Symmetry Considerations Research Articles

Probing nonadiabatic dynamics with attosecond pulse trains and soft x-ray Raman spectroscopy.

Linear off-resonant x-ray Raman techniques are capable of detecting the ultrafast electronic coherences generated when a photoexcited wave packet passes through a conical intersection. A hybrid femtosecond or attosecond probe pulse is employed to excite the system and stimulate the emission of the signal photon, where both fields are components of a hybrid pulse scheme. In this paper, we investigate how attosecond pulse trains, as provided by high-harmonic generation processes, perform as probe pulses in the framework of this spectroscopic technique, instead of single Gaussian pulses. We explore different combination schemes for the probe pulse as well as the impact of parameters of the pulse trains on the signals. Furthermore, we show how Raman selection rules and symmetry consideration affect the spectroscopic signal, and we discuss the importance of vibrational contributions to the overall signal. We use two different model systems, representing molecules of different symmetries, and quantum dynamics simulations to study the difference in the spectra. The results suggest that such pulse trains are well suited to capture the key features associated with the electronic coherence.

Exceptional points and scattering of discrete mechanical metamaterials

Exceptional points (EPs) are complex singularities of parametric linear operators where two or more eigenvalues and eigenvectors coalesce. EPs are attracting increasing interest in mechanical metamaterials due to their strong potentials for wave filtering, cloaking, and sensing applications. This work studies the band topology and scattering behaviors near EPs, using discrete models of metamaterial (MM) systems. The questions of existence of EPs and their physical manifestations will be addressed with particular focus on symmetry considerations and scattering behavior. Discrete mass-spring models with adjustable parameters are used here to elucidate the EP-related phenomena in a fundamental form. The transfer and scattering matrices are analyzed to provide practical insights on the restrictions associated with reciprocity and fundamental symmetries. By including complex stiffness in frequency domain as a representation of non-conservative mechanical loss or gain, the MM arrays can be tuned to achieve bi-directional transparency or one-way reflection when operating at the EPs. This analytical study will contribute to the understandings of EPs in mechanical context and the design of micro-structured media for novel applications.

Gravity from symmetry: duality and impulsive waves

We show that we can derive the asymptotic Einstein’s equations that arises at order 1/r in asymptotically flat gravity purely from symmetry considerations. This is achieved by studying the transformation properties of functionals of the metric and the stress-energy tensor under the action of the Weyl BMS group, a recently introduced asymptotic symmetry group that includes arbitrary diffeomorphisms and local conformal transformations of the metric on the 2-sphere. Our derivation, which encompasses the inclusion of matter sources, leads to the identification of covariant observables that provide a definition of conserved charges parametrizing the non-radiative corner phase space. These observables, related to the Weyl scalars, reveal a duality symmetry and a spin-2 generator which allow us to recast the asymptotic evolution equations in a simple and elegant form as conservation equations for a null fluid living at null infinity. Finally we identify non-linear gravitational impulse waves that describe transitions among gravitational vacua and are non-perturbative solutions of the asymptotic Einstein’s equations. This provides a new picture of quantization of the asymptotic phase space, where gravitational vacua are representations of the asymptotic symmetry group and impulsive waves are encoded in their couplings.

Optical conductivity and far-field radiation of silicene

Silicene is a silicon analogue of graphene. From symmetry considerations, we develop the matrix of Hamiltonian, including spin-orbit coupling in silicene. This work analyzes the heat and angular momentum radiation from silicene through the theory of far-field radiation and optical conductivity. We discuss the relation between the radiation and spin-orbit coupling parameters. Our results show the effects of different parameters, such as temperature and sublattice potential, on optical conductivity and radiation of silicene. In particular, the threshold frequency of optical conductivity causes the appearance of the second peak in energy radiation spectrum. We also find that the ratio of the perpendicular electric field to the intrinsic spin-orbit coupling is related to the strength of angular momentum radiation, which may promote the application of silicene.

