Symmetry Space Research Articles

The energy quantization in hydrogen atom and proton–electron mass ratio in light of symmetrical special relativity

In this paper, we show the existence of an invariant minimum speed in space–time by forming the basis of a deformed special relativity so-called symmetrical special relativity (SSR). Such observer-independent minimum speed emerges from Dirac’s large number hypothesis (LNH), which leads us to build SSR-theory. This allows us to understand that the hydrogen atom represents the most stable bound state in the universe as being a fundamental structure of the symmetrical space–time with two limits of speed, namely the speed of light c and a minimum speed V. Such minimum speed is associated with a background reference frame for representing the vacuum energy related to the cosmological constant. So the symmetry in space–time given by the invariant minimum speed, which has origin in the electrical and gravitational bound states in hydrogen atom is able to provide a deeper understanding of the proton-electron mass ratio, i.e. [Formula: see text] given in terms of the universal minimum speed V. Furthermore, we investigate how the minimum speed in space–time plays a fundamental role in the quantization of energy in hydrogen atom.

Perturbative Framework for Engineering Arbitrary Floquet Hamiltonian.

We develop a systematic perturbative framework to engineer an arbitrary target Hamiltonian in the Floquet phase space of a periodically driven oscillator based on Floquet-Magnus expansion. The high-order errors in the engineered Floquet Hamiltonian are mitigated by adding high-order driving potentials perturbatively. We introduce a transformation method that allows us to obtain an analytical expression of the leading-order correction drive for engineering a target Hamiltonian with discrete rotational and chiral symmetries in phase space. We also provide a numerically efficient procedure to calculate high-order correction drives and apply it to engineer the target Hamiltonian with degenerate eigenstates of multi-component cat states that are important for fault-tolerant hardware-efficiency bosonic quantum computation.

Quantum Brownian motion induced by a scalar field in Einstein’s universe under Dirichlet and Neumann boundary conditions

In this paper, the quantum Brownian motion of a point particle induced by the quantum vacuum fluctuations of a real massless scalar field in Einstein’s universe under Dirichlet and Neumann boundary conditions is studied. Using the Wightman functions, general expressions for the renormalized dispersion of the physical momentum are derived. Distinct expressions are found for the dispersion associated with each component of the particle’s physical momentum, indicating that the global properties of homogeneity and isotropy of space are lost, as a consequence of the introduced boundary conditions. Divergences also arise and are related to the compact nature of Einstein’s universe and the introduced boundary conditions.

Kohn-Sham inversion for open-shell systems.

Methods based on density-functional theory usually treat open-shell atoms and molecules within the spin-unrestricted Kohn-Sham (KS) formalism, which breaks symmetries in real and spin space. Symmetry breaking is possible because the KS Hamiltonian operator does not need to exhibit the full symmetry of the physical Hamiltonian operator, but only the symmetry of the spin density, which is generally lower. Symmetry breaking leads to spin contamination and prevents a proper classification of the KS wave function with respect to the symmetries of the physical electron system. Formally well-justified variants of the KS formalism that restore symmetries in real space, in spin space, or in both have been introduced long ago, but have rarely been used in practice. Here, we introduce numerically stable KS inversion methods to construct reference KS potentials from reference spin-densities for all four possibilities to treat open shell systems, non-symmetrized, spin-symmetrized, space-symmetrized, and fully-symmetrized. The reference spin-densities are obtained by full configuration interaction and high-level coupled cluster methods for the considered atoms and diatomic molecules. The decomposition of the total energy in contributions such as the non-interacting kinetic, the exchange, and the correlation energy is different in the four KS formalisms. Reference values for these differences are provided for the considered atoms and molecules. All KS inversions, except the fully symmetrized one, lead in some cases to solutions violating the Aufbau principle. In the purely spin-symmetrized KS formalism, this represents a violation of the KS v-representability condition, i.e., no proper KS wave functions exist in those cases.

Shear viscoelasticity in anisotropic holographic axion model

Abstract In this work, we investigate the shear elasticity and the shear viscosity in a simple holographic axion model with broken translational symmetry and rotational symmetry in space via the perturbation computation. We find that, in the case of spontaneous symmetry breaking, the broken translations and anisotropy both enhance the shear elasticity of the system. While in all cases, the broken symmetries introduce a double suppression on the shear viscosity, which is in contrast to the result from the study of the p-wave holographic superfluid where the shear viscosity is enhanced when the rotational symmetry is broken spontaneously.

