Strong Symmetry Research Articles

Spontaneous strong symmetry breaking in open systems: Purification perspective

Spontaneous strong symmetry breaking in open systems: Purification perspective

Quasisymmetrically rigid self-similar carpets

Abstract We define balanced self-similar quasi-round carpets and compare the carpet moduli of some path families relating to such a carpet. Then, using some known results on quasiconformal geometry of carpets, we prove that the group of quasisymmetric self-homeomorphisms of every balanced self-similar quasi-round carpet is finite. Furthermore, we prove that some balanced self-similar carpets in the unit square with strong geometric symmetry are quasisymmetrically rigid by using the quasisymmetry of weak tangents of carpets.

Universal Time-Entanglement Trade-Off in Open Quantum Systems

We demonstrate a surprising connection between pure steady-state entanglement and relaxation time scales in an extremely broad class of Markovian open systems, where two (possibly many-body) systems, A and B, interact locally with a common dissipative environment. This setup also encompasses a broad class of adaptive quantum dynamics based on continuous measurement and feedback. As steady-state entanglement increases, there is generically an emergent strong symmetry that leads to a dynamical slow-down. Using this, we can prove rigorous bounds on relaxation times set by steady-state entanglement. We also find that this time must necessarily diverge for maximal entanglement. To test our bound, we consider the dynamics of a random ensemble of local Lindbladians that support pure steady states, finding that the bound does an excellent job of predicting how the dissipative gap varies with the amount of entanglement. Our work provides general insights into how dynamics and entanglement are connected in open systems and has specific relevance to quantum reservoir engineering. Published by the American Physical Society 2024

Electromagnetic Surface Waves in a Relativistic Magnetized Plasma Propagating in a Cylindrical Column

Dispersion relations of electromagnetic surface waves in a magnetized relativistic plasma propagating in a cylindrical column surrounded by vacuum are derived by means of the relativistic fluid equations. The zero order relativistic beam is assumed to stream along the direction of the axial magnetic field. The coupled equations of the E- and B-wave modes are solved analytically in terms of the cylindrical coordinates in weak or intermediate values of the magnetic field in which the cyclotron frequency is much smaller than the relativistic Doppler-shifted frequency. The entangled field components of the E- and B-waves are decoupled by assuming that the flow is incompressible. The surface wave dispersion relations of the E- and B-wave modes show a strong similarity and symmetry. The static magnetic field splits the E- and B-waves, thus doubling the modes in unmagnetized plasma. By taking the radius of the cylinder infinite, the dispersion relations in a semi-infinite plasma are derived.

Nijenhuis geometry IV: conservation laws, symmetries and integration of certain non-diagonalisable systems of hydrodynamic type in quadratures

Abstract The paper contains two lines of results: the first one is a study of symmetries and conservation laws of gl -regular Nijenhuis operators. We prove the splitting theorem for symmetries and conservation laws of Nijenhuis operators, show that the space of symmetries of a gl -regular Nijenhuis operator forms a commutative algebra with respect to (pointwise) matrix multiplication. Moreover, all the elements of this algebra are strong symmetries of each other. We establish a natural relationship between symmetries and conservation laws of a gl -regular Nijenhuis operator and systems of the first and second companion coordinates. Moreover, we show that the space of conservation laws is naturally related to the space of symmetries in the sense that any conservation laws can be obtained from a single conservation law by multiplication with an appropriate symmetry. In particular, we provide an explicit description of all symmetries and conservation laws for gl -regular operators at algebraically generic points. The second line of results contains an application of the theoretical part to a certain system of partial differential equations of hydrodynamic type, which was previously studied by different authors, but mainly in the diagonalisable case. We show that this system is integrable in quadratures, i.e. its solutions can be found for almost all initial curves by integrating closed 1-forms and solving some systems of functional equations. The system is not diagonalisable in general, and construction and integration of such systems is an actively studied and explicitly stated problem in the literature.

Tailoring Dzyaloshinskii-Moriya Interaction and Spin-Hall Topological Hall Effect in Insulating Magnetic Oxides by Interface Engineering.

