Physica Scripta

Quantum algorithms can potentially overcome the boundary of computationally hard problems. One of the cornerstones in modern optics is the beam propagation algorithm, facilitating the calculation of how waves with a particular dispersion relation propagate in time and space. This algorithm solves the wave propagation equation by Fourier transformation, multiplication with a transfer function, and subsequent back transformation. This transfer function is determined from the respective dispersion relation, which can often be expanded as a polynomial. In the case of paraxial wave propagation in free space or picosecond pulse propagation, this expansion can be truncated after the quadratic term. The classical solution to the wave propagation requires ${ \mathcal O }({NlogN})$ computation steps, where N is the number of points into which the wave function is discretized. Here, we show that the propagation can be performed as a quantum algorithm with ${ \mathcal O }\left({\left({logN}\right)}^{2}\right)$ single-controlled phase gates, indicating exponentially reduced computational complexity. We herein demonstrate this quantum beam propagation method (QBPM) and perform such propagation in both one- and two-dimensional systems for the double-slit experiment and Gaussian beam propagation. We highlight the importance of the selection of suitable observables to retain the quantum advantage in the face of the statistical nature of the quantum measurement process, which leads to sampling errors that do not exist in classical solutions.

First conceptualised in Olaf Stapledon's 1937 novel 'Star Maker', before being popularised by Freeman Dyson in the 1960s, Dyson Spheres are structures which surround a civilisation's sun to collect all the energy being radiated. This article presents a discussion of the features of such a feat of engineering, reviews the viability, scale and likely design of a Dyson structure, and analyses details about each stage of its construction and operation. It is found that a Dyson Swarm, a large array of individual satellites orbiting another celestial body, is the ideal design for such a structure as opposed to the solid sun-surrounding structure which is typically associated with the Dyson Sphere. In our solar system, such a structure based around Mars would be able to generate the Earth's 2019 global power consumption of 18.35 TW within fifty years once its construction has begun, which itself could start by 2040 using biennial launch windows. Alongside a 4.17 km² ground-based heliostat array, the swarm of over 5.5 billion satellites would be constructed on the surface of Mars before being launched by electromagnetic accelerators into a Martian orbit. Efficiency of the Dyson Swarm ranges from 0.74–2.77% of the Sun's 3.85 × 10²⁶ W output, with large potential for growth as both current technologies improve, and future concepts are brought to reality in the time before and during the swarm's construction. Not only would a Dyson Swarm provide a near-infinite, renewable power source for Earth, it would also allow for significant expansions in human space exploration and for our civilisation as a whole.

The concept of the Fermi surface is at the very heart of our understanding of the metallic state. Displaying intricate and often complicated shapes, the Fermi surfaces of real metals are both aesthetically beautiful and subtly powerful. A range of examples is presented of the startling array of physical phenomena whose origin can be traced to the shape of the Fermi surface, together with experimental observations of the particular Fermi surface features.

Squeezed light generation has come of age. Significant advances on squeezed light generation have been made over the last 30 years—from the initial, conceptual experiment in 1985 till today's top-tuned, application-oriented setups. Here we review the main experimental platforms for generating quadrature squeezed light that have been investigated in the last 30 years.

We introduce quantum spatio-temporal dynamics (QSD) as modeled by the Nexus Paradigm (NP) of quantum gravity to resolve the problem of energy- momentum localization in a gravitational field. Currently, the gravitational field as described using the language of geometry modeled under General Relativity (GR) fails to provide a generally accepted definition of energy-momentum. Attempts at resolving this problem using geometric methods have resulted in various energy-momentum complexes whose physical meaning remain dubious since the resulting complexes are non-tensorial under a general coordinate transformation. In QSD, the tangential manifold is the affine connection field in which energy-momentum localization is readily defined. We also discover that the positive mass condition is a natural consequence of quantization and that dark energy is a Higgs like field with negative energy density everywhere. Finally, energy-momentum localization in quantum gravity shows that a free falling object will experience larger vacuum fluctuations (uncertainties in location) in strong gravity than in weak gravity and that the amplitudes of these oscillations define the energy of the free falling object.