STNeRF: symmetric triplane neural radiance fields for novel view synthesis from single-view vehicle images

This paper presents STNeRF, a method for synthesizing novel views of vehicles from single-view 2D images without the need for 3D ground truth data, such as point clouds, depth maps, CAD models, etc., as prior knowledge. A significant challenge in this task arises from the characteristics of CNNs and the utilization of local features can lead to a flattened representation of the synthesized image when training and validation with images from a single viewpoint. Many current methodologies tend to overlook local features and rely on global features throughout the entire reconstruction process, potentially resulting in the loss of fine-grained details in the synthesized image. To tackle this issue, we introduce Symmetric Triplane Neural Radiance Fields (STNeRF). STNeRF employs a triplane feature extractor with spatially aware convolution to extend 2D image features into 3D. This decouples the appearance component, which includes local features, and the shape component, which consists of global features, and utilizes them to construct a neural radiance field. These neural priors are then employed for rendering novel views. Furthermore, STNeRF leverages the symmetric properties of vehicles to liberate the appearance component from reliance on the original viewpoint and to align it with the symmetry of the target space, thereby enhancing the neural radiance field network’s ability to represent the invisible regions. The qualitative and quantitative evaluations demonstrate that STNeRF outperforms existing solutions in terms of both geometry and appearance reconstruction. More supplementary materials and the implementation code are available for access at the following link: https://github.com/ll594282475/STNeRF.

Strong Magneto‐chiroptical Effects through Introducing Chiral Transition‐metal Complex Cations to Lead Halide

The interplay between chirality with magnetism can break both the space and time inversion symmetry and have wide applications in information storage, photodetectors, multiferroics and spintronics. Herein, we report the chiral transition‐metal complex cation‐based lead halide, R‐CDPB and S‐CDPB. In contrast with the traditional chiral metal halides with organic cations, a novel strategy for chirality transfer from the transition‐metal complex cation to the lead halide framework is developed. The chiral complex cations directly participate the band structure and introduce the d‐d transitions and tunable magneto‐chiroptical effects in both the ultraviolet and full visible range into R‐CDPB and S‐CDPB. Most importantly, the coupling between magnetic moment of the complex cation and chiroptical properties is confirmed by the magneto‐chiral dichroism. For the band‐edge transition, the unprecedented modulation of +514% for S‐CDPB and ‐474% for R‐CDPB was achieved at ‐1.3 Tesla. Our findings demonstrate a novel strategy to combine chirality with magnetic moment, and provide a versatile material platform towards magneto‐chiroptical and chiro‐spintronic applications.

Strong Magneto-Chiroptical Effects through Introducing Chiral Transition-Metal Complex Cations to Lead Halide.

The interplay between chirality with magnetism can break both the space and time inversion symmetry and have wide applications in information storage, photodetectors, multiferroics and spintronics. Herein, we report the chiral transition-metal complex cation-based lead halide, R-CDPB and S-CDPB. In contrast with the traditional chiral metal halides with organic cations, a novel strategy for chirality transfer from the transition-metal complex cation to the lead halide framework is developed. The chiral complex cations directly participate the band structure and introduce the d-d transitions and tunable magneto-chiroptical effects in both the ultraviolet and full visible range into R-CDPB and S-CDPB. Most importantly, the coupling between magnetic moment of the complex cation and chiroptical properties is confirmed by the magneto-chiral dichroism. For the band-edge transition, the unprecedented modulation of +514 % for S-CDPB and -474 % for R-CDPB was achieved at -1.3 Tesla. Our findings demonstrate a novel strategy to combine chirality with magnetic moment, and provide a versatile material platform towards magneto-chiroptical and chiro-spintronic applications.

