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We apply the well known Rayleigh-Ritz method (RRM) to the projection of a Hamiltonian operator chosen recently for the extension of the Rayleigh-Ritz variational principle to ensemble states. By means of a toy model we show that the RRM eigenvalues approach to those of the projected Hamiltonian from below in most cases but a few ones. We also discuss the effect of an energy shift and the projection of the identity operator.

We analyse the exact solutions of a conditionally-solvable Schr\"odinger equation with a rational potential. From the nodes of the exact eigenfunctions we derive a connection between the otherwise isolated exact eigenvalues and the actual eigenvalues of the Hamiltonian operator.

We show that a perturbed Coulomb problem discussed recently is conditionally solvable. We obtain the exact eigenvalues and eigenfunctions and compare the former with eigenvalues calculated by means of a numerical method. We discuss the meaning of the numbers that determine the exact solutions which arise from the Frobenius (power-series) method.

We revisit the quantum-mechanical two-dimensional harmonic oscillator with an electric field confined to a circular box of impenetrable walls. In order to obtain the energy spectrum we resort to the Rayleigh-Ritz method with polynomial and Gaussian basis sets. We compare present results with those derived recently by other authors. We discuss the limits of large and small box radius and also do some calculations with perturbation theory.

In this short note we resort to the well known Hellmann-Feynman theorem to prove that some non-relativistic Hamiltonian operators support an infinite number of bound states.

This work describes the development and validation of a digital twin for a semi-autogenous grinding (SAG) mill controlled by an expert system. The digital twin consists of three modules emulating a closed-loop system: fuzzy logic for the expert control, a state-space model for regulatory control, and a recurrent neural network for the SAG mill process. The model was trained with 68 hours of data and validated with 8 hours of test data. It predicts the mill's behavior within a 2.5-minute horizon with a 30-second sampling time. The disturbance detection evaluates the need for retraining, and the digital twin shows promise for supervising the SAG mill with the expert control system. Future work will focus on integrating this digital twin into real-time optimization strategies with industrial validation.

Dibaryons are the simplest system in which the baryon-baryon interaction, and hence the underlying quark-quark interaction, can be studied in a clear way. Although the only dibaryon known today is the deuteron (and possibly the $d^*$), fully heavy dibaryons are good candidates for bound states because in such systems the kinetic energy is small and the high symmetry of the wave function favours binding. In this study, the possible existence of $\Omega_{ccc}\Omega_{ccc}$ and $\Omega_{bbb}\Omega_{bbb}$ dibaryons is investigated in the framework of a constituent quark model that satisfactorily describes the deuteron, the $d^*(2380)$ and the $NN$ interaction. $J^P=0^+$ candidates are found in both systems with binding energies of the order of MeV., Comment: 9 pages, 8 figures

Significant advancements in the field of wood species identification are needed worldwide to support sustainable timber trade. In this work we contribute to automate the identification of wood species via high-resolution macroscopic images of timber. The main challenge of this problem is that fine-grained patterns in timber are crucial in order to accurately identify wood species, and these patterns are not properly learned by traditional convolutional neural networks (CNNs) trained on low/medium resolution images. We propose a Timber Deep Learning Identification with Patch-based Inference Voting methodology, abbreviated TDLI-PIV methodology. Our proposal exploits the concept of patching and the availability of high-resolution macroscopic images of timber in order to overcome the inherent challenges that CNNs face in timber identification. The TDLI-PIV methodology is able to capture fine-grained patterns in timber and, moreover, boosts robustness and prediction accuracy via a collaborative voting inference process. In this work we also introduce a new data set of marcroscopic images of timber, called GOIMAI-Phase-I, which has been obtained using optical magnification in order to capture fine-grained details, which contrasts to the other datasets that are publicly available. More concretely, images in GOIMAI-Phase-I are taken with a smartphone with a 24x magnifying lens attached to the camera. Our data set contains 2120 images of timber and covers 37 legally protected wood species. Our experiments have assessed the performance of the TDLI-PIV methodology, involving the comparison with other methodologies available in the literature, exploration of data augmentation methods and the effect that the dataset size has on the accuracy of TDLI-PIV., Comment: 17 pages and 6 figures

We argue that several potentials proposed recently for the analysis of the vibrational-rotational spectra of diatomic molecules and their thermodynamic properties exhibit a flaw. One can easily show that the parameters $D_e $ and $r_e$ in those potentials are not the dissociation energy and equilibrium bond length, respectively, as the proposers believe. We show how to overcome the mistake in a simple and quite general way.

