapless topological phase.

Jahn-Teller distortion of Mn3+-occupied octahedra in red beryl from Utah indicated by optical spectroscopy

Red beryl from Utah is chemically homogeneous and contains only Fe < 0.163, Mn < 0.018, and Mg < 0.016 apfu. Channel sites contain only up to Cs 0.011, K 0.009, Rb 0.004, and Na 0.004 apfu. This suggests only very slight tetrahedral (Cs,K,Rb)Li□-1Be-1 substitution, octahedral Na(Fe2+,Mg)□-1Al-1 substitution can be excluded. Fe and Mn are trivalent as documented by Mössbauer spectroscopy and optical absorption spectroscopy. Red beryl optimized formula is ∼[(Cs,Rb,K)0.02□0.98]Σ1.00□1.00(Al1.79Fe3+0.16Mn3+0.02Ti4+0.02Mg0.01)Σ2.00Be3(Si6O18). Location of Mn3+ was estimated to the octahedral Al3+ site, other choices are improbable due to the bond-length requirements. No Mn3+-induced Jahn-Teller structural distortion was detected due to site symmetry restrictions and small Mn3+ content. However, optical spectroscopy shows broad band at ∼7190 cm−1 assigned to the excited level of the spin-allowed pseudo-tetragonal split E ground state of elongated six-fold Mn3+ coordination. Crystal field calculations indicate that the local Mn3+ environment complies well with crystal chemical expectations for Jahn-Teller distorted Mn3+O6 octahedra.

Hyperboloidal Evolution and Global Dynamics for the Focusing Cubic Wave Equation

The focusing cubic wave equation in three spatial dimensions has the explicit solution $\sqrt{2}/t$. We study the stability of the blowup described by this solution as $t \to 0$ without symmetry restrictions on the data. Via the conformal invariance of the equation we obtain a companion result for the stability of slow decay in the framework of a hyperboloidal initial value formulation. More precisely, we identify a codimension-1 Lipschitz manifold of initial data leading to solutions which converge to Lorentz boosts of $\sqrt{2}/t$ as $t\to\infty$. These global solutions thus exhibit a slow nondispersive decay, in contrast to small data evolutions.

Poly-symmetry in processor-sharing systems

We consider a system of processor-sharing queues with state-dependent service rates. These are allocated according to balanced fairness within a polymatroid capacity set. Balanced fairness is known to be both insensitive and Pareto-efficient in such systems, which ensures that the performance metrics, when computable, will provide robust insights into the real performance of the system considered. We first show that these performance metrics can be evaluated with a complexity that is polynomial in the system size if the system is partitioned into a finite number of parts, so that queues are exchangeable within each part and asymmetric across different parts. This in turn allows us to derive stochastic bounds for a larger class of systems which satisfy less restrictive symmetry assumptions. These results are applied to practical examples of tree data networks, such as backhaul networks of Internet service providers, and computer clusters.

Mean curvature flow with free boundary in embedded cylinders or cones and uniqueness results for minimal hypersurfaces

In this paper we study the mean curvature flow of embedded disks with free boundary on an embedded cylinder or generalised cone of revolution, called the support hypersurface. We determine regions of the interior of the support hypersurface such that initial data is driven to a curvature singularity in finite time or exists for all time and converges to a minimal disk. We further classify the type of the singularity. We additionally present applications of these results to the uniqueness problem for minimal hypersurfaces with free boundary on such support hypersurfaces; the results obtained this way do not require a-priori any symmetry or topological restrictions.