Chiral spin textures, as exotic phases in magnetic materials, hold immense promise for revolutionizing logic, and memory applications. Recently, chiral spin textures have been observed in centrosymmetric magnetic insulators (FMI), due to an interfacial Dzyaloshinskii-Moriya interaction (iDMI). However, the source and origin of this iDMI remain enigmatic in magnetic insulator systems. Here, the source and origin of the iDMI in Pt/Y3Fe5O12 (YIG)/substrate structures are deeply delved by examining the spin-Hall topological Hall effect (SH-THE), an indication of chiral spin textures formed due to an iDMI. Through carefully modifying the interfacial chemical composition of Pt/YIG/substrate with a nonmagnetic Al3+ doping, the obvious dependence of SH-THE on the interfacial chemical composition for both the heavy metal (HM)/FMI and FMI/substrate interfaces is observed. The results reveal that both interfaces contribute to the strength of the iDMI, and the iDMI arises due to strong spin-orbit coupling and inversion symmetry breaking at both interfaces in HM/FMI/substrate. Importantly, it is shown that nonmagnetic substitution and interface engineering can significantly tune the SH-THE and iDMI in ferrimagnetic iron garnets. The approach offers a viable route to tailor the iDMI and associated chiral spin textures in low-damping insulating magnetic oxides, thus advancing the field of spintronics.

Edge Modes and Symmetry-Protected Topological States in Open Quantum Systems

Topological order offers possibilities for processing quantum information that can be immune to imperfections. However, the question of its stability out of equilibrium is relevant for experiments, where coupling to an environment is unavoidable. In this work, we demonstrate the robustness of certain aspects of Z2×Z2 symmetry-protected topological (SPT) order against a wide class of dissipation channels in the Lindblad and quantum trajectory formalisms of an open quantum system. This is illustrated using the one-dimensional ZXZ cluster Hamiltonian along with Pauli-string jump operators. We show that certain choices of dissipation retaining strong symmetries support a steady-state manifold consisting of two nonlocal qubits and for Hamiltonian perturbations preserving the global symmetry, states in this manifold remain metastable. In contrast, this metastability is destroyed upon breaking the above-mentioned symmetry. While the localized qubits of the cluster Hamiltonian are not conserved by the Lindbladian evolution, they do correspond to weak symmetries and thus retain a memory of their initial state at all times in the quantum trajectories. We utilize this feature to construct protocols to retrieve the quantum information either by monitoring jumps or error mitigation. Our work thus proposes a novel framework to study the dynamics of dissipative SPT phases and opens up the possibility of engineering entangled states relevant to quantum information processing. Published by the American Physical Society 2024

Symmetry-enforcing neural networks with applications to constitutive modeling

The use of machine learning techniques to homogenize the effective behavior of arbitrary microstructures has been shown to be not only efficient but also accurate. In a recent work, we demonstrated how to combine state-of-the-art micromechanical modeling and advanced machine learning techniques to homogenize complex microstructures exhibiting non-linear and history dependent behaviors (Logarzo et al., 2021). The resulting homogenized model, termed smart constitutive law (SCL), enables the adoption of microstructurally informed constitutive laws into finite element solvers at a fraction of the computational cost required by traditional concurrent multiscale approaches. In this work, the capabilities of SCLs are expanded via the introduction of a novel methodology that enforces material symmetries at the neuron level, applicable across various neural network architectures. This approach utilizes tensor-based features in neural networks, facilitating the concise and accurate representation of symmetry-preserving operations, and is general enough to be extend to problems beyond constitutive modeling. Details on the construction of these tensor-based neural networks and their application in learning constitutive laws are presented for both elastic and inelastic materials. The superiority of this approach over traditional neural networks is demonstrated in scenarios with limited data and strong symmetries, through comprehensive testing on various materials, including isotropic neo-Hookean materials and tensegrity lattice metamaterials. This work is concluded by a discussion on the potential of this methodology to discover symmetry bases in materials and by an outline of future research directions.