We overview the main equations of the Rayleigh-Ritz variational method and discuss their connection with the problem of simultaneous diagonalization of two Hermitian matrices.

This paper reports how CdSe core-only nanoplatelets coupled with plasmonic Al nanoparticle lattices can exhibit exciton-polariton lasing. By improving a procedure to synthesize monodisperse 4-monolayer CdSe nanoplatelets, we could resolve polariton decay dynamics and pathways. Experiment and theory confirmed that the system is in the strong coupling regime based on anti-crossings in the dispersion diagrams and magnitude of the Rabi splitting values. Notably, polariton lasing is observed only for cavity lattice periodicities that exhibit specific dispersive characteristics that enable polariton accumulation. The threshold of polariton lasing is 25-fold lower than reported photon lasing values from CdSe nanoplatelets in similar cavity designs. This open-cavity platform offers a simple approach to control exciton polaritons anticipated to benefit quantum information processing, optoelectronics, and chemical reactions.

We test the analytical expressions for the first two eigenvalues of the harmonic oscillator with a Gaussian perturbation proposed recently. Our numerical eigenvalues show that those expressions are valid in an interval of the coupling parameter that is greater than the one estimated by the authors. We also calculate critical values of the coupling parameter and several exceptional points in the complex plane.

Spaceplates have emerged in the context of nonlocal metasurfaces, enabling the compression of optical systems by minimizing the required empty space between their components. In this work, we design and analyze spaceplates that support resonances with opposite symmetries, operating under the so-called Huygens' condition. Using the temporal coupled-mode theory, we demonstrate that the spatial compression provided by Huygens' spaceplates is twice that of conventional single-resonance counterparts. Additionally, they can support broader operational bandwidths and numerical apertures, facilitating the reduction of chromatic aberrations. Moreover, Huygens' spaceplates maintain nearly full transparency over a wide frequency and angular range, allowing their straightforward cascading for multi-frequency broadband operation. Finally, we propose a physical implementation of a Huygens' spaceplate for optical frequencies based on a photonic crystal slab geometry., Comment: 9 pages, 5 figures

In this manuscript we characterize the completeness of a normed space through the strong lacunary (N-theta) and lacunary statistical convergence (S-theta) of series. A new characterization of weakly unconditionally Cauchy series through N-theta and S-theta is obtained. We also relate the summability spaces associated with these summabilities with the strong p-Cesaro convergence summability space.

Computational models are an essential tool for the design, characterization, and discovery of novel materials. Hard computational tasks in materials science stretch the limits of existing high-performance supercomputing centers, consuming much of their simulation, analysis, and data resources. Quantum computing, on the other hand, is an emerging technology with the potential to accelerate many of the computational tasks needed for materials science. In order to do that, the quantum technology must interact with conventional high-performance computing in several ways: approximate results validation, identification of hard problems, and synergies in quantum-centric supercomputing. In this paper, we provide a perspective on how quantum-centric supercomputing can help address critical computational problems in materials science, the challenges to face in order to solve representative use cases, and new suggested directions., Comment: 65 pages, 15 figures; comments welcome

We discuss in detail a well known method for obtaining the frequencies of the normal modes of coupled harmonic oscillators that is based on the simultaneous diagonalization of two symmetric matrices. We apply it to some simple illustrative examples recently chosen for the presentation of an alternative approach based on a set of constants of the motion. We show that the traditional method is simpler, even in the case of equal frequencies. We also discuss a problem that commonly appears in elementary courses on quantum mechanics that also requires the diagonalization of two symmetric matrices.