Spectral representation of cosmological correlators

Cosmological correlation functions are significantly more complex than their flat-space analogues, such as tree-level scattering amplitudes. While these amplitudes have simple analytic structure and clear factorisation properties, cosmological correlators often feature branch cuts and lack neat expressions. In this paper, we develop off-shell perturbative methods to study and compute cosmological correlators. We show that such approach not only makes the origin of the correlator singularity structure and factorisation manifest, but also renders practical analytical computations more tractable. Using a spectral representation of massive cosmological propagators that encodes particle production through a suitable iϵ prescription, we remove the need to ever perform nested time integrals as they only appear in a factorised form. This approach explicitly shows that complex correlators are constructed by gluing lower-point off-shell correlators, while performing the spectral integral sets the exchanged particles on shell. Notably, in the complex mass plane instead of energy, computing spectral integrals amounts to collecting towers of poles as the simple building blocks are meromorphic functions. We demonstrate this by deriving a new, simple, and partially resummed representation for the four-point function of conformally coupled scalars mediated by tree-level massive scalar exchange in de Sitter. Additionally, we establish cosmological largest-time equations that relate different channels on in-in branches via analytic continuation, analogous to crossing symmetry in flat space. These universal relations provide simple consistency checks and suggest that dispersive methods hold promise for developing cosmological recursion relations, further connecting techniques from modern scattering amplitudes to cosmology.

The Effect of Halogen Doping on Li Mobility of Thiophosphate Solid Electrolytes

An all-solid-state battery is considered one of the most promising next-generation energy storage systems. It can combine the Li metal anode with a high-voltage cathode to deliver greater energy density than Li-ion batteries, while eliminating fire hazards, by using nonflammable solid electrolytes. The key to enabling all-solid-state batteries therefore lies in developing solid electrolytes that have superior Li conductivity and electrochemical stability. In crystalline materials, electrochemical properties are often dictated by space symmetry and anion chemistry. However, it is difficult to design crystalline materials that have high ionic conductivity and excellent electrochemical stability at the same time. Unlike crystalline systems, noncrystalline materials are not bound by symmetrical constraints, resulting in great flexibility in tailoring the electrochemical properties. In this study, we have investigated local structures and electrochemical properties of a noncrystalline 0.75Li2S-0.25P2S5 (a-LPS) and a-LPS-yLiX (a-LPSXy, y=11, 13, and 15 wt% and X=Halogen atoms) system. We obtained these compositions systematically by mechanochemical reactions. The local structures of a-LPS and a-LPSXy were analyzed using synchrotron scattering. Additionally, we evaluated their Li conductivity and electrochemical stability by electrochemical impedance spectroscopy and cyclic voltammetry. The pair-distribution function analysis (PDF) indicates halogen doping leads to local structure variation, which may contribute to improving Li mobility in a short-range.Among others, we found that iodine addition to a-LPS increases Li conductivity substantially. We constructed all solid-state batteries using a-LPSI11 as a solid electrolyte, a layered sulfide cathode (TiS2) and Li metal as anode. With a compatible electrochemical window of cathode redox reactions, the cell operates reversibly with very small polarization. However, the cell shows capacity decay mostly due to cathodic instability against Li. In contrast, all-solid cell using the a-LPSF11 electrolyte shows much improved capacity retention with the expense of Li conductivity, suggesting that doping elements can dictate the electrochemical properties. We also tested the a-LPSF11 electrolyte against a layered oxide cathode (LiNi0.5Co0.2Mn0.3O2, NCM523), assembled all-solid-state battery shows good cyclability after the formation of cathode-electrolyte interphases. Our work demonstrates how doping can tailor the local structure of a-LPS and the resulting electrochemical properties.

Generalized Coherent Wave Control at Dynamic Interfaces

AbstractCoherent wave control is of key importance across a broad range of fields such as electromagnetics, photonics, and acoustics. It enables us to amplify or suppress the outgoing waves via engineering amplitudes and phases of multiple incidences. However, within a purely spatially (temporally) engineered medium, coherent wave control requires the frequency of the associated incidences to be identical (opposite). In this work, this conventional constraint is broken by generalizing coherent wave control into a spatiotemporally engineered medium is broken, i.e., the system featuring a dynamic interface. Owing to the broken translational symmetry in space and time, both the subluminal and superluminal interfaces allow interference between scattered waves regardless of their different frequencies and wavevectors. Hence, one can flexibly eliminate the backward‐ or forward‐propagating waves scattered from the dynamic interfaces by controlling the incident amplitudes and phases. The work not only presents a generalized way for reshaping arbitrary waveforms but also provides a promising paradigm to generate ultrafast pulses using low‐frequency signals. It has also implemented suppression of forward‐propagating waves in microstrip transmission lines with fast photodiode switches.

Universality of Dynamical Symmetries in Chaotic Maps.