Let ${{ \mathcal O }}_{c}$ be the category of finite-length modules for the Virasoro Lie algebra at central charge c whose composition factors are irreducible quotients of reducible Verma modules. For any $c\in {\mathbb{C}}$, this category admits the vertex algebraic braided tensor category structure of Huang–Lepowsky–Zhang. Here, we begin the detailed study of ${{ \mathcal O }}_{{c}_{p,q}}$ where ${c}_{p,q}=1-\tfrac{6{\left(p-q\right)}^{2}}{{pq}}$ for relatively prime integers p, q ≥ 2; in conformal field theory, ${{ \mathcal O }}_{{c}_{p,q}}$ corresponds to a logarithmic extension of the central charge c_p,q Virasoro minimal model. We particularly focus on the Virasoro Kac modules ${{ \mathcal K }}_{r,s}$, $r,s\in {{\mathbb{Z}}}_{\geqslant 1}$, in ${{ \mathcal O }}_{{c}_{p,q}}$ defined by Morin-Duchesne–Rasmussen–Ridout, which are finitely-generated submodules of Feigin–Fuchs modules for the Virasoro algebra. We prove that ${{ \mathcal K }}_{r,s}$ is rigid and self-dual when 1 ≤ r ≤ p and 1 ≤ s ≤ q, but that not all ${{ \mathcal K }}_{r,s}$ are rigid when r > p or s > q. That is, ${{ \mathcal O }}_{{c}_{p,q}}$ is not a rigid tensor category. We also show that all Kac modules and all simple modules in ${{ \mathcal O }}_{{c}_{p,q}}$ are homomorphic images of repeated tensor products of ${{ \mathcal K }}_{\mathrm{1,2}}$ and ${{ \mathcal K }}_{\mathrm{2,1}}$, and we determine completely how ${{ \mathcal K }}_{\mathrm{1,2}}$ and ${{ \mathcal K }}_{\mathrm{2,1}}$ tensor with Kac modules and simple modules in ${{ \mathcal O }}_{{c}_{p,q}}$. In the process, we prove some fusion rule conjectures of Morin-Duchesne–Rasmussen–Ridout.

The solar system started to form about 4.56 Gyr ago and despite the long intervening time span, there still exist several clues about its formation. The three major sources for this information are meteorites, the present solar system structure and the planet-forming systems around young stars. In this introduction we give an overview of the current understanding of the solar system formation from all these different research fields. This includes the question of the lifetime of the solar protoplanetary disc, the different stages of planet formation, their duration, and their relative importance. We consider whether meteorite evidence and observations of protoplanetary discs point in the same direction. This will tell us whether our solar system had a typical formation history or an exceptional one. There are also many indications that the solar system formed as part of a star cluster. Here we examine the types of cluster the Sun could have formed in, especially whether its stellar density was at any stage high enough to influence the properties of today's solar system. The likelihood of identifying siblings of the Sun is discussed. Finally, the possible dynamical evolution of the solar system since its formation and its future are considered.

There are several definitions of energy density in quantum mechanics. These yield expressions that differ locally, but all satisfy a continuity equation and integrate to the value of the expected energy of the system under consideration. Thus, the question of whether there are physical grounds to choose one definition over another arises naturally. In this work, we propose a way to probe a system by varying the size of a well containing a quantum particle. We show that the mean work done by moving the wall is closely related to one of the definitions for energy density. Specifically, the appropriate energy density, evaluated at the wall corresponds to the force exerted by the particle locally, against which the work is done. We show that this identification extends to two and three dimensional systems.

Many researchers have argued that humanity will create artificial general intelligence (AGI) within the next twenty to one hundred years. It has been suggested that AGI may inflict serious damage to human well-being on a global scale ('catastrophic risk'). After summarizing the arguments for why AGI may pose such a risk, we review the fieldʼs proposed responses to AGI risk. We consider societal proposals, proposals for external constraints on AGI behaviors and proposals for creating AGIs that are safe due to their internal design.

