Complex Symmetry Research Articles

Higher-order and fractional discrete time crystals in Floquet-driven Rydberg atoms

Higher-order and fractional discrete time crystals (DTCs) are exotic phases of matter where the discrete time translation symmetry is broken into higher-order and non-integer category. Generation of these unique DTCs has been widely studied theoretically in different systems. However, no current experimental methods can probe these higher-order and fractional DTCs in any quantum many-body systems. We demonstrate an experimental approach to observe higher-order and fractional DTCs in Floquet-driven Rydberg atomic gases. We have discovered multiple n-DTCs with integer values of n = 2, 3, and 4, and others ranging up to 14, along with fractional n-DTCs with n values beyond the integers. The system response can transition between adjacent integer DTCs, during which the fractional DTCs are investigated. Study of higher-order and fractional DTCs expands fundamental knowledge of non-equilibrium dynamics and is promising for discovery of more complex temporal symmetries beyond the single discrete time translation symmetry.

The Ordered Structures Formed by Janus-like Particles on a Triangular Lattice.

The formation of ordered structures by Janus-like particles, composed of two parts (A and B), with orientation-dependent interactions on a triangular lattice was studied using Monte Carlo methods. The assumed lattice model allows each particle to take on one of the six orientations. The interaction between the A parts of neighboring particles was assumed to be attractive, while the AB and BB interactions were assumed to be repulsive. Moreover, it was assumed that the interaction between a pair of neighboring particles depended on the degrees to which their AA, AB, and BB parts face each other. It was shown that several ordered phases of different densities and structures may appear, depending on the magnitudes of AB and BB interactions. In particular, we found several structures composed of small clusters consisting of three (OT), four (OR), and seven (S) particles, surrounded by empty sites, the lamellar phases (OL, OL1, and OL3), the structures with hexagonal symmetry (R3×3 and K), as well as the structures with more complex symmetry (R5×5 and LAD). Several phase diagrams were evaluated, which demonstrated that the stability regions of different ordered phases are primarily determined by the strengths of repulsive AB and BB interactions.

Advanced terahertz refractive index sensor in all-dielectric metasurface utilizing second order toroidal quasi-BIC modes for biochemical environments

We present a novel design for an all-dielectric metasurface ultra-sensitive refractive index (RI) sensor, characterized by a high-quality factor (Qf) and figure of merit (FOM). This design incorporates two high-order toroidal modes, including electric toroidal quadrupole (\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{Q}_{T}^{e}$$\\end{document}​) and magnetic toroidal quadrupole (\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{Q}_{T}^{m}$$\\end{document}​) based on quasi‑bound states in the continuum (q-BIC) resonances. Our findings demonstrate the feasibility of switching between \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{Q}_{T}^{e}$$\\end{document} and \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{Q}_{T}^{m}$$\\end{document}​ through various symmetry-breaking mechanisms. To excite these high-order toroidal modes, we explored several symmetry-breaking strategies, including complex structural designs, symmetry disruption, and variations in the incident wave angle. Symmetry breaking in the structure induces new modes in the transmission spectrum, which are highly advantageous for sensing applications due to the presence of dark modes. The designed metasurface exhibits the capability to sense a broad range of RI in diverse environments, particularly in biochemical fields. Sensitivity (S) is significantly enhanced by the excitation of new resonance modes and adjustments in the incidence angle, increasing from 217 GHz/RIU in a symmetrical structure to 512.3 GHz/RIU for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{Q}_{T}^{e}$$\\end{document}​. The FOM improves from 197 RIU 1 to 8538 RIU− 1 for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{Q}_{T}^{e}$$\\end{document}​ and 152,395 RIU− 1 for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{Q}_{T}^{m}$$\\end{document}​. Additionally, the Qf rises from 872 to 17,983 and 921,351 for \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{Q}_{T}^{e}$$\\end{document}​ and \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\:{Q}_{T}^{m}$$\\end{document}​, respectively.