Enhancing 4-propylheptane dissociation with nickel nanocluster based on molecular dynamics simulations

In the present work, a 0.4nm nickel cluster has been theoretically studied. Its equilibrium structural parameters have been calculated by the DFT method based on the PBEH1PBE hybrid functional and split-valence basis set Lanl2DZ including effective core potentials. We have systematically considered diverse spin states of this cluster and find out its ground state. The relative stability of these states depends on the HOMO–LUMO gap. The interaction of the Ni6 with 4-propylheptane С10Н22 has been studied to simulate the process of catalytic cracking of hydrocarbons. The optimization of this structure has been performed by the ωPBE/Lanl2DZ_ecp method (the TeraChem V.1.9 program package) with no symmetry restrictions; the electron shells of the metal were described by effective core pseudopotentials. For visualization and quantitative estimation of the bonding bonds between the nickel nanocluster and 4-propylheptane, the analysis of weak interactions based on RGD has been performed. To confirm the proposition about the formation of Ni–H bonds, we have scrutinized critical points of electronic density. Values of laplasian of electronic density and Bader atomic charge distribution in the global minimum of the total energy have been estimated by the AIMAll 15.05.18 program suite. Finally, we have simulated interaction of Ni6 with 4-propylheptane in terms of the Born–Oppenheimer ab initio molecular dynamics. The results of the molecular dynamics simulation provide pair radial distribution function CH at 1500°C and a detailed picture of the processes occurring in the system.

Tricationic metastability by symmetry restrictions: B2 n+, n = 3,4

To explain the experimentally observed metastability of the trication B2 3+, we study this system by various ab-initio methods. Whereas the electronic ground state X2Σu + of B2 3+ turns out to be unstable, the potential energy curves of the lowest excited state 12Πu and of the quartet state 14Σg − form barriers that support quasi-bound vibronic states. The lifetimes of these states are not only determined by the respective (dissociative) tunnelling rates, but also by possible radiative electronic transitions and predissociation via spin-orbit coupling, where the latter furnish the decisive decay mechanism for the low-lying vibronic levels. In case of the quadruply charged system B2 4+, our computations do not predict any metastable states in the low-lying electronic spectrum. The deviation from a purely Coulombic repulsive behaviour in B2 4+ is quantified by fitting the potential energy curves to a modified Murrell-Sorbie function.

Skyrme tensor force in the collision16O+40Ca

The role of tensor force is investigated by using the time-dependent Hartree-Fock (TDHF) theory in the collision 16 O+40 Ca. The full tensor force is incorporated in our TDHF implementation. The calculations are performed in three-dimensional Cartesian coordinate without any symmetry restrictions. We study the effect of tensor force on Coulomb barrier, upper fusion threshold energy, and energy contribution of the time-odd and tensor terms in Skyrme energy functional. The Coulomb barrier obtained from the energy functional with frozen density approximation is compared with the available experimental data. We find that the tensor force may change the upper fusion threshold energy in the order of a few MeV for the collision 16 O+40 Ca. The tensor force has a non-negligible effect in heavy-ion collisions.

On the Cohomology of Contextuality

Recent work by Abramsky and Brandenburger used sheaf theory to give a mathematical formulation of non-locality and contextuality. By adopting this viewpoint, it has been possible to define cohomological obstructions to the existence of global sections. In the present work, we illustrate new insights into different aspects of this theory. We shed light on the power of detection of the cohomological obstruction by showing that it is not a complete invariant for strong contextuality even under symmetry and connectedness restrictions on the measurement cover, disproving a previous conjecture. We generalise obstructions to higher cohomology groups and show that they give rise to a refinement of the notion of cohomological contextuality: different "levels" of contextuality are organised in a hierarchy of logical implications. Finally, we present an alternative description of the first cohomology group in terms of torsors, resulting in a new interpretation of the cohomological obstructions.

PENENTUAN NILAI TUKAR: PENGUJIAN PURCHASING POWER PARITY DI INDONESIA

This paper provides a test of purchasing power parity (PPP) as an explanation for longtermforeign exchange rate movement. We impose symmetry and proportionality restrictions ofPPP to data drawn from the period 1969.1 through 2001.4. The tests are also run for sub-periods. Symmetry and proportionality restrictions find little support for the unit root tests though the Johansen test suggests that foreign exchange rate and inflation rate are linked in a long run sense. Error correction models are then estimated on the basis of the assumption that the United States inflation rate is exogenous. The error correction models result also rejects the PPP.Keywords: purchasing power parity, exchage rate

Forecasting Conditional Probabilities of Binary Outcomes under Misspecification

Abstract We consider constructing probability forecasts from a parametric binary choice model under a large family of loss functions (“scoring rules”). Scoring rules are weighted averages over the utilities that heterogeneous decision makers derive from a publicly announced forecast (Schervish, 1989). Using analytical and numerical examples, we illustrate howdifferent scoring rules yield asymptotically identical results if the model is correctly specified. Under misspecification, the choice of scoring rule may be inconsequential under restrictive symmetry conditions on the data-generating process. If these conditions are violated, typically the choice of a scoring rule favors some decision makers over others.