We review the concepts of temporal modes (TMs) in quantum optics, highlighting Roy Glauber's crucial and historic contributions to their development, and their growing importance in quantum information science. TMs are orthogonal sets of wave packets that can be used to represent a multimode light field. They are temporal counterparts to transverse spatial modes of light and play analogous roles—decomposing multimode light into the most natural basis for isolating statistically independent degrees of freedom. We discuss how TMs were developed to describe compactly various processes: superfluorescence, stimulated Raman scattering, spontaneous parametric down conversion, and spontaneous four-wave mixing. TMs can be manipulated, converted, demultiplexed, and detected using nonlinear optical processes such as three-wave mixing and quantum optical memories. As such, they play an increasingly important role in constructing quantum information networks.

In order to understand many complex situations in wave propagation, such as heat transfer, fluid dynamics, optical fibers, electrodynamics, physics, chemistry, biology, condensed matter physics, ocean engineering, and many other branches of nonlinear science, the majority of natural processes are routinely modelled and analysed using nonlinear evolution equations. In this study, the (3+1)-dimensional nonlinear evolution equation is investigated analytically. Initially, the Hirota bilinear approach is used to develop the bilinear version of the higher dimensional nonlinear model. Consequently, we are able to design periodic wave soliton solutions, lump wave and single-kink soliton solutions, and collisions between lumps and periodic waves. Later on, the unified method is applied to develop several new travelling wave solutions for the governing model substantially. Furthermore, numerous exact solutions are analyzed graphically to explore many fascinating nonlinear dynamical structures with the aid of 3D, contour, and 2D visualizations. A variety of higher dimensional nonlinear evolution models can also be investigated by employing present approaches arising in many fields of contemporary science and technology.

Comparison of EOS properties such as lattice parameters, bulk modulus, etc calculated by density functional theory (DFT) with experiments is used, in general, to assess the precision reachable in computations, when using different codes and potentials. DFT calculations using a large number of codes and potentials by different groups, have reported excellent precision (0.02 Å) in the lattice parameters of 71 elements. It is of interest to study the precision levels reachable in compounds of hexagonal NiAs type crystal structure, in which a wide range of electrical conductivity and magnetic order are found to occur. In this study, lattice parameters for 42 intermetallic compounds of the NiAs type structure are determined from internal radii using the Atom Pair Bond method. These values are compared with the lattice parameters reported from the high throughput DFT computational techniques such as AFLOW and Materials Project compilations. Precision in lattice parameters obtainable in the three methods is assessed in comparison with those reported from the experiments. Selection of a set of compounds of same crystal structure brings out the role of differences in the electronic structure of elements involved. In the APB method, lattice parameters are obtained by the best-fit equations defined by radii change in a large number of compounds with a particular structure, and do not involve several approximations, unlike in DFT. It is interesting to see that the simple APB approach could estimate lattice parameters with accuracies comparable to DFT methods.

In this study, we investigated the magnetic ordering and underlying mechanism of the Griffiths phase, observed in Ho₂NiMnO₆ through AC susceptibility measurements. Our results indicate that the transition around 86 K corresponds to a paramagnetic to ferromagnetic transition characterized by classical magnetic ordering. Notably, nonlinear AC susceptibility measurements revealed the existence of ferromagnetic clusters within a paramagnetic background well above the transition temperature, establishing this as the origin of the Griffiths-like phase within the Ni/Mn sublattice of Ho₂NiMnO₆. Our study on the Ho₂NiMnO₆ system provides insight into the intricate magnetic phenomena common to various other strongly correlated electron systems.

This study aims to examine the nonlinear partial differential equation known as the (1+1)-dimensional generalized Kundu-Eckhaus equation with extra-dispersion, which is used to model the transmission of ultra-short femtosecond pulses in an optical fiber. Two versatile techniques, namely the extended $\left(\tfrac{G^{\prime} }{{G}^{2}}\right)$-expansion as well as the extended $\exp (-\phi (\xi ))$-expansion techniques, are utilized to generate numerous precise answers. Diverse novel collections of exact traveling wave solutions, such as bright solitons, dark solitons, singular solitons, W-shape solutions, M-shape solutions, and rational solutions, are identified as a result. Several of the acquired solutions are interpreted physically through the use of figures. In addition, the modulation instability analysis of the considered equation is performed and presented via 3D and 2D graphs. In the field of nonlinear sciences, the proposed methods have great value and can be applied to other nonlinear evolutionary equations that are used to represent nonlinear physical models.