Automated model discovery for textile structures: The unique mechanical signature of warp knitted fabrics

Textile fabrics have unique mechanical properties, which make them ideal candidates for many engineering and medical applications: They are initially flexible, nonlinearly stiffening, and ultra-anisotropic. Various studies have characterized the response of textile structures to mechanical loading; yet, our understanding of their exceptional properties and functions remains incomplete. Here we integrate biaxial testing and constitutive neural networks to automatically discover the best model and parameters to characterize warp knitted polypropylene fabrics. We use experiments from different mounting orientations, and discover interpretable anisotropic models that perform well during both training and testing. Our study shows that constitutive models for warp knitted fabrics are highly sensitive to an accurate representation of the textile microstructure, and that models with three microstructural directions outperform classical orthotropic models with only two in-plane directions. Strikingly, out of 214=16,384 possible combinations of terms, we consistently discover models with two exponential linear fourth invariant terms that inherently capture the initial flexibility of the virgin mesh and the pronounced nonlinear stiffening as the loops of the mesh tighten. We anticipate that the tools we have developed and prototyped here will generalize naturally to other textile fabrics–woven or knitted, weft knit or warp knit, polymeric or metallic–and, ultimately, will enable the robust discovery of anisotropic constitutive models for a wide variety of textile structures. Beyond discovering constitutive models, we envision to exploit automated model discovery as a novel strategy for the generative material design of wearable devices, stretchable electronics, and smart fabrics, as programmable textile metamaterials with tunable properties and functions. Our source code, data, and examples are available at https://github.com/LivingMatterLab/CANN. Statement of significanceTextile structures are rapidly gaining popularity in many biomedical applications including tissue engineering, wound healing, and surgical repair. A precise understanding of their unique mechanical properties is critical to tailor them to their specific functions. Here we integrate mechanical testing and machine learning to automatically discover the best models for knitted polypropylene fabrics. We show that warp knitted fabrics possess a complex symmetry with three distinct microstructural directions. Along these, the behavior is dominated by an exponential linear term that characterize the initial flexibility of the virgin mesh and the nonlinear stiffening as the loops of the fabric tighten. We expect that our technology will generalize naturally to other fabrics and enable the robust discovery of complex anisotropic models for a wide variety of textile structures.

Quantum inspired kernel matrices: Exploring symmetry in machine learning

Quantum machine learning, an emerging field at the intersection of quantum computing and classical machine learning, has shown great promise in enhancing computational capabilities beyond classical bounds. A key element in this area of research is the utilization of Quantum Kernel Estimators, traditionally grounded in the symmetries of SU(2) groups associated with qubits. This study extends the conceptual framework of Quantum Kernel Estimators to incorporate a broader spectrum of symmetry groups. By harnessing the various structures of Lie groups, we develop novel quantum-inspired feature maps that offer more flexible and potentially powerful ways to encode and compress classical data into quantum states. We present a comprehensive theoretical introduction for this approach, followed by a methodology that integrates the developed feature maps into quantum-inspired kernel classifiers. Our results, derived from a series of computational experiments across various datasets, demonstrate the efficacy of this approach in comparison to traditional quantum and classical machine learning models. The findings not only underline the versatility of Lie-group theory in potentially enhancing quantum machine learning algorithms but also open new avenues for exploring complex symmetries in quantum information processing. This research bridges a gap between the study of symmetries and machine learning, paving the way for more sophisticated quantum algorithms capable of tackling complex, high-dimensional data in ways previously unattainable.

Ice Phase Classification Made Easy with Score-Based Denoising.

