Model Of Quantum Harmonic Oscillator Research Articles

Exploring Ion Polarizabilities and Their Correlation with van der Waals Radii: A Theoretical Investigation.

Polarizability (α) is a fundamental property which measures the tendency of the electron cloud of an atom, ion, or molecule to be distorted by electric field. Polarizability contributes to important physical properties such as molecular interactions or dielectric constants; thus, it is essential to have accurate polarizabilities in molecular simulations. However, it remains a challenge to develop polarizable force fields (FFs) for ions in computational chemistry. In particular, a comprehensive set of polarizabilities for ions has not been derived. Herein, we derived a systematic set of polarizabilities for atoms and ions across the periodic table based on high-level quantum mechanics calculations. These values have excellent agreement with experimental data. Furthermore, we examined the relationship between the obtained polarizabilities and the van der Waals (VDW) radii (RVDW) that we previously determined (J. Chem. Theory Comput., 2023, 19, 2064). Two relationships, RVDW ∝ α1/7 and RVDW ∝ α1/3, proposed in previous studies were examined in the present work. Our results indicated the former relationship, which was derived based on the quantum harmonic oscillator model, prevails for atoms and cations, but neither relationship provides a satisfactory fit for anions. This is consistent with the tight-binding nature of the electrons in atoms and cations, while it is more challenging to quantify the polarizabilities of anions because of their more dispersed electron clouds. Moreover, we compared different approaches to determine the dispersion coefficients, including the London equation, Slater-Kirkwood equation, symmetry-adapted perturbation theory (SAPT) calculations, and time-dependent density functional theory method, along with the approach based on VDW constants. Our results indicated that although different approaches predict deviated magnitudes for the dispersion coefficients, their predictions are highly correlated, implying that each of these approaches can be used to evaluate dispersion interactions after proper scaling. Finally, we have developed a parametrization strategy for the 12-6-4 model based on the obtained insights. We specifically compared the performance of the 12-6-4 model with SAPT and SobEDA analyses to model interactions involving Na+/Mg2+ and various ligands containing He, Ne, Ar, H2O, NH3, [H2PO4]-, and [HPO4]2-. Our results demonstrate that the 12-6-4 parameters effectively reproduce both the total interaction energy and the individual energy components (electrostatics, exchange-repulsion, dispersion, and induction), highlighting the physical robustness of the 12-6-4 model and the effectiveness of our parametrization approach. This study has significant implications for advancing the development of next-generation ion models and polarizable FFs.

Quantum harmonic oscillator model for simulation of intercity population mobility

Quantum harmonic oscillator model for simulation of intercity population mobility

Demonstrating Shrodenger equation involving harmonic oscillator potential with a position dependent mass in an external electric field

An external electric field is provided to the familiar one-dimensional quantum harmonic oscillator model with a various position mass m(x)=(a m_0)/(a+x). The Nikiforov-Uvarov approach is involved to investigate a particular solution to the exact Schrödinger equation. The exactly solvable confined model of the quantum harmonic oscillator in an external electric field was proposed. Starting with the BenDanial-Duke kinetic energy operator approximations, the construction of the position-dependent mass Schrödinger equation is studied. The analytic representation of the wave functions of the stationary states is expressed analytically and graphically using modified Laguerre polynomials as well as the energy spectrum. In contrast with the absence of an external electric field, when the energy spectrum totally overlaps with that of the harmonic oscillator potential in an external electric field: the energy spectrum becomes non-equidistant and varies depending on some factors. The Nikiforov-Uvarov approach succeeds broadly in demonstrating the wave function and energy spectrum and showing good sense.

The Wigner function of a semiconfined harmonic oscillator model with a position-dependent effective mass

We propose a phase-space representation concept in terms of the Wigner function for a quantum harmonic oscillator model that exhibits the semiconfinement effect through its mass varying with the position. The new method is used to compute the Wigner distribution function exactly for such a semiconfinement quantum system. This method suppresses the divergence of the integrand in the definition of the quantum distribution function and leads to the computation of its analytical expressions for the stationary states of the semiconfined oscillator model. For this quantum system, both the presence and absence of the applied external homogenous field are studied. Obtained exact expressions of the Wigner distribution function are expressed through the Bessel function of the first kind and Laguerre polynomials. Furthermore, some of the special cases and limits are discussed in detail.