We analyse recent contradictory results and conclusions about the spectrum of the screened Coulomb potential $V(r)=-r^{-1}e^{-C/r}$. The well known Hellmann-Feynman theorem shows that all the bound states of the Coulomb potential ($C=0$) remain bounded as $C$ increases. We derive a simple approximate analytical expression for the eigenvalues for sufficiently small values of the screening parameter $C$ and an approximate asymptotic expression for the asymptotic behaviour of the s-state eigenvalues when $C\rightarrow \infty $. Present results are expected to resolve the discrepancy about the spectrum of the quantum-mechanical model just mentioned.

We use an electric-dipole laser-driven transition to precisely measure the cyclotron-frequency ratios of the pairs $^{42}$Ca$^+$-$^{40}$Ca$^+$, $^{44}$Ca$^+$-$^{40}$Ca$^+$ and $^{48}$Ca$^+$-$^{40}$Ca$^+$ in a 7-tesla Penning trap. A single laser-cooled ($T\approx 1$~mK) ion serves, together with photon-counting and/or photon-imaging units, as a radiofrequency detector covering a broad-band frequency spectrum, in the present case from kHz to a few MHz. Such detectors ($^{40,42,44,48}$Ca$^{\scriptsize{+}}$) allow measuring extremely small forces, with measured normalized sensitivities down to $7.4(3.5)$ yN$/\sqrt{\text{Hz}}$ and $24.9(9.9)$ yN$/\sqrt{\text{Hz}}$ in the MHz and kHz regime, respectively. The direct determination of the ions' amplitudes makes a cyclotron-frequency measurement process more robust against inhomogeneities of the magnetic field and/or deviations of the electric quadrupole field due to mechanical imperfections of the trap., Comment: 6 pages, 3 figures

We compare the well known Rayleigh-Ritz variational method (RRVM) with a recently proposed approach based on supersymmetric quantum mechanics and the Gram-Schmidt orthogonalization method (SSQMGS). We apply both procedures to a particular class of double-well harmonic oscillators that had been conveniently chosen for the application of the latter approach. The RRVM eigenvalues converge smoothly from above providing much more accurate results with less computational effort. Present results show that the unproved SSQMGS upper bounds do not hold.

This study investigates the properties of the $T_{\psi\psi}$ tetraquark candidates within a coupled-channels calculation of the $c\bar c- c\bar c$ system, specifically focusing on the $J^P=0^\pm$, $1^\pm$, and $2^\pm$ sectors. The analysis includes various channels containing a $J/\psi$, $\psi^\prime$, $\eta_c$, and $\eta_c^\prime$ meson. By searching for poles in the scattering matrix, a total of 29 states in different $J^P$ sectors with masses ranging from 6.1 to 7.6 GeV/c$^2$ are identified. The study further investigates the masses, widths and branching ratios of these states, leading to the identification of two potential candidates for the experimental $T_{\psi\psi}(6200)$ tetraquark, one candidate for $T_{\psi\psi}(6600)$, two for $T_{\psi\psi}(6700)$, four for $T_{\psi\psi}(6900)$, and three for $T_{\psi\psi}(7200)$ tetraquarks. Additionally, the paper discusses strategies to discriminate between different candidates and explores possible detection channels for further $c\bar c- c\bar c$ states., Comment: 9 pages, 3 tables and 1 figure

We analyse a recent application of the Cornell potential with spin-spin interaction to the mass spectra of quarkonia and show that the authors have in fact used the Kratzer-Fues potential. They inadvertently converted one potential into the other by means of an invalid transformation.

We discuss a systematic construction of dimensionless quantum-mechanical equations. The process reduces the number of independent model parameters to a minimum and, at the same time, provides the natural units of length, energy, etc. in a clear, straightforward way. We compare this systematic procedure with the widely adopted one that consists of setting $\hbar=1$. As illustrative examples, we choose some simple one-dimensional models proposed recently for the study of localized states in inhomogeneous media.

