Search Results (37)

There are two ways of linearizing the Klein–Gordon equation: Dirac’s choice, which introduces a matter–antimatter pair, and a second approach using a bivector, which Dirac did not consider. In this paper, we show that a bivector provides the classical origin of quantum spin. At high precessional frequencies, a symmetry transformation occurs in which classical reflection becomes quantum parity. We identify a classical spin-1 boson and demonstrate how bosons deliver energy, matter, and torque to a surface. The correspondence between classical and quantum domains allows spin to be identified as a quantum bivector, $i\sigma$. Using geometric algebra, we show that a classical boson has two blades, corresponding to magnetic quantum number states $m=\pm 1$. We conclude that fermions are the blades of bosons, thereby unifying both into a single particle theory. We compare and contrast the Standard Model, which uses chiral vectors as fundamental, with the Bivector Standard Model, which uses bivectors, with two hands, as fundamental. Full article

The article presents the quantum signal-induced heap transform (QsiHT) method of the QR-decomposition of multi-qubit operations. This transform can be generated by a given signal, by using different paths, or orders, of processing the data. We propose using the concept of the fast path of calculation of the QsiHT and applying such transforms on each stage of the matrix decomposition. This allows us to build quantum circuits for multi-qubit unitary operation without permutations. Unitary operations with real and complex matrices are considered. The cases of 3- and 4-qubit operations are described in detail with quantum circuits. These circuits use a maximum of 28 and 120 Givens rotation gates for 3- and 4-qubit real operations, respectively. All rotations are performing only on adjacent bit planes. For complex unitary operation, each of the Givens gates is used in pairs with two Z-rotation gates. These two types of rotations and the global phase gate are the universal gate set for multi-qubit operations. The presented approach can be used for implementing quantum circuits for $n$-qubits when $n\ge 2$, with a maximum of ($4^n/2-2^{n-1})$ Givens rotations and no permutations. Full article

The wave–particle duality is the quintessence of quantum mechanics. This duality gives rise to distinct behaviors depending on the experimental setup, with the system exhibiting either wave-like or particle-like properties, depending on whether the focus is on interference (wave) or trajectory (particle). In the interaction with a beam splitter, photons with particle behavior can transform into a wave behavior and vice versa. In Wheeler’s delayed-choice gedanken experiment, this interaction is delayed so that the wave that initially travels through the interferometer can become a particle, avoiding the interaction. We show that this contradiction can be resolved using polarized entangled photon pairs. An analysis of Shannon’s entropy supports this proposal. Full article

Rotational spectra for hexafluoroacetone imine, the singly substituted ¹³C isotopologues, and the ¹⁵N isotopologue, have been recorded using both cavity and chirped pulse Fourier transform microwave spectrometers. The spectra observed present as being doubled with separations between each pair of transitions being on the order of a few tens of kilohertz which is consistent with a large amplitude motion producing two torsional substates. The observed splitting is most likely due to the combined motions of the CF3 groups, for which the calculated barrier is small. However, no transitions between states could be observed and, similarly, no Coriolis coupling parameters were required to achieve a satisfactory fit for the transition frequencies. Hence, and somewhat curiously, the two states have been fit independently of each other such that the two states may simply be considered near-equivalent conformers. The structural properties of hexafluoroacetone imine are compared with two isoelectronic molecules hexafluoroisobutene and hexafluoroacetone. Rotational constants, quartic centrifugal distortion constants, and the ¹⁴N nuclear electric quadrupole coupling tensor have been determined and are presented together with supporting quantum chemical calculations. Full article

Classical ghost imaging (CGI), an extension of quantum ghost imaging (QGI), enables object reconstruction by leveraging the spatial correlation between a pair of beams. Traditionally, CGI requires a camera or point scan to capture the spatial information of the illumination source with intensity fluctuations. In this work, we propose a novel CGI scheme that utilizes an incoherent source to illuminate both the object and the modulations, without introducing any mutual interference between them. Through theoretical analysis and experimental validation, we demonstrate that the reconstruction process relies solely on the modulations and correlation signals of two single-pixel detectors. Concurrently, this scheme is also extended to ghost diffraction, verifying the correlation between two planes that are Fourier transform pairs of the speckle field. Moreover, our study reveals the intricate relationships between the speckle field, modulations, and object, and experimentally verifies the impact of speckle fields on image quality. Notably, this work provides a more comparable framework between CGI and QGI, offering a promising avenue to explore the classical–quantum relationship. Full article

