Search Results (178)

Some classical texts on the Sturm–Liouville equation ${(p(x)y^{\prime })}^{\prime }-q(x)y+\lambda \rho (x)y=0$ are revised to highlight further properties of its solutions. Often, in the treatment of the ensuing integral equations, $\rho =const$ is assumed (and, further, $\rho =1$). Instead, here we preserve $\rho (x)$ and make a simple change only of the independent variable that reduces the Sturm–Liouville equation to $y^{″}-q(x)y+\lambda \rho (x)y=0$. We show that many results are identical with those with $\lambda \rho -q=const$. This is true in particular for the mean value of the oscillations and for the analog of the Riemann–Lebesgue Theorem. From a mechanical point of view, what is now the total energy is not a constant of the motion, and nevertheless, the equipartition of the energy is still verified and, at least approximately, it does so also for a class of complex $\lambda$. We provide here many detailed properties of the solutions of the above equation, with $\rho =\rho (x)$. The conclusion, as we may easily infer, is that, for large enough $\lambda$, locally, the solutions are trigonometric functions. We give the proof for the closure of the set of solutions through the Phragmén–Lindelöf Theorem, and show the separate dependence of the solutions from the real and imaginary components of $\lambda$. The particular case of $q(x)=\alpha \rho (x)$ is also considered. A direct proof of the uniform convergence of the Fourier series is given, with a statement identical to the classical theorem. Finally, the proof of J. von Neumann of the completeness of the Laguerre and Hermite polynomials in non-compact sets is revisited, without referring to generating functions and to the Weierstrass Theorem for compact sets. The possibility of the existence of a general integral transform is then investigated. Full article

This is a numerical investigation of optical and electronic characteristics of GaAs spherical quantum dots based on single and double quartic potentials and presenting a hydrogenic impurity at their center. The radial Schrödinger equation was solved using the finite difference method (FDM) to obtain the energy levels and the wavefunctions. These physical quantities were then used to compute the dipole matrix elements, the total optical absorption coefficient (TOAC), and the binding energies. The impact of the structural parameters in the confining potentials on the red and blue shifts of the TOAC is discussed in the presence and absence of hydrogenic impurity. Our results indicate that the structural parameter $k$ in both potentials plays a crucial role in tuning the TOAC. In the case of single quartic potential, increasing $k$ produces a blue shift; however, its augmentation in the case of double quartic potential displays a blue shift at first, and then a red shift. Furthermore, the augmentation of the parameter $k$ can control the binding energies of the two lowest states, ($1s$) and ($1p$). In fact, enlarging this parameter reduces the binding energies and converges them to constant values. In general, the modification of the potential’s parameters, which can engender two shapes of confining potentials (single quartic and double quartic), enables the experimenters to control the desired energy levels and consequently to adjust and select the suitable TOAC between the two lowest energy states (ground ($1s$) and first excited ($1p$)). Full article

Motivated by recent developments in the field of multilevel quantum batteries, we present the model of a quantum device for energy storage with anharmonic level spacing, based on a superconducting circuit in the transmon regime. It is charged via the sequential interaction with a collection of identical and independent ancillary two-level systems. By means of a numerical analysis, we show that, in case these ancillas are coherent, this kind of quantum battery can achieve remarkable performances in terms of the control of the stored energy and its extraction in regimes of parameters within reach in nowadays quantum circuits. Full article

In this paper, the optical properties and lattice thermal conductivity of Ti₂AlB₂ were studied by first-principles calculations. The real part of the dielectric constant, ε₁, attains a significant value of 47.26 at 0.12 eV, indicating strong polarization capabilities and energy storage capacity. Regarding optical properties, Ti₂AlB₂ exhibits significant absorption peaks at photon energies of 4.19 eV, 6.78 eV, and 10.61 eV, and 14.32 eV, with absorption coefficients of 184,168.1 cm⁻¹, 228,860.8 cm⁻¹, 366,350.8 and 303,440.6 cm⁻¹, indicating a strong absorption capacity. The loss function exhibits peaks at 19.80 eV and the refractive index reaches a maximum of 8.30 at 0.01 eV. Reflectivity is notably higher in the 0–5 eV range, exceeding 44%, which demonstrates excellent reflective properties. This suggests that Ti₂AlB₂ has potential as an optical coating material across certain frequency bands. The lattice thermal conductivity of Ti₂AlB₂ is obtained at 27.2 W/(m·K). The phonon relaxation time is greater in the low-frequency region, suggesting that phonons have a longer duration of action during the heat transport process, which may contribute to higher thermal conductivity. Although the phonon group velocity is generally low, several factors influence thermal conductivity, including phonon relaxation time and Grüneisen parameters. The high Grüneisen parameter of Ti₂AlB₂ indicates strong anharmonic vibrations, which may enhance phonon scattering and consequently reduce thermal conductivity. However, Ti₂AlB₂ still exhibits some lattice thermal conductivity, suggesting that the contributions of phonon relaxation time and group velocity to its thermal conductivity may be more significant. The unique optical properties and thermal conductivity of Ti₂AlB₂ indicate its potential applications in optical coatings and high-temperature structural materials. Full article