Silicon anodes hold great promise for next-generation Li-ion batteries. The main obstacle to exploiting their high performance is the challenge of linking experimental observations to atomic structures due to the amorphous nature of Li-Si alloys. We unveil the atomistic-scale structures of amorphous Li-Si using our recently developed density functional tight-binding model. Our claim is supported by the successful reproduction of experimental X-ray pair distribution functions, NMR and M\"ossbauer spectra using simple nearest neighbors models. The predicted structures are publicly available., Comment: 5 pages, 4 figures

When dealing with certain mathematical problems, it is sometimes necessary to show that some function induces a metric on a certain space. When this function is not a well renowned example of a distance, one has to develop very particular arguments that appeal to the concrete expression of the function in order to do so. The main purpose of this paper is to provide several sufficient results ensuring that a function of two variables induces a distance on the real line, as well as some necessary conditions, together with several examples that show the applicability of these results. In particular, we show how a hypothesis about the sign of the cross partial derivative of the candidate to distance is helpful for deriving such kind of results., Comment: 16 pages

The catalyst-free synthesis of graphene on dielectrics prevents the damage induced by the transfer process. Although challenging, to master this synthesis would boost the integration of graphene on consumer electronics since defects hinder its optoelectronic properties. In this work, the influence of the different surface terminations of c-plane sapphire substrates on the synthesis of graphene via plasma-enhanced chemical vapour deposition (PECVD) is studied. The different terminations of the sapphire surface are controlled by a plasma etching process. A design of experiments (DoE) procedure was carried out to evaluate the major effects governing the etching process of four different parameters: i.e. discharge power, time, pressure and gas employed. In the characterization of the substrate, two sapphire surface terminations were identified and characterized by means of contact angle measurements, being a hydrophilic (hydrophobic) surface the fingerprint of an Al- (OH-) terminated surface, respectively. The defects within the synthesized graphene were analysed by Raman spectroscopy. Notably, we found that the ID/IG ratio decreases for graphene grown on OH-terminated surfaces. Furthermore, two different regimes related to the nature of graphene defects were identified and depending on the sapphire terminated surface are bound either to vacancy or boundary like defects. Finally, studying the density of defects and the crystallite area, as well as their relationship with the sapphire surface termination paves the way for increasing the crystallinity of the synthesized graphene., Comment: 27 pages, 6 figures

We show that the effective secular equation proposed several years ago is suitable for estimating the location of the exceptional points of eigenvalue equations. As an illustrative example we choose the well known Mathieu

In this work we study some topological aspects of function spaces arising in Stieltjes differential calculus. Chief among them are compactness results related to the Ascoli-Arzel\`a and Kolmogorov-Riesz theorems, as well as their applications to Stieltjes-Sobolev spaces and decomposable functions.

The recently discovered $T_{cc}^+$ is evaluated as a $DD^*$ molecular structure in the $J^P=1^+$ sector. A coupled-channels calculation in charged basis, considering the $D^0D^{*\,+}$, $D^+D^{*\,0}$ and $D^{*\,0}D^{*\,+}$ channels, is done in the framework of a constituent quark model that successfully described other molecular candidates in the charmonium spectrum such as the $X(3872)$. The $T_{cc}^+$ is found as a $D^0D^{*\,+}$ molecule ($87\%$) with a binding energy of $387$ keV/c$^2$ and a width of $81$ keV, in agreement with the experimental measurements. The quark content of the state forces the inclusion of exchange diagrams to treat indistinguishable quarks between the $D$ mesons, which are found to be essential to bind the molecule. The $D^0D^0\pi^+$ line shape, scattering lengths and effective ranges of the molecule are also analyzed, which are found to be in agreement with the LHCb analysis. We search for further partners of the $T_{cc}^+$ in other charm and bottom sectors, finding different candidates. In particular, in the charm sector we find a shallow $J^P=1^+$ $D^+D^{*\,0}$ molecule ($83\%$), dubbed $T_{cc}^\prime$, just $1.8$ MeV above the $T_{cc}^+$ state. In the bottom sector, we find an isoscalar and an isovector $J^P=1^+$ bottom partners, as $BB^*$ molecules lying $21.9$ MeV/c$^2$ ($I=0$) and $10.5$ MeV/c$^2$ ($I=1$), respectively, below the $B^0B^{*\,+}$ threshold., Comment: 11 pages, 3 figures, 7 tables