The paper advances a new technique for constructing the exceptional differential polynomial systems (X-DPSs) and their infinite and finite orthogonal subsets. First, using Wronskians of Jacobi polynomials (JPWs) with a common pair of the indexes, we generate the Darboux–Crum nets of the rational canonical Sturm–Liouville equations (RCSLEs). It is shown that each RCSLE in question has four infinite sequences of quasi-rational solutions (q-RSs) such that their polynomial components from each sequence form a X-Jacobi DPS composed of simple pseudo-Wronskian polynomials (p-WPs). For each p-th order rational Darboux Crum transform of the Jacobi-reference (JRef) CSLE, used as the starting point, we formulate two rational Sturm–Liouville problems (RSLPs) by imposing the Dirichlet boundary conditions on the solutions of the so-called ‘prime’ SLE (p-SLE) at the ends of the intervals (−1, +1) or (+1, ∞). Finally, we demonstrate that the polynomial components of the q-RSs representing the eigenfunctions of these two problems have the form of simple p-WPs composed of p Romanovski–Jacobi (R-Jacobi) polynomials with the same pair of indexes and a single classical Jacobi polynomial, or, accordingly, p classical Jacobi polynomials with the same pair of positive indexes and a single R-Jacobi polynomial. The common, fundamentally important feature of all the simple p-WPs involved is that they do not vanish at the finite singular endpoints—the main reason why they were selected for the current analysis in the first place. The discussion is accompanied by a sketch of the one-dimensional quantum-mechanical problems exactly solvable by the aforementioned infinite and finite EOP sequences. Full article

This paper investigates the (2 + 1)-dimensional nonlocal Hirota–Maxwell–Bloch (NH-MB) system under various types of nonlocality. The mathematical consistency of possible nonlocal structures is analyzed, and three types that lead to a well-posed system are identified. The integrability of the system is established through its Lax pair representation, and a Darboux transformation is constructed. Exact soliton solutions are obtained for both the defocusing and focusing cases. The results obtained may find applications in nonlinear optics, quantum theory, and the theory of integrable systems. Full article

Classical edge detection algorithms often struggle to process large, high-resolution image datasets efficiently. Quantum image processing offers a promising alternative, but current implementations face significant challenges, such as time-consuming data acquisition, complex device requirements, and limited real-time processing capabilities. This work presents a novel paired transform-based quantum representation for efficient image processing. This representation enables the parallelization of convolution operations, simplifies gradient calculations, and facilitates the processing of one-dimensional and two-dimensional signals. We demonstrate that our approach achieves improved processing speed compared to classical methods while maintaining comparable accuracy. The successful implementation of real-world images highlights the potential of this research for large-scale quantum image processing, architecture-specific optimizations, and applications beyond edge detection. Full article