Other-Sacrificing Options: Reply to Lange

In “Other-Sacrificing Options” (2020), Benjamin Lange argues that, when distributing benefits and burdens, we may discount the interests of the people to whom we stand in morally negative relationships relative to the interests of other people. Lange’s case for negative partiality proceeds in two steps. First, he presents a hypothetical example that commonly elicits intuitions favourable to negative partiality. Second, he invokes symmetry considerations to reason from permissible positive partiality towards intimates to permissible negative partiality towards adversaries. In this paper, I argue that neither the intuition elicited by Lange’s example nor the invoked symmetry considerations support a permission for negative partiality. This does not mean that negative partiality is unjustified. It means only that the justification, if there is one, must take a different form. I end by suggesting an alternative justification of negative partiality, one that mirrors gratitude-based justifications of positive partiality rather than justifications based on intimacy.

Measuring CP Violating Phase in Beauty Baryon Decays.

One of the outstanding problems in physics is to explain the baryon-antibaryon asymmetry observed in nature. According to the well-known Sakharov criterion for explaining the observed asymmetry, it is essential that CP violation exist. Even though CP violation has been observed in meson decays and is an integral part of the standard model (SM), measurements in meson decays indicate that CP violation in the SM is insufficient to explain the observed baryon-antibaryon asymmetry. The SM predicts the existence of yet to be observed CP violation in baryon decays. A critical test of the SM requires that CP violation be measured in baryon decays as well, in order to verify that it agrees with the measurement using meson decays. In this Letter we propose a new method to measure the CP violating phase in b baryons, using interference arising implicitly due to Bose symmetry considerations of the decaying amplitudes.

Protection of Quantum Information in a Chain of Josephson Junctions

Symmetry considerations are key towards our understanding of the fundamental laws of Nature. The presence of a symmetry implies that a physical system is invariant under specific transformations and this invariance may have deep consequences. For instance, symmetry arguments state that a system will remain in its initial state if incentives to actions are equally balanced. Here, we apply this principle to a chain of qubits and show that it is possible to engineer the symmetries of its Hamiltonian in order to keep quantum information intrinsically protected from both relaxation and decoherence. We show that the coherence properties of this system are strongly enhanced relative to those of its individual components. Such a qubit chain can be realized using a simple architecture consisting of a relatively small number of superconducting Josephson junctions.

Impact of Stress-Induced Rock Damage on Elastic Symmetry: From Transverse Isotropy to Orthotropy

In this article we explore the change in elastic symmetry and anisotropy of two geological materials with stress-induced damage. Two independent uniaxial deformation experiments on two layered and natural geomaterials, a shale and a sandstone, support this analysis. Both samples were loaded along their bedding planes at a constant strain rate up to mechanical failure. During deformation, an array of ultrasonic P- and S-wave transducers were employed to monitor the evolution of the ultrasonic velocities up to and beyond sample failure. We report here the impact on elastic symmetry and anisotropy of a uniaxial load applied parallel to the bedding plane of the transversely isotropic shale and sandstone samples. Based on symmetry considerations we analyse whether this load and the resulting stress-induced damage preserve the original transverse isotropy of the rock prior to loading, or lead to orthotropy (orthorhombic symmetry). Our results show that the two transverse isotropic samples retained their transverse isotropy in the initial stages of loading/damage. However for the more anisotropic shale sample the main failure mode was splitting of the bedding planes. In contrast the sandstone sample failed along a shear plane inclined to the bedding plane. In addition, the experimental data are further analysed using continuum damage mechanics to identify the evolution of the general fourth order anisotropic damage tensor during loading. We found that the highest damage variable of the damage tensor was D_{11} for the shale and D_{55} for the sandstone sample. The next highest damage variables for the shale sample were related to the bedding plane (x_2–x_3 plane) symmetry: D_{23}, D_{32}, D_{44}. However the damage variables obtained for the less anisotropic and more brittle sandstone sample were harder to interpret due to the mixed mode of fracturing present.