The nutritional quality of rice seeds is mainly determined by the content of key components such as protein, fat, and starch. Traditional chemical detection methods are time-consuming, labor-intensive, inefficient, and harmful to the environment. To overcome these limitations, this study developed a non-destructive detection method using near-infrared spectroscopy (1000–2200 nm) combined with linear regression modeling to achieve efficient and simultaneous multi-component analysis through the principle of anharmonic molecular vibration. By combining nutrient data from chemical analysis with spectroscopic measurements, we established a comprehensive rice seed composition dataset. After preprocessing with Gaussian denoising, first-order derivative transformation, SPA wavelength selection, and multiplicative scatter correction (MSC), we constructed partial least squares regression (PLS) and orthogonal partial least squares (OPLS), as well as artificial neural network (ANN) models. The OPLS model performed well in fat prediction (R² = 0.971, Q² = 0.926, RMSE = 0.175, RMSECV = 0.186), followed by starch (R² = 0.956, Q² = 0.907, RMSE = 0.159, RMSECV = 0.146) and protein (R² = 0.967, Q² = 0.936, RMSE = 0.164, RMSECV = 0.156). Our results confirm that the combination of the moving average, first order derivative, SPA, and MSC preprocessing of the OPLS model significantly improves the prediction. The developed non-destructive testing equipment provides a practical solution for automated, high-precision sorting of rice seeds based on nutrient composition. Full article

Fluxonium qubits, designed to mitigate charge noise and enhance anharmonicity, are among the most promising superconducting platforms for quantum computing. To understand and exploit their quantum properties and design novel fluxonium-based architectures with improved functionalities, these systems require an accurate Hamiltonian formulation to capture their energy level structure and quantum dynamics. This work presents a systematic method for constructing the Hamiltonian for multi-loop circuits that partitions the system into a set of uncoupled harmonic oscillators and a coupled anharmonic part originating from the Josephson circuit elements, allowing clear identification of independent modes and isolating the nonlinearity in the Josephson terms. While demonstrated for fluxonium-type multi-loop circuits, this method can be generalized to other superconducting qubit architectures within the broader context of circuit QED, making it a versatile tool for exploring different circuit configurations. Our systematic and flexible modeling approach forms the theoretical basis for the qubit measurement and control experiments validating multi-loop fluxonium architectures. Full article

The merging of pore designs is a potential strategy for achieving ultra-low lattice thermal conductivity (κ), for which phonon anharmonicity and size effect are indispensable for discovering novel functional materials in thermal applications. In this study, monolayer holey graphyne (HGY) and boron nitride holey graphyne (BN-HGY) were examined for their phonon thermal transport properties through first-principles calculation and phonon Boltzmann function. HGY exhibits an intrinsic lattice thermal conductivity (κ) of 38.01 W/mK at room temperature, which exceeds BN-HGY’s 24.30 W/mK but is much lower than 3550 W/mK for BTE graphene. The phonon–phonon scattering behavior of BN-HGY is obviously increased compared to HGY due to the enhancement of anharmonicity, which leads to a shorter phonon lifetime and lower κ. Additionally, at room temperature, the representative mean free path (rMFP) of BN-HGY is substantially higher than that of HGY, and the κ of BN-HGY decreases faster at a larger rMFP (within a unit nm). This work will be constructive to further the application of HGY and BN-HGY as thermal management materials. Full article

Direct Ink Writing (DIW) is an advanced additive manufacturing 3D-printing technique with significant potential for producing hydrogels in biomedical and engineering applications. This study presents a comprehensive rheological analysis of the yielding and recovery properties critical for ensuring the printability of carboxymethyl cellulose (CMC)-based hydrogels incorporating atenolol, an antihypertensive agent, as the active ingredient. The viscoelastic properties under shear conditions were examined using Large Amplitude Oscillatory Shear (LAOS) testing. To obtain both qualitative and quantitative insight into hydrogel dynamics, Lissajous-Bowditch plots and Fourier Transform (FT) coefficients were analyzed. The evaluation of stress signal anharmonicity and the decomposition of stress into its elastic and viscous components allowed for distinguishing structural evolution under flow among the tested hydrogels. Additionally, the analysis of the Sequence of Physical Processes (SPP) during each deformation cycle provided deeper insight into oscillatory yielding behavior, emphasizing the role of elastic strains in determining printability. Overall, the study offers valuable understanding of the nonlinear viscoelastic behavior of CMC-based hydrogels, providing a framework for optimizing hydrogel formulations in DIW applications. Full article