The present study investigates the impact of P doping and stretching loads on phonon dispersion, electronic properties, and optical characteristics of P-doped hexagonal boron arsenide (h-BAs_(1-x)P_x), where the doping level x varies from 0 to 1, employing the density functional theory (DFT) method. The findings reveal that the chemical bonds in h-BAs_(1-x)P_x monolayers are indeed covalent. Furthermore, an increase in P concentration from 0.0% to 100% leads to enhancement in the band gap, approximately 18.42%. However, regardless of variations in P concentration or the application of tensile strains up to 4%, the electronic nature of h-BAs_(1-x)P_x remains unaltered. These monolayers continue to exhibit characteristics of a direct band gap semiconductor at the K wave vector. On the other hand, there exists an intricate interplay between strain and optical properties. Investigating the dielectric functions, absorption coefficient, refractive index, and reflectivity coefficient of h-BAs_(1-x)P_x monolayers provides insights into their behavior in the ultraviolet spectrum.

The laser powder bed fusion LPBF method in additive manufacturing for metals have proven to produce a final product with higher relative density, when compare to other metal additive manufacturing processes like WAAM, DED and it takes less time even for complex designs. Despite the use of many metal-based raw materials in the LPBF method for production of products. Maraging steel (martensitic steel) is used in aeronautical and aircraft applications in view of its advantages including low weight, high strength, long-term corrosion resistance, low cost, availability, and recyclability. A research gap concerns the selection of design, dimension, accuracy, process parameters according to different grades, and unawareness of various maraging steels other than specific maraging steels. In this comprehensive review, the research paper provides information about on LPBF maraging steel grades, their process parameters and defects, microstructure characteristics, heat treatments, and the resulting mechanical characteristics changes. In addition, detailed information about the aging properties, fatigue, residual and future scope of different maraging steel grades in LPBF for various applications are discussed.

The progress in IC miniaturization dictated by Moore's Law has taken a leap from mere circuit integration to IoT enabled System-on-Chip (SoC) deployments. Such systems are connoted by contemporary advancements in the semiconductor industry roadmaps namely, 'More-Moore' and 'More-than-Moore' (MtM). For meaningful integration of digital and non-digital blocks, a power performance tradeoff is essential for maximum and fruitful utilization of the silicon area. Using the techniques under the MtM nomenclature allows the use of unconventional steep slope devices like Tunneling FETs, Negative Capacitance (NC) FETs, Gate-all-around FETs (GAA) and FinFETs etc, which can exhibit reasonable performance with lower supply voltages. Following the Device Technology Co-optimization (DTCO) and System Technology Co-optimization (STCO) the advanced 3D heterogenous integration technologies allow sensors, analog/mixed signal and passive components to be assimilated within the same package as the CMOS blocks. Appropriate device engineering techniques like multi-gate architectures, vertical stacking transistors, compound semiconductors and alternate carrier transport phenomena are required to improve the current drive and scaling performance of advanced CMOS devices. CMOS based codesign is essential to realize new topologies for energy economical computation, sensing and information processing as the beyond CMOS steep slope devices are independently incapable of replacing conventional bulk CMOS devices. This article presents a detailed qualitative review of the various aspects of MtM beyond CMOS steep slope switches and their prospective integration technologies. For system level integration, various aspects of device performance and optimizations, related device-circuit interactions, dielectric technologies at the advance nanometer nodes have been probed into. Additionally, novel circuit topologies, synthesis algorithms and processor level performance evaluation using steep slope switches have been investigated. An exclusive compact overview for contemporary insights into integrated device-system development methodology and its performance evaluation is presented.