Magnetic Generation and Switching of Topological Quantum Phases in a Trivial Semimetal α−EuP3

Topological materials have drawn increasing attention owing to their rich quantum properties, as highlighted by a large intrinsic anomalous Hall effect (AHE) in Weyl and nodal-line semimetals. However, the practical applications for topological electronics have been hampered by the difficulty in the external control of the band topology. Here we demonstrate a magnetic-field-induced switching of band topology in $\alpha{\mathrm{-EuP}}_3$, a magnetic semimetal with a layered crystal structure derived from black phosphorus. When the magnetic field is applied perpendicular to the single mirror plane of the monoclinic structure, a giant AHE signal abruptly emerges at a certain threshold magnetization value, giving rise to a prominently large anomalous Hall angle of $\left|\Theta_{\mathrm{AHE}}\right| \sim 20^{\circ}$. When the magnetic field is applied along the inter-layer direction, which breaks the mirror symmetry, the system shows a pronounced negative longitudinal magnetoresistance. On the basis of electronic structure calculations and symmetry considerations, these anomalous magneto-transport properties can be considered as manifestations of two distinct topological phases: topological nodal-line and Weyl semimetals, respectively. Notably, the nodal-line structure is composed of bands with the same spin character and spans a wide energy range around the Fermi level. These topological phases are stabilized via the exchange coupling between localized Eu-4$f$ moments and mobile carriers conducting through the phosphorus layers. Our findings provide a realistic solution for external manipulation of band topology, enriching the functional aspects of topological materials.

Analytical solution for a vibrating rigid sphere with an elastic shell in an infinite linear elastic medium

The analytical solution is given for a vibrating rigid core sphere, oscillating up and down without volume change, situated at the center of an elastic material spherical shell, which in turn is situated inside an infinite (possible different) elastic medium. The solution is based on symmetry considerations and the continuity of the displacement both at the core and the shell-outer medium boundaries as well as the continuity of the stress at the outer edge of the shell. Furthermore, a separation into longitudinal and transverse waves is used. Analysis of the solution shows that a surprisingly complex range of physical phenomena can be observed when the frequency is changed while keeping the material parameters the same, especially when compared to the case of a core without any shell. With a careful choice of materials, shell thickness and vibration frequency, it is possible to filter out most of the longitudinal waves and generate pure tangential waves in the infinite domain (and vice-versa, we can filter out the tangential waves and generate longitudinal waves). When the solution is applied to different frequencies and with the help of a fast Fourier transform (FFT), a pulsed vibration is shown to exhibit the separation of the longitudinal (L) and transverse (T) waves (often called P- and S-waves in earthquake terminology).

Three-Dimensional Finite Element Modelling of Sheet Metal Forming for the Manufacture of Pipe Components: Symmetry Considerations

The manufacture of parts by metal forming is a widespread technique in sectors such as oil and gas and automotives. It is therefore important to make a research effort to know the correct set of parameters that allow the manufacture of correct parts. This paper presents a process analysis by means of the finite element model. The use case presented in this paper is that of a 3-m diameter pipe component with a thickness of 22 mm. In this type of application, poor selection of process conditions can result in parts that are out of tolerance, both in dimensions and shape. A 3D finite element model is made, and the symmetry of the tube section generated in 2D is analysed. As a novelty, an analysis of the process correction as a function of the symmetrical deformation of the material in this case in the form of a pipe is carried out. The results show a correct fitting of the model and give guidelines for manufacturing.

Magnetisation and Mean Field Theory in the Ising Model

In this set of notes, a complete, pedagogical tutorial for applying mean field theory to the two-dimensional Ising model is presented. Beginning with the motivation and basis for mean field theory, we formally derive the Bogoliubov inequality and discuss mean field theory itself. We proceed with the use of mean field theory to determine a magnetisation function, and the results of the derivation are interpreted graphically, physically, and mathematically. We give a new interpretation of the self-consistency condition in terms of intersecting surfaces and constrained solution sets. We also include some more general comments on the thermodynamics of the phase transition. We end by evaluating symmetry considerations in magnetisation, and some more subtle features of the Ising model. Together, a self-contained overview of the mean field Ising model is given, with some novel presentation of important results.