Identifying signs of regularity and uncovering dynamical symmetries in complex and chaotic systems is crucial both for practical applications and for enhancing our understanding of complex dynamics. Recent approaches have quantified temporal correlations in time series, revealing hidden, approximate dynamical symmetries that provide insight into the systems under study. In this paper, we explore universality patterns in the dynamics of chaotic maps using combinations of complexity quantifiers. We also apply a recently introduced technique that projects dynamical symmetries into a "symmetry space", providing an intuitive and visual depiction of these symmetries. Our approach unifies and extends previous results and, more importantly, offers a meaningful interpretation of universality by linking it with dynamical symmetries and their transitions.

Quantum Cosmology in Bianchi-I model: A study of symmetry analysis

The paper deals with Noether symmetry analysis for anisotropic Bianchi-I space–time as well as conformal Symmetry of the physical space. Subsequently, quantum cosmology has been formulated for this model, using canonical quantization programme and also by causal interpretation. Finally, it has been examined whether quantum description may avoid the classical singularity or not.

Conformal Yang-Mills field in (A)dS space

Ordinary-derivative (second-derivative) Lagrangian formulation of classical conformal Yang-Mills field in the (A)dS space of six, eight, and ten dimensions is developed. For such conformal field, we develop two gauge invariant Lagrangian formulations which we refer to as generic formulation and decoupled formulation. In both formulations, the usual Yang-Mills field is accompanied by additional vector and scalar fields where the scalar fields are realized as Stueckelberg fields. In the generic formulation, the usual Yang-Mills field is realized as a primary field, while the additional vector fields are realized as auxiliary fields. In the decoupled formulation, the usual Yang-Mills field is realized as massless field, while the additional vector fields together with the Stueckelberg are realized as massive fields. Some massless/massive fields appear with the wrong sign of kinetic terms, hence demonstrating explicitly that the considered models are not unitary. The use of embedding space method allows us to treat the isometry symmetries of (A)dS space manifestly and obtain conformal transformations of fields in a relatively straightforward way. By accompanying each vector field by the respective gauge parameter, we introduce an extended gauge algebra. Levy-Maltsev decomposition of such algebra is noted. Use of the extended gauge algebra setup allows us to present concise form for the Lagrangian and gauge transformations of the conformal Yang-Mills field. Higher-derivative representation of the Lagrangian is also obtained.

Carrollian $\mathscr Lw_{1+\infty}$ representation from twistor space

We construct an explicit realization of the action of the \mathscr Lw_{1+∞}ℒw1+∞ loop algebra on fields at null infinity. This action is directly derived by Penrose transform of the geometrical action of \mathscr Lw_{1+∞}ℒw1+∞ symmetries in twistor space, ensuring that it forms a representation of the algebra. Finally, we show that this action coincides with the canonical action of \mathscr Lw_{1+∞}ℒw1+∞ Noether charges on the asymptotic phase space.

Fractal surface states in three-dimensional topological quasicrystals

We study topological states of matter in quasicrystals, which do not rely on crystalline order. In the absence of a band-structure description and spin-orbit coupling, we show that a three-dimensional quasicrystal can nevertheless form a topological insulator. It relies on a combination of noncrystallographic rotational symmetry of quasicrystals and electronic orbital space symmetry, which is the quasicrystalline counterpart of the topological crystalline insulator. The resulting topological state obeys a nontrivial twisted bulk-boundary correspondence and lacks a good metallic surface. The topological surface states, localized on the top and bottom planes respecting the quasicrystalline symmetry, exhibit a different kind of multifractality with probability density concentrated mostly on high-symmetry patches. They form a near-degenerate manifold of immobile states whose number scales proportionally to the macroscopic sample size. This can present an opportunity for a platform for topological surface physics distinct from the crystalline counterpart. Published by the American Physical Society 2024

The cosmological constant and energy quantization in hydrogen atom in light of a doubly special relativity with a minimum speed

We show the existence of an invariant minimum speed in space–time as a new fundamental constant of nature by forming the basis of a doubly special relativity so-called Symmetrical Special Relativity (SSR). Such an observer-independent minimum speed emerges from the Dirac’s Large Number Hypothesis (LNH), which leads us to build SSR-theory. This allows us to understand that the hydrogen atom represents the most stable bound state in the universe as being a fundamental structure in space–time with two speed limits, i.e., the speed of light c and a minimum speed V. So the symmetry in space–time given by an invariant minimum speed, which has origin in the electrical and gravitational bound states in hydrogen atom is able to provide a deeper understanding of the proton–electron mass ratio. We investigate how the minimum speed plays a fundamental role in the quantization of energy in hydrogen atom. The minimum speed V is related to a preferred background frame (ultra-referential SV) represented by the surface of a dark cone forbidden to the world line of any particle. It is related to the vacuum energy that leads to the cosmological constant. An investigation of SSR is done and a hypothetical experiment of Bose–Einstein condensation is proposed to detect the minimum speed as a possible Lorentz violation at very low energies.