Designing of efficient thermoelectric material is the need of hour to avoid the adverse effect on environment. Two-dimensional (2D) transition metal oxides (TMOs) and transition metal dichalogenides (TMDCs) are receiving attention of researchers due to their wide range of electronic properties, high temperature and air stability, tunable electron transport properties for high thermoelectric efficiency (ZT). Two- dimensionalization in these materials lead to the increase in their thermoelectric efficiency as compared to their bulk counterpart due to the quantum confinement effect. These materials possess high thermoelectric efficiency even at high temperature (500–800 K) but their application still lagging behind commercially due to low ZT value. Various approaches such as strain engineering, defect engineering etc. Were adopted to further enhance the ZT value of these materials. Controlling chalcogen atomic defect provides an alternative avenue for engineering a wide range of physical and chemical properties of 2D TMOs/TMDCs. In this review we will systematically present the progress made in the study of electronic, phononic, transport properties and Seebeck coefficient of 2D TMOs/TMDCs such as XO₂ (X=Cr, Mo, Zr) and MX₂ (M= Cr, Mo, Zr; X= S, Se, Te) by using first principle approach. Methodologies such as strain engineering and doping to enhance the ZT values has also been discussed. In the last section we have discussed the experimental results of thermoelectric parameters of TMDCs and compare them with the existing theoretical results. It is concluded from this study that there are plenty of rooms which can be explored both theoretically and experimentally to design efficient thermoelectric materials for energy harvesting.

Known as green inorganic products and environmentally beneficial, ionic liquids (ILs) are increasingly used in the ionothermal synthesis of zeolites and zeotype materials compared to the hydrothermal method. This safe and successful process offers new opportunities to produce several molecular sieves with different morphologies and structures for promising applications. In this review, we summarize the history of the most successful phases of zeolites and zeotype materials, with different structures such as AEL, AEI, AFI, AST, ATS, CHA, -CLO, ITW, LEV, LTA, MFI, MTN, MTT, SOD, TON, IRR, and STW, from ILs discovery until 2022. The use of the ionothermal method compared to the hydrothermal route is evaluated and reported in this paper, besides synthesis parameters affecting the final product formation, such as IL dosage, cation size and shape, water content, (P, Si, F, IL/Al) ratios, crystallization time and temperature, mineralizing agent, Me/Al ratio, the addition of a secondary template (co-SDA), the use of IL as both SDA and solvent, competition in forming the framework, and the use of eutectic mixture and deep eutectic solvent (DES). Furthermore, we collected the various applications of these materials and highlighted the advantages of the ionothermal process, offering a comprehensive understanding of this topic.

This review paper focuses on the current advancements in improving the optical and electrical properties of n-type and p-type oxides and sulphide semiconductors. The demand for high-performance semiconductors has grown significantly in recent years due to their wide range of application in electronic and optoelectronic devices. However, the inherent limitations of these materials such as low conductivity, poor optical absorption, and low carrier mobility have hindered their widespread adoption. This paper provides an overview of various techniques that have been employed to improve the optical and electrical properties of n-type and p-type oxides and sulphide semiconductors. These techniques include doping with impurities, defect engineering, surface passivation, and bandgap engineering. The paper also discusses the recent progress in the synthesis of these materials using different methods such as chemical vapor deposition, sol–gel, and hydrothermal methods. Furthermore, this review paper highlights the applications of these improved materials in various fields such as solar cells, light-emitting diodes, photocatalysis, and sensing. Finally, the paper concludes with the prospects of these materials and the challenges that need to be addressed to achieve their full potential. Overall, this review paper provides valuable insights into the current state-of-the-art techniques for improving the optical and electrical properties of n-type and p-type oxides and sulphide semiconductors, which can potentially lead to the development of high-performance devices.

Nonlinear absorption properties of PbMo0.75W0.25O4 single crystal fabricated by the Czochralski method were studied. The band gap energy of the crystal was determined as 3.12 eV. Urbach energy which represents the defect states inside the band gap was found to be 0.106 eV. PbMo0.75W0.25O4 single crystal has a broad photoluminescence emission band between 376 and 700 nm, with the highest emission intensity occurring at 486 nm and the lowest intensity peak at 547 nm, depending on the defect states. Femtosecond transient absorption measurements reveal that the lifetime of localized defect states is found to be higher than the 4 ns pulse duration. Open aperture (OA) Z-scan results demonstrate that the PbMo0.75W0.25O4 crystal exhibits nonlinear absorption (NA) that includes simultaneous two-photon absorption (TPA) as the dominant mechanism at the 532 nm excitations corresponding to 2.32 eV energy. NA coefficient (βeff) increased from 7.24 x 10-10 m/W to 8.81 x 10-10 m/W with increasing pump intensity. At higher intensities βeff tends to decrease with intensity increase. This decrease is an indication that saturable absorption (SA) occurred along with the TPA, called saturation of TPA. The lifetime of the defect states was measured by femtosecond transient absorption spectroscopy. Saturable absorption behavior was observed due to the long lifetime of the localized defect states. Closed aperture (CA) Z-scan trace shows the sign of a nonlinear refractive index. The optical limiting threshold of PbMo0.75W0.25O4 single crystal at the lowest intensity was determined as 3.45 mJ/cm2. Results show that the PbMo0.75W0.25O4 single crystal can be a suitable semiconductor material for optical limiting applications in the visible region.