Quantum harmonic oscillator model for fine-grained expressway traffic volume simulation considering individual heterogeneity

Accurate and robust fine-grained expressway traffic volume simulation is a critical issue in intelligent transportation systems and real-time traffic-related applications. However, the fine-grained expressway traffic volumes aggregated from vehicle trajectories heavily rely on individual heterogeneity, making it challenging for modeling and accurate simulation. In order to eliminate the influence of individual heterogeneity on the modeling and simulation of the fine-grained expressway traffic volume, this paper proposes a novel method named Quantum Harmonic Oscillator Model for Fine-grained Expressway Traffic Volume Simulation (FGTVS-QHO). FGTVS-QHO adopts the wave function of the quantum harmonic oscillator model to describe the irregular evolution of the location of the vehicle. Then several optimization strategies are applied to the numerical solution of the wave function. FGTVS-QHO is validated with the expressway traffic volumes of six exits along the Nanjing-Shanghai Expressway in China. The simulation performance of FGTVS-QHO is compared with the methods of Long and Short-Term Memory (LSTM) networks and Autoregressive Integrated Moving Average (ARIMA). FGTVS-QHO shows higher simulation accuracy, less time cost, and lower parameter complexity. Especially, the average simulation accuracy of FGTVS-QHO is improved by 24.80% and 58.05% compared with the above two methods, respectively. The scale effects of FGTVS-QHO also indicate that it is adaptive to simulate the expressway traffic volume at fine time granularity. This paper provides a new potential method for fine-grained expressway traffic volume simulation with strong individual heterogeneity.

Quantum oscillations in the stock market

This paper develops a quantum harmonic oscillator model of price fluctuations in a stock market, which builds on a previously-published quantum model of supply and demand, and can be viewed as a quantized version of a classical econometrics model first proposed in 1933. An advantage of the approach is that it interprets market behavior in terms of entropic forces which, when expressed in quantum terms, can account for a variety of behavioral effects of the sort studied in quantum cognition and quantum decision theory. The model helps to interpret quantities such as force, mass, frequency and energy in a financial setting, and is consistent with observed phenomena such as the square-root behavior of price impact.

Quantum noise of a harmonic oscillator under classical feedback control**Project supported by the National Natural Science Foundation of China (Grant Nos. 11534002, U1930402, and U1930403).

Quantum sensing has been receiving researcher’s attention these years due to its ultrahigh sensitivity and precision. However, the bandwidth of the sensors may be low, thus limiting the scope of their practical applications. The low-bandwidth problem is conquered by feedback control methods, which are widely utilized in classic control fields. Based on a quantum harmonic oscillator model operating near the resonant point, the bandwidth and sensitivity of the quantum sensor are analyzed. The results give two important conclusions: (a) the bandwidth and sensitivity are two incompatible performance parameters of the sensor, so there must be a trade-off between bandwidth and sensitivity in practical applications; (b) the quantum white noise affects the signal to be detected in a non-white form due to the feedback control.

An optimal secure and verifiable education content searching scheme for cloud-assisted edge computing

Cloud-assisted edge computing transforms service delivery by providing cloud-like services near the radio access network, ensuring low-latency services for mobile devices and alleviating significant pressure on the backbone network. The encryption and storage of multimedia data on untrusted cloud servers have prompted the adoption of searchable encryption for controlled keyword searches on ciphertext. Elevating online learning experiences requires sophisticated data analysis techniques, with Big Data playing a substantial role in efficiently processing extensive learning data and enhancing the value of E-learning platforms. Over time, E-learning management systems evolve into rich repositories of learning materials, enabling subject matter experts to reuse content for creating new online materials. To tackle challenges, we propose an optimal, secure, and verifiable education content searching scheme tailored for cloud-assisted edge computing. We introduce a lightweight encryption scheme for secure data storage and design a multi-scale quantum harmonic oscillator model to enhance content searching effectiveness and ensure accurate retrieval of educational information. Performance evaluation, utilizing benchmark datasets like Kaggle web contented, the CISI test set, and data from MAHE University, consistently validates the efficiency and feasibility of the proposed scheme for E-learning applications.