Hidden-charm pentaquark-like $P_{\psi s}^\Lambda(4459)^0$ and $P_{\psi s}^\Lambda(4338)$ resonances are studied in a constituent quark model as molecular meson-baryon structures. Such states are found in the $J^P(I)=\frac{1}{2}^-(0)$ channel with masses and widths compatible with the experimental measurements in a coupled-channels calculation with all the parameters constrained from previous studies. Other candidates are explored in the $J^P=\frac{1}{2}^-$, $\frac{3}{2}^-$ and $\frac{5}{2}^-$ channels in the charm and bottom sectors, with isospins $0$ ($P_{\psi s}^\Lambda$ and $P_{\Upsilon s}^\Lambda$) and $1$ ($P_{\psi s}^\Sigma$ and $P_{\Upsilon s}^\Sigma$). Additionally, the formalism is extended to study the $P_{\psi ss}^N$ ($P_{\Upsilon ss}^N$) pentaquarks, where eight candidates are predicted as $\bar D_s \Xi_c$ molecules in $I=\frac{1}{2}$, with $J^P=\frac{1}{2}^-$, $\frac{3}{2}^-$ and $\frac{5}{2}^-$ for the charm sector and nine candidates as $B_s \Xi_b$ for the bottom one., Comment: 8 pages, 1 figure, 7 tables

We study a general one-mode non-Hermitian quadratic Hamiltonian that does not exhibit $\mathcal{PT}$-symmetry. By means of an algebraic method we determine the conditions for the existence of real eigenvalues as well as the location of the exceptional points. We also put forward an algebraic alternative to the generalized Bogoliubov transformation that enables one to convert the quadratic operator into a simpler form in terms of the original creation and annihilation operators. We carry out a similar analysis of a two-mode oscillator that consists of two identical one-mode oscillators coupled by a quadratic term.

This paper introduces a new opensource quantum tool-set called QuantumSolver based on Qiskit to help developers without knowledge in quantum computing. The developed library includes a set of algorithms with different features: random number generation, Bernstein-Vazirani algorithm and quantum key distribution using the BB84 protocol. This paper described the main details about the implementation of the toolset, focusing in the challenges that the authors faced. Finally, this document analyzes the results obtained with some conclusions that authors compares with the included features., Comment: 10 pages, 4 figures, sumited to CAITS, SAM, CSCE, Springer Nature, Indexed by Computing Research and Education (CORE) with ranking C, Indexed by CS Conference Rankings (0.83), Indexed by GII-GRIN in Class WiP

We show that a method proposed recently, based on the characteristic polynomial of an effective Hamiltonian, had been developed several years earlier by other authors in a clearer and more general way. We outline both implementations of the approach and compare them by means of the calculation of the exceptional point closest to origin for a toy model.

The production of single-charmed baryons $\Lambda_c^+ \Lambda_c^-$, $\Lambda_c^+ \Sigma_c^-$+h.c. and $\Sigma_c^+ \Sigma_c^-$ in $p\bar p$ collisions is studied in the framework of a constituent quark model which has satisfactorily described the $N\bar N$ system and the strangeness production $p\bar p\to \Lambda\bar \Lambda$, $\Lambda\bar\Sigma$ and $\Sigma\bar\Sigma$ processes. Predictions on the total cross sections are analyzed for different approaches to the underlying $n\bar n\to c\bar c$ process, mediated by one gluon annihilation diagrams. The results indicate that the cross section is of the order of $1$ nb between $10-14$ GeV for $\Lambda_c^+\Lambda_c^-$ and $\Lambda_c^+ \Sigma_c^-$ channels, and around $0.01-0.1$ nb for $\Sigma_c^+\Sigma_c^-$. This estimations can be relevant for their future search in facilities like $\bar{P}$ANDA., Comment: 7 pages, 6 figures

We discuss results obtained recently for a quantum-mechanical model given by a neutral particle with a magnetic quadrupole moment in a radial electric field and a scalar potential proportional to the radial variable in cylindrical coordinates that also includes the noninertial effects of a rotating reference frame. We show that the conjectured allowed values of the cyclotron frequency are a mere artifact of the truncation of the power series used to solve the radial eigenvalue equation. Our analysis proves that the analytical expression for the eigenvalues are far from correct.