Scintillator samples are synthesized by a university-SME collaboration and the light yield, light emission and light transmission properties are studied with the aim of determining the fluor content that gives the highest light yield. Three plastic scintillator samples with different fluor additives are produced and their optical properties are found to be comparable with a high-light-yield EJ-204 reference sample. Amongst the three, the sample with 0.75% PPO + 0.75 %PTP and 0.04% POPOP + 0.04% Bis-MSB provides the highest light yield. The authors plan to use the same fluor additive concentration to produce application-specific scintillators that are not commercially available for nuclear reactor monitoring and medical applications.

The spectrum required for future optical communication systems is being extended towards the C-, L- and U-bands, resulting in a significant interest in the spectral region around 2 μm wavelength. Since Holmium doped fiber amplifiers (HDFAs) provide amplification in this spectral region, they have become a focus of researchers working on doped fiber amplifiers. A major factor resulting in the performance degradation of HDFAs is the inhomogeneous energy transfer within Ho³⁺ ion-pairs in high-concentration Holmium-doped fibers (HDFs), an effect generally known as pair-induced quenching (PIQ). In this paper, we study the luminal and temporal dynamics of pulses of different repetition rates at 2.05 μm in high-concentration HDFs considering the effects of ion-pairs. Input pulses having repetition rates of 25 GHz and 500 kHz are generated using wavelength tunable actively mode-locked Holmium-doped fiber laser (AML-HDFL) based on a single ring cavity and bidirectional pumping. The characteristics of the pulses propagating through high-concentration HDF are analyzed based on different metrics such as average power, peak power, pulse energy, full-width at half maximum (FWHM), and time delay without and with ion-pairs for values of fraction of ion-pairs k = 0 and k = 10%, respectively. The results obtained at optimized length of HDF show that ion-pairs significantly degrade the average power, peak power, and energy of the output pulses for both of the repetition rates. For both k = 0 and k = 10%, the FWHM and shape of the output pulses remain same in the presence of the ion-pairs while, time delay of 4 ps and 19 ns is observed in the output pulses at repetition rates of 25 GHz and 500 kHz, respectively. The effects of increasing the pump and signal power on the average power and energy of the output pulses for k = 0 and k = 10% are also discussed for both repetition rates. This analysis provides important guidelines for designers of 2 μm fiber lasers and amplifiers based on high-concentration HDFs.

A sensor region in a single-mode optical fiber loop was created and utilized in order to study the coating effect on sensor durability and system sensitivity by the Fiber Loop Ringdown Spectroscopy (FLRDS) technique. The sensor system was simply designed without any additional optical components. The bending loss theory in the single-mode fiber (SMF) was taken into account in data calculation. After stretching was performed on 10.0 cm long coated and noncoated sensorheads from the mid-points, the strain detection limits were determined as 5.3345 με and 6.7497 με with bare and coated sensorheads, respectively. The purpose of this study is to analyze the effect of N,N-Diethyl-p-phenylenediamine (NDPD) coating of the sensorhead on the sensor durability and sensitivity. The baseline stability of the system was obtained as 1.18% by considering a hundred consecutive data. Regarding to obtained results, the difference between calculated total optical losses of FLRDS systems with noncoated and NDPD coated sensorheads shows that coating sensorhead enhanced the sensor durability and the system sensitivity. An FLRDS system with high sensitivity, simple design and easy setup offers real-time measurement with continuous monitoring and provides advantages on durability by modification the sensorhead such as NDPD coating. Due to its attractive features such as low cost, simplicity, easy setup, high sensitivity, increased durability and continuous monitoring, an FLRDS system has a wide range of application areas in structural health monitoring, transportation, early detection, biomedical, chemical trace elements, rail and asphalt applications for continuous monitoring in a real-time merit.