Accurate identification of ice phases is essential for understanding various physicochemical phenomena. However, such classification for structures simulated with molecular dynamics is complicated by the complex symmetries of ice polymorphs and thermal fluctuations. For this purpose, both traditional order parameters and data-driven machine learning approaches have been employed, but they often rely on expert intuition, specific geometric information, or large training data sets. In this work, we present an unsupervised phase classification framework that combines a score-based denoiser model with a subsequent model-free classification method to accurately identify ice phases. The denoiser model is trained on perturbed synthetic data of ideal reference structures, eliminating the need for large data sets and labeling efforts. The classification step utilizes the smooth overlap of atomic position (SOAP) descriptors as the atomic fingerprint, ensuring Euclidean symmetries and transferability to various structural systems. Our approach achieves a remarkable 100% accuracy in distinguishing ice phases of test trajectories using only seven ideal reference structures of ice phases as model inputs. This demonstrates the generalizability of the score-based denoiser model in facilitating phase identification for complex molecular systems. The proposed classification strategy can be broadly applied to investigate structural evolution and phase identification for a wide range of materials, offering new insights into the fundamental understanding of water and other complex systems.

Embracing disorder in quantum materials design

Many of the most exciting materials discoveries in fundamental condensed matter physics are made in systems hosting some degree of intrinsic disorder. While disorder has historically been regarded as something to be avoided in materials design, it is often of central importance to correlated and quantum materials. This is largely driven by the conceptual and theoretical ease to handle, predict, and understand highly uniform systems that exhibit complex interactions, symmetries, and band structures. In this Perspective, we highlight how flipping this paradigm has enabled exciting possibilities in the emerging field of high entropy materials, focusing primarily on high entropy oxide and chalcogenide quantum materials. These materials host high levels of cation or anion compositional disorder while maintaining unexpectedly uniform single crystal lattices. The diversity of atomic scale interactions of spin, charge, orbital, and lattice degrees of freedom are found to emerge into coherent properties on much larger length scales. Thus, altering the variance and magnitudes of the atomic scale properties through elemental selection can open new routes to tune global correlated phases, such as magnetism, metal–insulator transitions, ferroelectricity, and even emergent topological responses. The strategy of embracing disorder in this way provides a much broader pallet from which functional states can be designed for next-generation microelectronic and quantum information systems.

Complex symmetry in the Fock space of several variables

In this paper we study the complex symmetry in the several variable Fock space by using the techniques of weighted composition operators and semigroups. We characterize unbounded weighted composition operators that are (real) complex symmetric with respect to a concrete conjugation. Using this characterization, we study complex symmetric semigroups and their generators. We realize such generators as first-order differential operators.

Complexity growth patterns in the Big History: Preliminary results of a quantitative analysis

The paper presents preliminary results of a quantitative analysis of two patterns of complexity growth in the Big History – decelerating universal (cosmic) evolutionary development evidenced in the Universe for a few billions of years after the Big Bang (around 13.8 billion BP) and accelerating global (biosocial) evolutionary development observed for about 4 billion years on the planet Earth since the emergence of life on it and until the early 1970s. It is shown that the first pattern can be described with an astonishing accuracy (R2 = 0.999996) by the following equation: y = C1/(t-t1*), where y is the rate of the universal complexity growth (measured as a number of phase transitions [accompanied by the growth of complexity] per a unit of time), C1 is a constant, and t-t1* is the time since the Big Bang Singularity (t1*~13.8 billion years BP). In the meantime, it was earlier shown that the second pattern could be described with an almost as high accuracy (R2 = 0.9989 to 0.9991) by the following equation: y = C2/(t2*-t), where y is the rate of accelerating global (biosocial) evolutionary development, C2 is another constant, and t2*-t is the time till the 21st century Singularity (t2*, estimated to be around 2027, or 2029 CE). Thus, the post-Big-Bang hyperbolic decrease of universal complexity growth rate and the hyperbolic increase of the growth rate of global complexity in the last 4 billion years proceeded following the same law. We are dealing here with a perfect symmetry: (1) the rate of the universal (cosmic) complexity growth decreases when we move from the Big Bang Singularity, whereas the rate of the global complexity growth increase when we approach the 21st century Singularity; (2) more specifically, as the time since the Big Bang Singularity increases n times, the universal (cosmic) complexity growth rate decreases the same n times, whereas when the time till the 21st century Singularity decreased n times, the global complexity growth rate increased the same n times. A somehow more complex symmetry is observed as regards the interaction between energy dynamics and complexity growth within both processes. The implications of the symmetry of both patterns are discussed.