Bi3+-activated Na3Ca2TaO6: A novel narrow-band blue-emitting phosphor towards backlight display applications

Developing efficient and stable narrow-band blue phosphors has always been crucial for advancing LED backlighting technology. In this study, a host of Na3Ca2TaO6 with a strong rigid structure and high cationic site symmetry was selected, while Bi3+ was utilized as the activator. A novel narrow-band blue-emitting phosphor Na3Ca2TaO6:Bi3+ was obtained through high temperature solid phase sintering. The excitation peak of Na3Ca2TaO6:0.005Bi3+ is at 370 nm, which can effectively match the near-ultraviolet chip. Under near-ultraviolet light excitation, the Na3Ca2TaO6:0.005Bi3+ sample exhibits narrow-band blue emission, characterized by a dominant peak at 421 nm and a full width at half maximum of 47 nm. Additionally, Na3Ca2TaO6:Bi3+ demonstrates the color purity of 93.7 %, a quantum efficiency of 56.3 % and thermal stability of 80 %@150 °C. Based on crystal structure data, spectral data, and empirical formulas, it can be inferred that Bi3+ occupies the Na2 and Ca site and forms two luminous centers in Na3Ca2TaO6. When Na3Ca2TaO6:Bi3+ is utilized as the blue light component in WLED devices packaging, an impressive NTSC color gamut of 89.4 % can be achieved. The present study is anticipated to serve as a valuable point of reference for the future advancement of phosphors specifically tailored for backlight display applications.

Fractal analysis on the surface topography of Monocrystalline silicon wafers sawn by diamond wire

The direct impact of diamond wire slicing on the cost of subsequent silicon wafer processing underscores the significance of reducing slicing costs for both the integrated circuit and photovoltaic industries. Effectively and reasonably evaluating monocrystalline silicon wafer quality is thus a crucial challenge. In this paper, fractal theory was used to analyze the monocrystalline silicon wafer sawn surfaces combining with surface roughness measurement. The findings reveal the presence of scratches, pits, and prominent saw marks on the sawn surface. Notably, the surface roughness is significantly higher along the feed direction compared to that along the wire direction. Moreover, an increase in the ratio of feed speed to wire speed leads to a rougher surface. The fractal dimension of the sawn surface is inversely proportional to its roughness, indicating that a higher fractal dimension corresponds to a finer surface texture. Moreover, the two dimensional fractal dimension can effectively capture the anisotropic characteristics of monocrystalline silicon wafers. The two dimensional fractal dimension of the wafer surface obtained by removing materials in ductile mode has a strong symmetry. However, the two dimensional fractal dimension of the surface obtained in brittle mode fluctuates obviously and is weakly symmetric. By combining traditional surface roughness analysis with fractal methods, we can gain insights into the material removal mechanisms involved in slicing monocrystalline silicon wafers using diamond wire, which is of great significance for optimizing diamond wire slicing.

Strong symmetry breaking rhythms created by folded nodes in a pair of symmetrically coupled, identical Koper oscillators.

The Koper model is a prototype system with two slow variables and one fast variable that possesses small-amplitude oscillations (SAOs), large-amplitude oscillations (LAOs), and mixed-mode oscillations (MMOs). In this article, we study a pair of identical Koper oscillators that are symmetrically coupled. Strong symmetry breaking rhythms are presented of the types SAO-LAO, SAO-MMO, LAO-MMO, and MMO-MMO, in which the oscillators simultaneously exhibit rhythms of different types. We identify the key folded nodes that serve as the primary mechanisms responsible for the strong nature of the symmetry breaking. The maximal canards of these folded nodes guide the orbits through the neighborhoods of these key points. For all of the strong symmetry breaking rhythms we present, the rhythms exhibited by the two oscillators are separated by maximal canards in the phase space of the oscillator.

Strong Symmetry Breaking in Coupled, Identical Lengyel–Epstein Oscillators via Folded Singularities

We study pairs of symmetrically coupled, identical Lengyel-Epstein oscillators, where the coupling can be through both the fast and slow variables. We find a plethora of strong symmetry breaking rhythms, in which the two oscillators exhibit qualitatively different oscillations, and their amplitudes differ by as much as an order of magnitude. Analysis of the folded singularities in the coupled system shows that a key folded node, located off the symmetry axis, is the primary mechanism responsible for the strong symmetry breaking. Passage through the neighborhood of this folded node can result in splitting between the amplitudes of the oscillators, in which one is constrained to remain of small amplitude, while the other makes a large-amplitude oscillation or a mixed-mode oscillation. The analysis also reveals an organizing center in parameter space, where the system undergoes an asymmetric canard explosion, in which one oscillator exhibits a sequence of limit cycle canards, over an interval of parameter values centered at the explosion point, while the other oscillator executes small amplitude oscillations. Other folded singularities can also impact properties of the strong symmetry breaking rhythms. We contrast these strong symmetry breaking rhythms with asymmetric rhythms that are close to symmetric states, such as in-phase or anti-phase oscillations. In addition to the symmetry breaking rhythms, we also find an explosion of anti-phase limit cycle canards, which mediates the transition from small-amplitude, anti-phase oscillations to large-amplitude, anti-phase oscillations.