ChemInform Abstract: Excited State Decay of Cyclometalated Polypyridine Ruthenium Complexes: Insight from Theory and Experiment

AbstractReview: 176 refs.

Piezoelectricity in planar boron nitride via a geometric phase

Due to their low surface mass density, two-dimensional materials with a strong piezoelectric response are interesting for nanoelectromechanical systems with high force sensitivity. Unlike graphene, the two sublattices in a monolayer of hexagonal boron nitride (hBN) are occupied by different elements, which breaks inversion symmetry and allows for piezoelectricity. This has been confirmed with density functional theory calculations of the piezoelectric constant of hBN. Here, we formulate an entirely analytical derivation of the electronic contribution to the piezoelectric response in this system based on the concepts of strain-induced pseudomagnetic vector potential and the modern theory of polarization that relates the polar moment to the Berry curvature. Our findings agree with the symmetry restrictions expected for the hBN lattice and reproduce well the magnitude of the piezoelectric effect previously obtained ab-initio.

Reinterpreting the magnetoelectric coupling of polarizability tensors of infinite cylinders using symmetry: A simple TM/TE view

Recently, Strickland et al retrieved dynamic polarizabilities of infinitely long wires at oblique incidence, reporting non-zero magnetoelectric coupling, seemingly defying existing theorems which forbid this in centrosymmetric scatterers. We reconcile this finding with existing symmetry restrictions on microscopic polarizabilities using a property of line dipoles. This motivates a reformulation of cylinder polarizability, yielding diagonal tensors that decompose the response into TM and TE contributions, simplifying subsequent treatment by homogenization theories. A transformation is derived between Strickland et al.'s formulation and our reformulation, allowing magnetoelectric coupling to be identified as the contrast between TM and TE responses, and enabling simple geometric insights into all its scaling and symmetry properties.

Bifurcations analysis of the twist-Fréedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions: the asymmetric case

In the paper, Bifurcation analysis of the twist-Fréedericksz transition in a nematic liquid-crystal cell with pre-twist boundary conditions (2009 Eur. J. Appl. Math.20, 269–287) by da Costa et al. the twist-Fréedericksz transition in a nematic liquid-crystal one-dimensional cell of lenght L was studied, imposing an antisymmetric net twist Dirichlet condition at the cell boundaries. In the present paper, we extend that study to the more general case of net twist Dirichlet conditions without any kind of symmetry restrictions. We use phase-plane analysis tools and appropriately defined time maps to obtain the bifurcation diagrams of the model when L is the bifurcation parameter, and related these diagrams with the one in the antisymmetric situation. The stability of the bifurcating solutions is investigated by applying the method of Maginu (1978 J. Math. Anal. Appl.63, 224–243).

Nonparametric estimation of trend in directional data

Consider measured positions of the paleomagnetic north pole over time. Each measured position may be viewed as a direction, expressed as a unit vector in three dimensions and incorporating some error. In this sequence, the true directions are expected to be close to one another at nearby times. A simple trend estimator that respects the geometry of the sphere is to compute a running average over the time-ordered observed direction vectors, then normalize these average vectors to unit length. This paper treats a considerably richer class of competing directional trend estimators that respect spherical geometry. The analysis relies on a nonparametric error model for directional data in Rq that imposes no symmetry or other shape restrictions on the error distributions. Good trend estimators are selected by comparing estimated risks of competing estimators under the error model. Uniform laws of large numbers, from empirical process theory, establish when these estimated risks are trustworthy surrogates for the corresponding unknown risks.