3-Complex Symmetric and Complex Normal Weighted Composition Operators on the Weighted Bergman Spaces of the Half-Plane

One of the aims of this paper is to characterize 3-complex symmetric weighted composition operators induced by three types of symbols on the weighted Bergman space of the right half-plane with the conjugation Jf(z)=f(z¯)¯. It is well known that the complex symmetry is equivalent to 2-complex symmetry for the weighted composition operators studied in the paper. However, the interesting fact that 3-complex symmetry is not equivalent to 2-complex symmetry for such operators is found in the paper. Finally, the complex normal of such operators on the weighted Bergman space of the right half-plane with the conjugation J is characterized.

Complex Symmetry of Linear Combinations of Composition Operators on the McCarthy–Bergman Space of Dirichlet Series

The complex symmetric linear combinations of composition operators on the McCarthy–Bergman spaces of Dirichlet series are completely characterized. The normality and self-adjointness of complex symmetric linear combinations of composition operators on such spaces are also characterized. Some images are given in order to find some interesting phenomena of J\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$${\\mathcal {J}}$$\\end{document}-symmetric such combinations.

Conformational polymorphs of the homoleptic scorpionate sandwich complex [(TpPh,Me)2Ni], TpPh,Me=hydrotris(3-phenyl-5-methylpyrazol-1-yl)borate: Ligand substituent effects include intramolecular non-covalent interactions

The homoleptic scorpionate sandwich complex [(TpPh,Me)2Ni] (1), where TpPh,Me = hydrotris(3-phenyl-5-methylpyrazol-1-yl)borate, crystallizes as a mixture of two polymorphs. A major monoclinic fraction crystallizes as well-formed parallelepipeds and a minor triclinic fraction forms irregularly shaped, anhedral crystals. These exhibit distinct melting points (288 and 294 °C, respectively) as observed by differential scanning calorimetry. We obtained X-ray crystal structures of both polymorphs at 100 K. The complex adopts different conformations between the two lattices. These are supported by distinctive ensembles of intramolecular non-covalent interactions, specifically π-stacking and perpendicular C–H···π contacts between opposing 3-phenylpyrazolyl arms on the co-ligands. The conformation found in the major monoclinic polymorph consists of a counter-rotation of the ligands that reduces the ideal complex symmetry from D3d to D3 and results in three-fold pair-wise association of 3-phenylpyrazolyl arms. In contrast, an alternate conformation of 1 in the minor triclinic polymorph consists of two triads, with an ideal complex symmetry of C2h. Also affected are the tetragonality of the ligand fields and interligand N–Ni–N′ bond angles. A review of sandwich complex structures [(TpR)2M], where R is an aromatic substituent, shows these conformations are adopted broadly. Hence, substituent effects in second-generation scorpionate ligands are not merely steric in origin.

Factors influencing the shape, size, symmetry and scar of the nipple-areola complex after bilateral reduction mammoplasty.

Asymmetry and scar formation of the nipple-areola complex (NAC) after reduction mammoplasty with periareolar suture are common complications and can significantly affect patient satisfaction. The aim of this study was to investigate possible procedure-specific influencing factors on asymmetry and shape disturbances of the nipple-areola complex to optimize postoperative outcome and thus improve patient satisfaction. 78 patients were followed-up after a 5-year period as part of a retrospective cohort study. Objective parameters as areolar diameter, symmetry, scar patterns, dimensions of the breast, and anthropometric measurements were recorded. All patients underwent surgery according to an established treatment algorithm depending on the preoperative measurements. Follow up was 1 week, 6 week, 6 months and 3 years postoperatively. The periareolar suture-technique significantly influenced the symmetry and shape of the NAC. Compared to the intraoperative determined diameter and the postoperative diameter, the net-suture technique showed the highest NAC symmetry and minimal divergence. Patients who underwent Hall-Findlay mammoplasty showed significantly higher rates of asymmetry and deformity of the NAC with teardrop formation in comparison to Lejour mammoplasty. Scar formation was affected by periareolar ruffle formation especially after purse string suture. Regardless of what reduction mammoplasty techniques and periareolar suturing-technique are used, a tension-free suture of the NAC is crucial for shape, symmetry and scar formation. The net suture technique resulted in significantly higher symmetry of the NAC.