The Davydov–Chaban Hamiltonian, which describes the quadrupole collective states of triaxial nuclei involving two polar coordinates and three Euler rotation angles, is numerically solved in a basis of Bessel functions of the first kind for a sixth-order anharmonic oscillator potential and a triaxial deformation, respectively. The proposed model is designed to describe a phase transition, as well as coexistence and mixing between an approximately spherical shape and a triaxial deformed one. Full article

A new method for the precise semiempirical determination of the basic parameters (structural parameters and parameters of the intramolecular potential energy surface, PES) of a molecule on the basis of highly accurate experimental data from the microwave and submillimeter-wave regions is suggested. The options and advantages of this method in comparison with the other methods of molecular PES determination are discussed using a diatomic molecule as an appropriate illustration. The HCl molecule is exploited as a suitable example. It is shown with this example that the use of a very limited number (ten for H³⁵Cl and five for D³⁵Cl) of submillimeter-wave line positions allows one to determine the values of the equilibrium rotational parameter, harmonic frequency, and anharmonic coefficients of the third, fourth, and fifth order with accuracy of 0.01%, 0.01%, 0.01%, 2.1%, and 10.1%, respectively, in comparison with the analogous results obtained from extensive infrared studies. Full article

Two-dimensional (2D) layered materials have received much attention due to the unique properties stemming from their van der Waals (vdW) interactions, quantum confinement, and many-body interactions of quasi-particles, which drive their exotic optical and electronic properties, making them critical in many applications. Here, we review our past years’ findings, focusing on many-body interactions in 2D layered materials, including phonon anharmonicity, electron–phonon coupling (e-ph), exciton dynamics, and phonon anisotropy based on temperature (polarization)-dependent Raman spectroscopy and Photoluminescence (PL). Our review sheds light on the role of quasi-particles in tuning the material properties, which could help optimize 2D materials for future applications in electronic and optoelectronic devices. Full article

In this work, we investigate the transition from regular dynamics to chaotic behavior in a one-dimensional quartic anharmonic classical oscillator driven by a time-dependent external square-wave force. Owing to energy conservation, the motion of an undriven quartic anharmonic oscillator is regular, periodic, and stable. For a driven quartic anharmonic oscillator, the equations of motion cannot be solved analytically due to the presence of an anharmonic term in the potential energy function. Using the fourth-order Runge–Kutta method to numerically solve the equations of motion for the driven quartic anharmonic oscillator, we find that the oscillator motion under the influence of a sufficiently small driving force remains regular, while by gradually increasing the driving force, a series of nonlinear resonances can occur, grow, overlap, and ultimately disappear due to the emergence of chaos. Full article

We investigate perovskite oxides from different perspectives, namely their pseudo-harmonic dynamical properties, their dynamical properties when strong anharmonicity exists, and the intriguing functionalities arising from domain walls. Taking these viewpoints together yields a rather complex picture of this material class, which has not been found in previous approaches. It opens pathways to novel applications and reveals the rich ground states beyond the fictitious belief in the ‘simplicity of perovskites and such structures’. Full article

With the help of a microscopic model and Green’s function technique, we studied the multiferroic and phonon properties of the recently reported new multiferroic Pr₂FeAlO₆ (PFAO) compound, which belongs to the double perovskite A₂BB’O₆ family. The magnetization decreases with the increase in temperature and disappears at the ferromagnetic Curie temperature $T_C^{FM}$. The polarization increases with the application of an external magnetic field, indicating strong magnetoelectric coupling and confirming the multiferroic behavior of PFAO. In the curves of dependence of the phonon energy and their damping with respect to temperature, a kink is observed at $T_C^{FM}$. This is due to the strong anharmonic spin–phonon interactions, which play a crucial role below $T_C^{FM}$ and are frequently observed in other double perovskite compounds. Above $T_C^{FM}$, only anharmonic phonon–phonon coupling remains. The phonon mode is controlled by an external magnetic field. Full article

Here, we present a general framework for computing the infrared anharmonic vibrational spectra of polyatomic molecules using Born–Oppenheimer molecular dynamics (BOMD) with PyRAMD software. To account for nuclear quantum effects, we suggest using a simplified Wigner sampling (SWS) approach simultaneously coupled with Andersen and Berendsen thermostats. We propose a new criterion for selecting the parameter of the SWS based on the molecules’ harmonic vibrational frequencies and usage of the large-time-step blue shift correction, allowing for a decrease in computational expenses. For the Fourier transform of the dipole moment autocorrelation function, we propose using the regularized least-squares analysis, which allows us to obtain higher-frequency resolution than with the direct application of fast Fourier transform. Finally, we suggest the usage of the pre-parameterized scaling factors for the IR spectra from BOMD, also providing the scaling factors for the spectra at the BLYP-D3(BJ)/6-31G, PBE-D3(BJ)/6-31G, and PBEh-3c levels of theory. Full article