Improved parameterization of the quantum harmonic oscillator model based on localized wannier functions to describe Van der Waals interactions in density functional theory

Recently, the quantum harmonic oscillator model has been combined with maximally localized Wannier functions to account for long‐range dispersion interactions in density functional theory calculations (Silvestrelli, J. Chem. Phys. 2013, 139, 054106). Here, we present a new, improved set of values for the three parameters involved in this scheme. To test the new parameter set we have computed the potential energy curves for various systems, including an isolated Ar2 dimer, two N2 dimers interacting within different configurations, and a water molecule physisorbed on pristine graphene. While the original set of parameters generally overestimates the interaction energies and underestimates the equilibrium distances, the new parameterization substantially improves the agreement with experimental and theoretical reference values. © 2016 Wiley Periodicals, Inc.

Van Der Waals-Corrected Density Functional Theory Simulation of Adsorption Processes on Noble-Metal Surfaces: Xe on Ag(111), Au(111), and Cu(111)

The DFT/vdW-WF2s1 method based on the generation of localized Wannier functions, recently developed to include the van der Waals interactions in the Density Functional Theory and describe adsorption processes on metal surfaces by taking metal-screening effects into account, is applied to the case of the interaction of Xe with noble-metal surfaces, namely Ag(111), Au(111), and Cu(111). The study is also repeated by adopting the DFT/vdW-QHO-WF variant relying on the Quantum Harmonic Oscillator model which describes well many-body effects. Comparison of the computed equilibrium binding energies and distances, and the $C_3$ coefficients characterizing the adatom-surface van der Waals interactions, with available experimental and theoretical reference data shows that the methods perform well and elucidate the importance of properly including screening effects. The results are also compared with those obtained by other vdW-corrected DFT schemes, including PBE-D, vdW-DF, vdW-DF2, rVV10, and by the simpler Local Density Approximation (LDA) and semilocal (PBE) Generalized Gradient Approximation (GGA) approaches.

Including screening in van der Waals corrected density functional theory calculations: The case of atoms and small molecules physisorbed on graphene

The Density Functional Theory (DFT)/van der Waals-Quantum Harmonic Oscillator-Wannier function (vdW-QHO-WF) method, recently developed to include the vdW interactions in approximated DFT by combining the quantum harmonic oscillator model with the maximally localized Wannier function technique, is applied to the cases of atoms and small molecules (X=Ar, CO, H2, H2O) weakly interacting with benzene and with the ideal planar graphene surface. Comparison is also presented with the results obtained by other DFT vdW-corrected schemes, including PBE+D, vdW-DF, vdW-DF2, rVV10, and by the simpler Local Density Approximation (LDA) and semilocal generalized gradient approximation approaches. While for the X-benzene systems all the considered vdW-corrected schemes perform reasonably well, it turns out that an accurate description of the X-graphene interaction requires a proper treatment of many-body contributions and of short-range screening effects, as demonstrated by adopting an improved version of the DFT/vdW-QHO-WF method. We also comment on the widespread attitude of relying on LDA to get a rough description of weakly interacting systems.

Van der Waals interactions in density functional theory by combining the quantum harmonic oscillator-model with localized Wannier functions

We present a new scheme to include the van der Waals (vdW) interactions in approximated Density Functional Theory (DFT) by combining the quantum harmonic oscillator model with the maximally localized Wannier function technique. With respect to the recently developed DFT/vdW-WF2 method, also based on Wannier Functions, the new approach is more general, being no longer restricted to the case of well separated interacting fragments. Moreover, it includes higher than pairwise energy contributions, coming from the dipole-dipole coupling among quantum oscillators. The method is successfully applied to the popular S22 molecular database, and also to extended systems, namely graphite and H2 adsorbed on the Cu(111) metal surface (in this case metal screening effects are taken into account). The results are also compared with those obtained by other vdW-corrected DFT schemes.