Complex Connections between Symmetry and Singularity Analysis

In this paper, it is noted that three apparently disparate areas of mathematics—singularity analysis, complex symmetry analysis and the distributional representation of special functions—have a basic commonality in the underlying methods used. The insights obtained from the first of these provides a much-needed explanation for the effectiveness of the latter two. The consequent explanations are provided in the form of two theorems and their corollaries.

Commutants and complex symmetry of finite Blaschke product multiplication operator in

AbstractConsider the multiplication operator MB in $L^2(\mathbb{T})$, where the symbol B is a finite Blaschke product. In this article, we characterize the commutant of MB in $L^2(\mathbb{T})$. As an application of this characterization result, we explicitly determine the class of conjugations commuting with $M_{z^2}$ or making $M_{z^2}$ complex symmetric by introducing a new class of conjugations in $L^2(\mathbb{T})$. Moreover, we analyse their properties while keeping the whole Hardy space, model space and Beurling-type subspaces invariant. Furthermore, we extended our study concerning conjugations in the case of finite Blaschke products.

Controlling the symmetry of hexamonodentate 3d-transition metal complexes through symmetry propagation from high-symmetry Ti-Mo and Zr-Mo clusters via hydrogen-bonding interactions.

The symmetry of one of the simplest hexamonodentate complexes, [M(H2O)6]2+ (M = Fe, Co, Ni, and Zn), was controlled by tuning interactions in the second coordination sphere. Highly symmetric Ti-Mo or Zr-Mo cluster cations acted as symmetry templates, imposing a crystallographic trigonal coordination geometry in the hexamonodentate complexes through intermolecular hydrogen-bonding interactions. Magnetic measurements revealed that the ideal trigonal symmetry results in weak spin-orbit coupling for high-spin FeII complexes, despite the T-term ground state in the octahedral geometry. In contrast, high-spin CoII analogues with the T-term ground state exhibited strong spin-orbit coupling. DFT studies supported that a d6 FeII ion in the D3 symmetry has a 5A1 ground state while a d7 CoII in the same symmetry has a 4E ground state. Single-ion magnet behavior was observed in the CoII complexes. These results demonstrate that incorporating a diamagnetic, highly symmetric cluster enables precise symmetry control in single-ion magnets containing only monodentate ligands.

Complex Rayleigh–van-der-Pol–Duffing Oscillators: Dynamics, Phase, Antiphase Synchronization, and Image Encryption

This paper introduces the complex Rayleigh–van-der- Pol–Duffing oscillators (RVDOs), which are hyperchaotic and can be autonomous or nonautonomous. The fundamental dynamics of the autonomous and nonautonomous complex RVDOs, including dissipation, symmetry, fixed points, and stability, are studied. These oscillators are found in various necessary fields of physics and engineering. The paper proposes a scheme to achieve phase synchronization (PS) and antiphase synchronization (APS) for different dimensional models. These kinds of synchronization are considered a generalization of several other types of synchronization. We use the active control method based on Lyapunov’s stability theory for this scheme. By analytically determining the control functions, the scheme achieved PS and APS. Our scheme is applied to study the PS of hyperchaotic behaviors for two distinct hyperchaotic nonautonomous and autonomous complex RVDOs. Additionally, the scheme is employed to achieve the APS of a chaotic real nonautonomous RVDO and a hyperchaotic complex autonomous RVDO, including those with different dimensions. Our work presents numerical results that plot the amplitudes and phases of these hyperchaotic behaviors, demonstrating the achievement of the PS and APS. The encryption and decryption of grayscale images are researched based on APS. The experimental results of image encryption and decryption are computed with information entropy, visual analysis, and histograms.