A Critical Review of Works Pertinent to the Einstein-Bohr Debate and Bell’s Theorem

This review is related to the Einstein-Bohr debate and to Einstein–Podolsky–Rosen’s (EPR) and Bohm’s (EPRB) Gedanken-experiments as well as their realization in actual experiments. I examine a significant number of papers, from my minority point of view and conclude that the well-known theorems of Bell and Clauser, Horne, Shimony and Holt (CHSH) deal with mathematical abstractions that have only a tenuous relation to quantum theory and the actual EPRB experiments. It is also shown that, therefore, Bell-CHSH cannot be used to assess the nature of quantum entanglement, nor can physical features of entanglement be used to prove Bell-CHSH. Their proofs are, among other factors, based on a statistical sampling argument that is invalid for general physical entities and processes and only applicable for finite “populations”; not for elements of physical reality that are linked, for example, to a time-like continuum. Bell-CHSH have, furthermore, neglected the subtleties of the theorem of Vorob’ev that includes their theorems as special cases. Vorob’ev found that certain combinatorial-topological cyclicities of classical random variables form a necessary and sufficient condition for the constraints that are now known as Bell-CHSH inequalities. These constraints, however, must not be linked to the observables of quantum theory nor to the actual EPRB experiments for a variety of reasons, including the existence of continuum-related variables and appropriate considerations of symmetry.

Symmetry Analysis of Magnetoelectric Effects in Perovskite-Based Multiferroics.

In this article, we performed symmetry analysis of perovskite-based multiferroics: bismuth ferrite (BiFeO3)-like, orthochromites (RCrO3), and Ruddlesden–Popper perovskites (Ca3Mn2O7-like), being the typical representatives of multiferroics of the trigonal, orthorhombic, and tetragonal crystal families, and we explored the effect of crystallographic distortions on magnetoelectric properties. We determined the principal order parameters for each of the considered structures and obtained their invariant combinations consistent with the particular symmetry. This approach allowed us to analyze the features of the magnetoelectric effect observed during structural phase transitions in BixR1−xFeO3 compounds and to show that the rare-earth sublattice has an impact on the linear magnetoelectric effect allowed by the symmetry of the new structure. It was shown that the magnetoelectric properties of orthochromites are attributed to the couplings between the magnetic and electric dipole moments arising near Cr3+ ions due to distortions linked with rotations and deformations of the CrO6 octahedra. For the first time, such a symmetry consideration was implemented in the analysis of the Ruddlesden–Popper structures, which demonstrates the possibility of realizing the magnetoelectric effect in the Ruddlesden–Popper phases containing magnetically active cations, and allows the estimation of the conditions required for its optimization.

Shadows and soft exchange in celestial CFT

We study exponentiated soft exchange in $d+2$ dimensional gauge and gravitational theories using the celestial CFT formalism. These models exhibit spontaneously broken asymptotic symmetries generated by gauge transformations with non-compact support, and the effective dynamics of the associated Goldstone "edge" mode is expected to be $d$-dimensional. The introduction of an infrared regulator also explicitly breaks these symmetries so the edge mode in the regulated theory is really a $d$-dimensional pseudo-Goldstone boson. Symmetry considerations determine the leading terms in the effective action, whose coefficients are controlled by the infrared cutoff. Computations in this model reproduce the abelian infrared divergences in $d=2$, and capture the re-summed (infrared finite) soft exchange in higher dimensions. The model also reproduces the leading soft theorems in gauge and gravitational theories in all dimensions. Interestingly, we find that it is the shadow transform of the Goldstone mode that has local $d$-dimensional dynamics: the effective action expressed in terms of the Goldstone mode is non-local for $d>2$. We also introduce and discuss new magnetic soft theorems. Our analysis demonstrates that symmetry principles suffice to calculate soft exchange in gauge theory and gravity.