Development of a platform for experimental and computational studies of magnetic and radiative effects on astrophysically relevant jets at OMEGA

Accurate modeling of astrophysical jets is critical for understanding accretion systems and their impact on the interstellar medium. While astronomical observations can validate models, they have limitations. Controlled laboratory experiments offer a complementary approach for qualitative and quantitative demonstration. Laser experiments offer a complementary approach. This article introduces a new platform on the OMEGA laser facility for high-velocity (1500 kms−1), high-aspect-ratio (∼36) jet creation with strong cylindrical symmetry. This platform's capabilities bridge observational gaps, enabling controlled initial conditions and direct measurements of plasma characteristics, crucial for refining astrophysical jet dynamics and improving the models accuracy.

Observation of time-reversal symmetry breaking in the band structure of altermagnetic RuO2.

Altermagnets are an emerging elementary class of collinear magnets. Unlike ferromagnets, their distinct crystal symmetries inhibit magnetization while, unlike antiferromagnets, they promote strong spin polarization in the band structure. The corresponding unconventional mechanism of time-reversal symmetry breaking without magnetization in the electronic spectra has been regarded as a primary signature of altermagnetism but has not been experimentally visualized to date. We directly observe strong time-reversal symmetry breaking in the band structure of altermagnetic RuO2 by detecting magnetic circular dichroism in angle-resolved photoemission spectra. Our experimental results, supported by ab initio calculations, establish the microscopic electronic structure basis for a family of interesting phenomena and functionalities in fields ranging from topological matter to spintronics, which are based on the unconventional time-reversal symmetry breaking in altermagnets.

Morphological and functional parameters in X-linked retinoschisis patients-A multicentre retrospective cohort study.

X-linked retinoschisis (XLRS) is a potential target for gene supplementation approaches. To establish potential structural and functional endpoints for clinical trials, a comprehensive understanding of the inter-eye symmetry, relationship between structural and functional parameters, and disease progression is vital. In this retrospective multicentre study, 118 eyes of 59 XLRS patients with RS1 mutations were assessed. Information from center databases included: RS1 variant; age at presentation; best-corrected visual acuity (BCVA), central retinal thickness (CRT), macular volume (MV) at presentation and at the last follow up; full-field electroretinogram (ERG) findings; presence of peripheral retinoschisis and complications (vitreous hemorrhage, retinal detachment); treatment with systemic or topical carbonic anhydrase inhibitors (CAI). Inter-eye symmetry revealed strong correlation in CRT (r = 0.77; p < 0.0001) and moderate correlations in MV (r = 0.51, p < 0.0001) and BCVA (r = 0.49; p < 0.0001). Weak or no correlations were observed between BCVA and structural parameters (CRT, MV). Peripheral retinoschisis was observed in 40 (68%), retinal detachment in 9 (15%), and vitreous hemorrhage in 5 (8%) patients, respectively. Longitudinal examinations (mean, 4.3 years) showed no BCVA changes; however, a reduction of the CRT (p = 0.02), and MV (p = 0.01) was observed. Oral and/or topical CAI treatment did not significantly alter the CRT (p = 0.34). The XLRS phenotype demonstrates a strong CRT symmetry between the eyes within individual patients and stable BCVA over several years. BCVA exhibits a weak correlation with the morphological parameters of retinal thickness (CRT MV). In our cohort, longitudinal functional changes were not significant, likely attributed to the short average follow-up period. Furthermore, CAI treatment didn't influence both morphological and functional outcomes.

Atomic-Layer Controlled Transition from Inverse Rashba-Edelstein Effect to Inverse Spin Hall Effect in 2D PtSe2 Probed by THz Spintronic Emission.