Position Vectors of Curves in Isotropic Space $I^3$ and Their Relation to the Frenet Frame

This paper investigates position vectors of arbitrary curves in isotropic 3-space (denoted by I^3). We first establish the relationship between a curve’s position vector and the Frenet frame. Then, we derive a natural representation of any curve’s position vector using curvature and torsion. Furthermore, we define various curves within isotropic space, including straight lines, plane curves, helices, general helices, Salkowski curves, and anti-Salkowski curves. Finally, graphical illustrations accompany illustrative examples to elucidate the discussed concepts.

Enhanced Photodetection Performance of WSe2/V2O5 Nanocomposite on Flexible Substrate: Synergistic Advantages and Improved Efficiency.

The two-dimensional (2D) chalcogenide WSe2/V2O5 composite nanostructures were synthesized using the hydrothermal method and extensively characterized with various spectroscopic techniques. X-ray diffraction analysis confirmed the hexagonal crystal structure exhibiting space symmetry of P63/mmc. Scanning electron microscopy images provided insights into the irregular and nonuniform morphology. Optical spectrum analysis indicated a band gap value of 2.01 eV for 15% WSe2/V2O5 nanostructures, as determined by the Wood and Tauc equation. Photoluminescence (PL) excitation spectra at emission wavelengths of 550 and 750 nm exhibited broad emission attributed to self-trapped excitons for V2O5 and WSe2 nanostructures. Under excitation at λexc = 365 nm, PL emission spectra displayed distinct peaks at 550 and 750 nm, demonstrating the ability to emit vivid red light. A device optimized for photoresponsivity (R) of approximately 7.80 × 10-1 A W-1 and detectivity (D) of around 8.65 × 1011 Jones, and quantum efficiency of approximately 3.42 × 10-2 A W-1 were achieved at a wavelength of 390 nm while using a lamination sheet as a substrate. These findings underscore the capability of devices for efficient photoconversion at specified wavelengths, indicating potential applications in sensing, imaging, and optical communication. The photoresponsivity of the device remained stable at 3.38 × 10-3 A W-1 at 0° and 3.09 × 10-3 A W-1 at 55° bending angle. This indicates the resilience of device to mechanical strain, making it ideal for flexible and wearable sensor applications. The structural, morphological, and optical characterizations confirm the suitability of luminescent WSe2/V2O5 chalcogenide for practical optoelectronic applications, especially in display technologies.

Intermediate-spin state of Co ions in magnetic and thermoelectric properties of double perovskite Ba2CoNbO6

Double perovskite Ba2CoNbO6, obtained by pyrolysis of nitrate-organic mixtures, was studied by XRD, XRF, DFT, AC/DC-magnetization, specific-heat, thermoelectric, and ESR methods. The sample has cubic symmetry space group Pm3m with a = b = c = 4.0074(11) Å. Deficiency in oxygen ions shows the presence of Co ions in both 3+ and 2+ valency. According to AC-magnetization and specific-heat data, Ba2CoNbO6 demonstrates spin-glass ordering at TSG = 30 K at external field value of 0.1 kOe. This temperature of spin glass transition drops with field power increase down to complete suppression at 10 kOe. The effective magnetic moment determined using the Curie-Weiss approximation is 4.29 μB, which is consistent with the theoretical estimation for Co ions in the intermediate-spin state. The peak at T = 90 K, observed in the temperature dependence of the specific heat and accompanied by a peak in the ESR linewidth, is possibly due to the structural transition at this temperature. The Seebeck coefficient of the compound is S = 4–6.5 μV/K and the band gap obtained within the small-polaron-jump conductivity model is ΔE = 0.284 eV in the temperature range of 350–550 K connected with DFT calculation. An intensity ESR line, related to Co2+ ions, was observed in ESR spectra.