Parameter symmetries of neutrino oscillations in vacuum, matter, and approximation schemes

Expressions for neutrino oscillations contain a high degree of symmetry, but typical forms for the oscillation probabilities mask these symmetries of the oscillation parameters. We elucidate the ${2}^{7}$ parameter symmetries of the vacuum parameters and draw connections to the choice of definitions of the parameters as well as interesting degeneracies. We also show that in the presence of matter an additional set of ${2}^{7}$ parameter symmetries of the matter parameters exists. Due to the complexity of the exact expressions for neutrino oscillations in matter, numerous approximations have been developed; we show that under certain assumptions approximate expressions have at most ${2}^{6}$ additional parameter symmetries of the matter parameters. We also include one parameter symmetry related to the large mixing angle (LMA)-dark degeneracy that holds under the assumption of $CPT$ invariance; this adds one additional factor of 2 to all of the above cases. Explicit, nontrivial examples are given of how physical observables in neutrino oscillations, such as the probabilities, $CP$ violation, the position of the solar and atmospheric resonance, and the effective $\mathrm{\ensuremath{\Delta}}{m}^{2}$'s for disappearance probabilities, are invariant under all of the above symmetries. We investigate which of these parameter symmetries apply to numerous approximate expressions in the literature and show that a more careful consideration of symmetries improves the precision of approximations.

Equivariant representations for molecular Hamiltonians and N-center atomic-scale properties.

Symmetry considerations are at the core of the major frameworks used to provide an effective mathematical representation of atomic configurations that is then used in machine-learning models to predict the properties associated with each structure. In most cases, the models rely on a description of atom-centered environments and are suitable to learn atomic properties or global observables that can be decomposed into atomic contributions. Many quantities that are relevant for quantum mechanical calculations, however-most notably the single-particle Hamiltonian matrix when written in an atomic orbital basis-are not associated with a single center, but with two (or more) atoms in the structure. We discuss a family of structural descriptors that generalize the very successful atom-centered density correlation features to the N-center case and show, in particular, how this construction can be applied to efficiently learn the matrix elements of the (effective) single-particle Hamiltonian written in an atom-centered orbital basis. These N-center features are fully equivariant-not only in terms of translations and rotations but also in terms of permutations of the indices associated with the atoms-and are suitable to construct symmetry-adapted machine-learning models of new classes of properties of molecules and materials.

Signatures of quartic asymmetric exchange in a class of two-dimensional magnets

Indirect quartic interaction of spins is suggested to play an important role in two dimensional magnets with trigonal prismatic symmetry such as Fe$_3$GeTe$_2$ monolayer. The proposed interaction is described by terms in micromagnetic energy that are linear in magnetization gradients. Such terms enable the stability of non-collinear magnetic textures. We investigate signatures of the quartic interaction in magnon spectra in the presence of anisotropy and external magnetic field. We also show how magnetic spirals, which are induced by the proposed interaction, can be manipulated by external field. Our analysis is based on symmetry considerations and can be used to quantify the quartic interaction strength in experiments with magnetic monolayers.

SU(3) flavor symmetry considerations for the [formula omitted] coupled channels system

We study the impact of SU(3) flavor symmetry breaking on the properties of dynamically generated Λ⁎ states within an effective separable potential model describing the coupled channels K¯N system. The model is based on the chiral meson-baryon Lagrangian at next-to-leading order, and constitutes an improvement over a previous model developed by our group, with its applicability being extended to higher energies covering the Λ(1670) resonance region. It is demonstrated that the ratios of channel couplings to the resonant states can vary dramatically when the flavor breaking is gradually switched off, tracing a path to the restored SU(3) symmetry. We conclude that the couplings determined from physical observables cannot be used to reliably relate a given resonance to a specific flavor multiplet.

Analisys of interlaminar stresses in composite laminates by finite difference method

In this work, full stress tensor components regarding stress state for a simmetrical composite laminate under uniform uniaxial extension have been determined. Off-plane stresses are specially meaningful due to the fact that they are responsible for failure mechanisms such as delamination and shear stress cracking. A finite difference scheme has been used to solve internal equilibrium equations subjected to stress-free boundary conditions along boundary lines; moreover symmetry considerations have been made. In such way, we get an improvement in solutions in contrast with results obtained following bidimensional reasoning and using laminate based elements. Off-plane stresses for differents ply-sequences have been evaluated and maximum and minimum values for different fibers orientations were explored.