Few sketches on connections between the Riccati and Ermakov–Milne–Pinney equations

AbstractIn this work, we focus on some connections that exist between the Riccati and Ermakov–Milne–Pinney equations, particularly those which are established via the Schrödinger equation. Some formulas that express the general solution of the Riccati and Schrödinger equations in terms of a particular solution of the Riccati equation are obtained. It is shown that the difference between the general and particular solutions of the normal Riccati equation satisfies the Ermakov–Milne–Pinney equation with λ = −1/4. The formulas derived in this work are discussed in view of their quantum chemical applications, especially related to the WKB approach that is applied to describe the semiclassical behavior of molecules. This discussion is illustrated by a simple model of quantum harmonic oscillator. © 2009 Wiley Periodicals, Inc. Int J Quantum Chem, 2009

IR spectral density of weak H-bonds involving indirect damping. I. A new approach using non-Hermitean effective Hamiltonians

Abstract A new approach of the combined effects of quantum direct and indirect dampings (within the adiabatic approximation) on the infrared lineshapes of the ν X–H stretching mode of simple and single weak H-bonds is proposed. The approach is based on our precedent model dealing only with bare weak H-bonds [B. Boulil, O. Henri-Rousseau , P. Blaise Chem. Phys. 126 (1988) 263; B. Boulil, J.-L. Dejardin, N. El-Ghandour, O. Henri-Rousseau, J. Mol. Struct. (Theochem) 314 (1994) 83]. As in this initial model, the indirect relaxation of the H-bond bridge is described by the aid of the driven damped quantum harmonic oscillator model [W. Louisell, L. Walker, Phys. Rev. 137 (1965) 204]. It is shown that the Hamiltonian characterizing the driven damped quantum harmonic oscillator may be obtained in a non-Hermitean reduced form, allowing, contrarily to the initial approach, the possibility of generalizations to more complex situations than those of bare H-bonds.

The q-Deformation of the Superoscillators and Their q-Supercoherent States

We discuss the superoscillators in thc supersymmetric quantum systems, and give the solution to the system. By making use of the annihilation and creation operators and their q-deformed operators, we also give the q-deformed quantum harmonic oscillator model in the supersymmetric quantum systems. The q-supercoherent states associated with the q-deformed supersymmetric quantum harmonic oscillators are constructed explicitly, and their properties are investigated. The uncertainty relations for q-supercoherent states are discussed as well.

Supersymmetric embedding of a model of a quantum harmonic oscillator interacting with infinitely many bosons

A mathematically rigorous analysis is given on supersymmetric embedding of a model of a one-dimensional quantum harmonic oscillator interacting with infinitely many bosons moving in the s-dimensional space Rs. The model is exactly soluble. By a rigorous explicit construction of supersymmetric quantum field theories, it was proven that the Hamiltonian of the model is supersymmetrically embeddable if it is non-negative. The index of the Dirac–Kähler-type operators associated with the supercharges of the supersymmetric quantum field theories is computed.

XII.—On the Theory of Unimolecular Gas Reactions: A Quantum Harmonic Oscillator Model

SynopsisThe writer's theory of unimolecular dissociation rates, based on the treatment of the molecule as a harmonically vibrating system, is put in a form which covers quantum as well as classical mechanics. The classical rate formulæ are as before, and are also the high-temperature limits of the new quantum formulæ. The high-pressure first-order rate k∞ is found first from the Gaussian distribution of co-ordinates and momenta of harmonic systems, and is justified for the quantum-mechanical case by Bartlett and Moyal's phase-space distributions. This leads to a re-formulation of k∞ as a molecular dissociation probability averaged over a continuum of states, and to a general rate for any pressure of the gas.The high-pressure rate k∞ is of the form ve-F/kT, where v and F depend, in the quantum case, on the temperature T; but v is always between the highest and lowest fundamental vibration frequencies of the molecule. Concerning the decline of the general rate k with pressure at fixed temperature, k/k∞ is to a certain approximation the same function of as was tabulated earlier for the classical case, apart from a constant factor changing the pressure scale in the quantum case.