This study is the first to convert two waste materials, waste rice noodles (WRN) and red mud (RM), into a low-cost, high-value magnetic photocatalytic composite. WRN was processed via a hydrothermal method to produce a solution containing carbon quantum dots (CQDs). Simultaneously, RM was dissolved in acid to form a Fe³⁺ ion-rich solution, which was subsequently mixed with the CQDs solution and underwent hydrothermal treatment. During this process, the Fe³⁺ ions in RM were transformed into the maghemite (γ-Fe₂O₃) phase, while CQDs were incorporated onto the γ-Fe₂O₃ surface, resulting in the CQDs/γ-Fe₂O₃ magnetic photocatalytic composite. Experimental results demonstrated that the WRN-derived CQDs not only facilitated the formation of the magnetic γ-Fe₂O₃ phase but also promoted a synergistic interaction between CQDs and γ-Fe₂O₃, enhancing electron-hole pair separation and boosting the production of reactive radicals such as O₂^·− and ·OH. Under optimized conditions (pH = 8, carbon loading: 10 wt%), the CQDs/γ-Fe₂O₃ composite exhibited good photocatalytic performance against methylene blue, achieving a 97.6% degradation rate within 480 min and a degradation rate constant of 5.99 × 10⁻³ min⁻¹, significantly outperforming RM and commercial γ-Fe₂O₃ powder. Beyond methylene blue, this composite also effectively degraded common organic dyes, including malachite green, methyl violet, basic fuchsin, and rhodamine B, with particularly high efficiency against malachite green, reaching a degradation rate constant of 5.465 × 10⁻² min⁻¹. Additionally, due to its soft magnetic properties (saturation magnetization intensity: 16.7 emu/g, residual magnetization intensity: 2.2 emu/g), the material could be conveniently recovered and reused after photocatalytic cycles. Even after 10 cycles, it retained over 98% recovery and 96% photocatalytic degradation efficiency, underscoring its potential for cost-effective, large-scale photocatalytic water purification. Full article

Background: For a single exposure in radiography, a dual-layer flat-panel detector (DFD) can provide spectral images and efficiently utilize the transmitted X-ray photons to improve the detective quantum efficiency (DQE) performance. In this paper, to acquire high DQE performance, we present a registration method for X-ray images acquired from a DFD, considering only spatial translations and scale factors. The conventional registration methods have inconsistent estimate accuracies depending on the captured object scene, even when using entire pixels, and have deteriorated frequency performance because of the interpolation method employed. Methods: The proposed method consists of two steps; the first step is conducting a spatial translation according to the Fourier shift theorem with a subpixel registration, and the second step is conducting a scale transformation using cubic interpolation to process the X-ray projections. To estimate the subpixel spatial translation, a maximum-amplitude method using a small portion of the slant-edge phantom is used. Results: The performance of the proposed two-step method is first theoretically analyzed and then observed by conducting extensive experiments and measuring the noise power spectrum and DQE. An example for registering chest images is also shown. For a DFD, the proposed method shows a better registration result than the conventional one-step registration. The DQE improvement was more than 56% under RQA 9 compared to the single flat-panel detector case. Conclusions: The proposed two-step registration method can efficiently provide aligned image pairs from the DFD to improve the DQE performance at low doses and, thus, increase the accuracy of clinical diagnosis. Full article

The circularly polarized laser sources are core components for many optical applications such as biomedicine, quantum technology, and AR/VR. However, conventional techniques make it difficult to further diminish the size of circularly polarized lasers. Thus, the high-contrast subwavelength chiral metasurface (HCCM) with a 980 nm operating wavelength is numerically investigated. The HCCM is composed of chiral metasurfaces modulating the circular dichroism of reflectance and 6 pairs of Distributed Bragg Reflectors (DBR) with 55% reflectivity. The reason that the HCCM has an ultra-high reflectivity (99.9%) at the operating wavelength of 980 nm is the combination of the optical refractive index difference between the GaAs metasurface and the AlOx substrate and weak destructive interference in the AlOx support layer. In addition, the circular dichroism of the chiral metasurfaces (2.1%) is mainly caused by the displacement of two square air holes in opposite directions, thus transforming the unit cell of the metasurface from C2 symmetry to chiral symmetry. The reflector has the advantages of a simple structure and miniaturization, which is expected to greatly reduce the fabrication difficulty and cost of the circular polarization VCSELs. Full article

The paper reveals some remarkable form-invariance features of the ‘Jacobi-reference’ canonical Sturm–Liouville equation (CSLE) in the particular case of the density function with the simple pole at the origin. It is proven that the CSLE under consideration preserves its form under the two second-order Darboux–Crum transformations (DCTs) with the seed functions represented by specially chosen pairs of ‘basic’ quasi-rational solutions (q-RSs), i.e., such that their analytical continuations do not have zeros in the complex plane. It is proven that both transformations generally either increase or decrease by 2 the exponent difference (ExpDiff) for the mentioned pole while keeping two other parameters unchanged. The change is more complicated in the latter case if the ExpDiff for the pole of the original CSLE at the origin is smaller than 2. It was observed that the DCTs in question do not preserve bound energy levels according to the conventional supersymmetry (SUSY) rules. To understand this anomaly, we split the DCT in question into the two sequential Darboux deformations of the Liouville potentials associated with the CSLEs of our interest. We found that the first Darboux transformation turns the initial CSLE into the Heun equation written in the canonical form while the second transformation brings us back to the canonical form of the hypergeometric equation. It is shown that the first of these transformations necessarily places the mentioned ExpDiff into the limit-circle (LC) range and then the second transformation keeps the pole within the LC region, violating the conventional prescriptions of SUSY quantum mechanics. Full article