For an undirected connected graph $G=G(V,E)$ with vertex set $V(G)$ and edge set $E(G)$, a subset $R$ of $V$ is said to be a resolving in $G$, if each pair of vertices (say $a$ and $b$; $a\neq b$) in $G$ satisfy the relation $d(a, k)\neq d(b, k)$, for at least one member $k$ in $R$. The minimum set $R$ with this resolving property is said to be a metric basis for $G$, and the cardinality of such set $R$, is referred to as the metric dimension of $G$, denoted by $dim_v(G)$. In this manuscript, we consider a complex molecular graph of one-heptagonal carbon nanocone (represented by $HCN_{s}$) and investigate its metric basis as well as metric dimension. We prove that just three specifically chosen vertices are enough to resolve the molecular graph of $HCN_{s}$. Moreover, several theoretical as well as applicative properties including comparison have also been incorporated.

In this work, we derive the optical tomograms of various q-deformed quantum states. We found that irrespective of the deformation parameter q, the Janus-faced nature of the quantum states manifests in their corresponding optical tomograms. A general method to estimate the quadrature moments from the optical tomograms of any q-deformed states is also derived. We also note that this technique can be used in high-precision experiments to observe deviations from the standard quantum mechanical behavior.

We study the dynamics of relativistic spinless particles moving in a plane when there is circular symmetry. The general formalism for solving the Klein–Gordon equation in cylindrical coordinates for such systems is presented, as well as the conserved observables and the corresponding quantum numbers. We look for bound solutions of the corresponding Klein–Gordon equation when one has vector and scalar circularly symmetric harmonic oscillator potentials. Both positive and negative bound solutions are considered when there is either equal vector and scalar potentials or symmetric vector and scalar potentials, and it is shown how both cases are related through charge conjugation. We compute the non-relativistic limit for those cases, and show that for symmetric scalar and vector potentials the limit does not exist in the first order of an harmonic oscillator frequency, recovering a known result from the Dirac equation with the same kind of potentials.

In this paper, we represent $n$-qubits as hypermatrices and consider various applications to quantum entanglement. In particular, we use the higher-order singular value decomposition of hypermatrices to prove that the $\pi$-transpose is an LU invariant. Additionally, through our construction we show that the matrix representation of the combinatorial hyperdeterminant of $2n$-qubits can be expressed as a product of the second Pauli matrix, allowing us to derive a formula for the combinatorial hyperdeterminant of $2n$-qubits in terms of the $n$-tangle.

We construct theoretically a set of space-time localized electromagnetic pulses, characterized by a wavenumber and a length . Their linear polarization becomes more perfect as increases and the pulse becomes more nearly monochromatic. Two measures of the degree of linear polarization are explored: one that gives the polarization at a point in space-time, and another that integrates the electric intensity over the focal plane of the pulse as the pulse passes through. The polarization measures and the total energy, momentum, and angular momentum of these pulses are calculated for all and . The fields of these pulses satisfy the Maxwell equations exactly.

In this paper, we present a new algorithm for generic combinatorial optimization, which we term quantum dueling. Traditionally, potential solutions to the given optimization problems were encoded in a 'register' of qubits. Various techniques are used to increase the probability of finding the best solution upon measurement. Quantum dueling innovates by integrating an additional qubit register, effectively creating a 'dueling' scenario where two sets of solutions compete. This dual-register setup allows for a dynamic amplification process: in each iteration, one register is designated as the 'opponent,' against which the other register's more favorable solutions are enhanced through a controlled quantum search. This iterative process gradually steers the quantum state within both registers toward the optimal solution. With a quantitative contraction for the evolution of the state vector, classical simulation under a broad range of scenarios and hyper-parameter selection schemes shows that a quadratic speedup is achieved, which is further tested in more real-world situations. In addition, quantum dueling can be generalized to incorporate arbitrary quantum search techniques and as a quantum subroutine within a higher-level algorithm. Our work demonstrates that increasing the number of qubits allows the development of previously unthought-of algorithms, paving the way for advancement of efficient quantum algorithm design.