Planar fault transformation and unfaulting of interstitial dislocation loops in irradiated L12-Ni3Al

The present study has systematically investigated unfaulting mechanism of single-layer interstitial dislocation Loops (IDLs) in irradiated L12-Ni3Al to extend the existing unfaulting theory from pristine FCC lattice to the L12 ordered lattice, employing atomistic simulations combining continuum theory. Two types of variants for the IDLs have been determined with different planar faults enclosed in the Frank loop. The unfaulting routes of IDLs by Shockley partial loops have been unveiled through examining the energy barriers of superlattice planar fault transformation. The symmetry breaking occurring in the unfaulting processes were further elucidated and summarized. A continuum model has been formulated to enable quantitative theoretical analysis of the energetics of IDLs and prediction of the unfaulting threshold. These findings clarify the effects of complex faults and symmetry breaking on unfaulting behaviors of IDLs in irradiated L12-Ni3Al, and could be transferable to other L12 systems, and more generally, other ordered alloy systems.

Методика вивчення симетрії елементарних частинок в ЗВО

The article addresses the current issue of teaching symmetry in elementary particles within technicalhigher education institutions. The study of symmetry in elementary particles plays a vital role in helpingstudents understand the fundamental laws of nature and the properties of fundamental particles. However,symmetry is a complex concept that requires deep understanding and analysis. To successfully master thisintricate topic in an educational environment, effective teaching methods and tools need to be developed.Modern students demand an active and engaging approach to learning, making the use of innovative methodscritically important.The article presents an analysis of contemporary approaches to teaching symmetry in elementaryparticles within higher education institutions. It places significant emphasis on innovative methodologiesdesigned to help students grasp complex symmetry concepts in physics. Specifically, it discusses the utilizationof modern pedagogical technologies, interactive tools, virtual laboratories, and computer simulations. Thepractical aspects of conducting laboratory work and experimental research focused on studying symmetry arealso explored.The article explores possible ways to enhance the effectiveness of teaching in this field. An essentialpart of the article involves analyzing the impact of symmetry education on the professional training of futureexperts in the field of physics and related sciences. Achievements in the study of symmetry also necessitate an33effective assessment system. It is crucial to consider the knowledge and skills acquired by students in this fieldso that they can independently analyze and apply symmetrical principles in their further research.The prospects for further scientific research involve the investigation of modern approaches to physicseducation, including the use of computer simulations, virtual laboratories, and interactive learning tools. Theseinnovations contribute to a better understanding of complex symmetry concepts. Research in this direction canhelp develop effective pedagogical approaches and tools that support students in the process of studyingsymmetry in elementary particles and enhance the quality of physics education.

Harnessing Proton-Coupled Electron Transfer for Hydrogenation of Aza-Arenes: Photochemistry of Quinoxaline Derivatives in Methanol.

Three quinoxaline derivatives are investigated both experimentally and theoretically to assess their ability for the methanol oxidation and harvesting of hydrogen. In inert solvents, the nonplanar compounds exhibit very weak fluorescence from the lowest excited singlet state, whereas the planar and rigid chromophore emits non-Kasha fluorescence from the S2(ππ*) state despite the proximity of the S1(nπ*) state. In methanol, hydrogen-bonded complexes with solvent molecules are formed, and in all chromophores, the lowest singlet state is populated after excitation of the S2(ππ*) state. The switch from non-Kasha emission of the planar compound in inert solvents to regular emission in methanol is related to reduced symmetry of the hydrogen-bonded complex with methanol which results in effective mixing of ππ* and nπ* states and fast internal conversion to the lowest excited singlet state. The S1(nπ*) state of the hydrogen-bonded complex has charge-transfer character, and for all compounds in methanol, hydrogen transfer to the chromophore is observed. The chromophores retain the transferred hydrogen atoms, serving both as photocatalysts and as hydrogen storage materials. Undesired dark side reactions that occur are also discussed.