2D materials, such as transition metal dichalcogenides, are ideal platforms for spin-to-charge conversion (SCC) as they possess strong spin-orbit coupling (SOC), reduced dimensionality and crystal symmetries as well as tuneable band structure, compared to metallic structures. Moreover, SCC can be tuned with the number of layers, electric field, or strain. Here, SCC in epitaxially grown 2D PtSe2 by THz spintronic emission is studied since its 1T crystal symmetry and strong SOC favor SCC. High quality of as-grown PtSe2 layers is demonstrated, followed by in situ ferromagnet deposition by sputtering that leaves the PtSe2 unaffected, resulting in well-defined clean interfaces as evidenced with extensive characterization. Through this atomic growth control and using THz spintronic emission, the unique thickness-dependent electronic structure of PtSe2 allows the control of SCC. Indeed, the transition from the inverse Rashba-Edelstein effect (IREE) in 1-3 monolayers (ML) to the inverse spin Hall effect (ISHE) in multilayers (>3 ML) of PtSe2 enabling the extraction of the perpendicular spin diffusion length and relative strength of IREE and ISHE is demonstrated. This band structure flexibility makes PtSe2 an ideal candidate to explore the underlying mechanisms and engineering of the SCC as well as for the development of tuneable THz spintronicemitters.

Revealing the Interplay between Strong Field Selection Rules and Crystal Symmetries

Revealing the Interplay between Strong Field Selection Rules and Crystal Symmetries

Robustness of quantum spin Hall effect-inspired edge modes depending on C6 symmetry in topological diffusion systems

We investigate the robustness of a quantum spin Hall effect-inspired topological edge modes in a thermal diffusion system consisting of honeycomb-shaped structures. The robustness of the edge modes deteriorates because of the contributions of C6 symmetry breaking, thus resulting in the appearance of a large gap at the band-crossing point in the decay rate spectra. An interaction between more than two boundaries also leads to poor robustness, whereas strong C6 symmetry breaking improves the robustness deteriorated by such boundary interactions. Our study provides a guide for designing a robust edge mode with a desired decay rate in topological diffusion systems.

Robust photogalvanic effect, full spin polarization and pure spin current in the BiC photodetector by vacancy and substitution-doping

The photogalvanic effects (PGEs) in low-dimensional devices have attracted great interests recently. Herein, based on non-equilibrium Green’s function combined with density functional theory, we investigated spin-dependent PGE phenomena in the BiC photodetector with the linearly polarized light and zero bias. Due to the presence of strong spin–orbit interaction (SOI) and C 3v symmetry for the BiC monolayer, the armchair and zigzag BiC photodetectors can produce robust spin-dependent PGEs which possess the cos(2θ) and sin(2θ) relations on the photon energies, respectively. Especially, the pristine armchair and armchair Bi-vacancy BiC photodetectors can produce fully spin polarization, and pure spin current was found in the pristine armchair and zigzag BiC photodetector, respectively. Furthermore, after introducing the Bi-vacancy, C-vacancy, Bi-doping and C-doping respectively, the BiC photodetector can produce higher spin-dependent PGEs for their C s symmetry. Additionally, the behaviors of spin-dependent photoresponse are highly anisotropic which can be tuned by the photon energy. This work suggested great potential applications of the BiC monolayer on PGE-driven photodetectors in low energy-consumption optoelectronics and spintronic devices.

Momentum-space spin texture induced by strain gradient in nominally centrosymmetric SrIrO3 films

ABSTRACT Spin texture in k-space is a consequence of spin splitting due to strong spin–orbit coupling and inversion symmetry breaking. It underlies fertile spin transport phenomena and is of crucial importance for spintronics. Here, we observe the spin texture in k-space of nominally centrosymmetric SrIrO3 grown on NdGaO3 (110) substrates, using non-linear magnetotransport measurements. We demonstrate that the spin texture is not only induced by the interface, which inherently breaks the inversion symmetry in strong spin–orbit coupled SrIrO3 films, but also originates from the film bulk. Structural analysis reveals that thicker SrIrO3 films exhibit a strain gradient, which could be considered as a continuous change in the lattice constant across different layers and breaks the inversion symmetry throughout the entire SrIrO3 films, giving rise to the spin texture in k-space. First-principles calculations reveal that the strain gradient creates large spin-splitting bands, inducing the spin texture with anisotropy, which is consistent with our experimental observations. Our results offer an efficient method for inducing the spin textures in k-space.