With the rapid advancement of Artificial Intelligence-driven object recognition, the development of cognitive tunable imaging sensors has become a critically important field. In this paper, we demonstrate an infrared (IR) sensor with spectral tunability controlled by the applied bias between the long-wave and mid-wave IR spectral regions. The sensor is a Quantum Well Infrared Photodetector (QWIP) containing asymmetrically doped double QWs where the external electric field alters the electron population in the wells and hence spectral responsivity. The design rules are obtained by calculating the electronic transition energies for symmetric and antisymmetric double-QW states using a Schrödinger–Poisson solver. The sensor is grown and characterized aiming detection in mid-wave (~5 µm) to long-wave IR (~8 µm) spectral ranges. The structure is grown using molecular beam epitaxy (MBE) and contains 25 periods of coupled double GaAs QWs and Al_0.38Ga_0.62As barriers. One of the QWs in the pair is modulation-doped to provide asymmetry in potential. The QWIPs are tested with blackbody radiation and FTIR down to 77 K. As a result, the ratio of the responsivities of the two bands at about 5.5 and 8 µm is controlled over an order of magnitude demonstrating tunability between MWIR and LWIR spectral regions. Separate experiments using parameterized image transformations of wideband LWIR imagery are performed to lay the framework for utilizing tunable QWIP sensors in object recognition applications. Full article

This paper exploits two remarkable features of the translationally form-invariant (TFI) canonical Sturm–Liouville equation (CSLE) transfigured by Liouville transformation into the Schrödinger equation with the shape-invariant Gendenshtein (Scarf II) potential. First, the Darboux–Crum net of rationally extended Gendenshtein potentials can be specified by a single series of Maya diagrams. Second, the exponent differences for the poles of the CSLE in the finite plane are energy-independent. The cornerstone of the presented analysis is the reformulation of the conventional supersymmetric (SUSY) quantum mechanics of exactly solvable rational potentials in terms of ‘generalized Darboux transformations’ of canonical Sturm–Liouville equations introduced by Rudyak and Zakhariev at the end of the last century. It has been proven by the author that the first feature assures that all the eigenfunctions of the TFI CSLE are expressible in terms of Wronskians of seed solutions of the same type, while the second feature makes it possible to represent each of the mentioned Wronskians as a weighted Wronskian of Routh polynomials. It is shown that the numerators of the polynomial fractions in question form the exceptional orthogonal polynomial (EOP) sequences composed of Wronskian transforms of the given finite set of Romanovski–Routh polynomials excluding their juxtaposed pairs, which have already been used as seed polynomials. Full article

A molecular formalism based on a decomposed energy space constructed by a modular basis of matter and radiation is proposed for relativistic quantum mechanics. In the proposed formalism, matter radiation interactions are incorporated via the dynamical transformation of the coupled particle/antiparticle pair in a multistate quantum mechanical framework. This picture generalizes relativistic quantum mechanics at minimal cost, unlike quantum field theories, and the relativistic energy–momentum relation is interpreted as energy transformations among different modules through a multistate Schrödinger equation. The application of two-state and four-state systems using a time-dependent Schrödinger equation with pair states as a basis leads to well-defined solutions equivalent to those obtained from the Klein–Gordon equation and the Dirac equation. In addition, the particle–antiparticle relationship is well manifested through a particle conjugation group. This work provides new insights into the underlying molecular mechanism of relativistic dynamics and the rational design of new pathways for energy transformation. Full article