Harmonic Potential Research Articles

Study on the Influence of External Electric Field Control and Vibrational Quantum Effect on the Charge Separation Mechanism in Fullerene-Based Systems.

Based on the DCV-C60 system of fullerene acceptor organic solar cell active materials, the charge transfer process of D-A type molecular materials under the action of an external electric field (Fext) was explored. Within the range of electric field application, the excited state characteristics exhibit certain regular changes. Based on reducing the excitation energy, the excitation mode shows a trend of developing toward low excited states. The effect of solvent polarity on the stability and reorganization energy of the charge transfer state was investigated. The dependence of charge separation parameters on specific molecular structures within the electric field range was studied, proving that the electric field set along the electron transfer direction can indeed accelerate charge separation. The influence of vibrational modes on the charge separation process was studied, and the results showed that the vibrational quantum tunneling effect significantly promoted the charge separation. Therefore, considering the vibrational excitation effect and the perturbation of the nuclear-electron interaction is crucial for more accurate simulation of the electron-vibration coupling process in the excited state.

Continuous feedback protocols for cooling and trapping a quantum harmonic oscillator

Continuous feedback protocols for cooling and trapping a quantum harmonic oscillator

A novel approach for spectroscopic study of Ωbbc baryon in the hypercentral constituent Quark model

In this paper, we determine the radial and orbital states mass spectra of the triply heavy baryon [Formula: see text] with total spin [Formula: see text] and 3/2 using the hypercentral constituent quark model (hCOM). The mass spectra are obtained by incorporating the color Coulomb plus linear confining term and the harmonic oscillator potential with first-order correction. Additionally, we considered spin–spin, spin-orbit and tensor interactions for hyperfine splitting calculation. Our computed mass spectra of the [Formula: see text] baryon is compared with existing literature. Further, we establish Regge trajectories of this baryon in ([Formula: see text]) and ([Formula: see text]) planes which are helpful in determining the unknown quantum number and [Formula: see text] values.

Compression of a line of spheres or bubbles in a transverse confining potential

ABSTRACT A line of spheres or bubbles, confined in a cylindrically symmetric harmonic potential, buckles under axial compression. Increasing compression results in a sequence of initially planar, and eventually non-planar, structures. We present a catalogue of these, drawing on both experiments and computer simulations. The latter make use of the theory of Morse and Witten to model bubble–bubble interaction. Numerical results are summarised in stability diagrams, of potential relevance to the creation of chiral photonic crystals from self-assembled packings of spheres.

Optimal Dynamical Gauge in the Quantum Rabi Model

Abstract We investigate the gauge dependence of physical observables in the quantum Rabi model (QRM) under di erent potential fields, arising from the Hilbert-space truncation of the atomic degrees of freedom. In both square-well and harmonic potentials, we find that the optimal gauge for the groundstate energy depends on the cavity frequency: the dipole gauge is optimal in the low-frequency limit, while the Coulomb gauge is optimal in the high-frequency limit. For a dynamical quantity such as the out-of-time-order correlator (OTOC), we demonstrate the necessity of introducing an optimal dynamical gauge. This study provides deeper insights into the intricate relationship between gauge choice and the dynamics of quantum electrodynamics (QED) systems, paving the way for more accurate theoretical frameworks.

Generalised Ornstein–Uhlenbeck process: memory effects and resetting

Abstract In this work we consider a generalised Ornstein-Uhlenbeck process for a stochastically driven particle in an harmonic potential which is governed by a Fokker-Planck equation in the presence of a memory kernel. We analyse the probability density function, the mean and the mean squared displacement by employing the subordination approach connecting the operational time of the process with the (generalised) laboratory time. We provide analytical results for the mean and the mean squared displacement in case of a power-law memory kernel which corresponds to the fractional Ornstein-Uhlenbeck process. The generalised Ornstein-Uhlenbeck process in the presence of Poissonian resetting is also investigated by using the renewal equation approach, and the nonequilibrium stationary state approached in the long time limit is obtained. The analytical results are confirmed by numerical simulations based on the coupled Langevin equations.

Phase transitions in chromatin: Mesoscopic and mean-field approaches.

By means of a minimal physical model, we investigate the interplay of two phase transitions at play in chromatin organization: (1) liquid-liquid phase separation within the fluid solvating chromatin, resulting in the formation of biocondensates; and (2) the coil-globule crossover of the chromatin fiber, which drives the condensation or extension of the chain. In our model, a species representing a domain of chromatin is embedded in a binary fluid. This fluid phase separates to form a droplet rich in a macromolecule (B). Chromatin particles are trapped in a harmonic potential to reproduce the coil and globular phases of an isolated polymer chain. We investigate the role of the droplet material B on the radius of gyration of this polymer and find that this radius varies nonmonotonically with respect to the volume fraction of B. This behavior is reminiscent of a phenomenon known as co-non-solvency: a polymer chain in a good solvent (S) may collapse when a second good solvent (here B) is added in low quantity and expands at higher B concentration. In addition, the presence of finite-size effects on the coil-globule transition results in a qualitatively different impact of the droplet material on polymers of various sizes. In the context of genetic regulation, our results suggest that the size of chromatin domains and the quantity of condensate proteins are key parameters to control whether chromatin may respond to an increase in the quantity of chromatin-binding proteins by condensing or expanding.

Dunkl-Schrödinger equation in higher dimensions

Abstract This paper presents analytical solutions for eigenvalues and eigenfunctions of the Schrödinger equation in higher dimensions, incorporating the Dunkl operator. Two fundamental quantum mechanical problems are examined in their exact forms: the d-dimensional harmonic oscillator and the Coulomb potential. In order to obtain analytical solutions to these problems, both Cartesian and polar coordinate systems were employed. Firstly, the Dunkl-Schrödinger equation is derived in d-dimensional Cartesian coordinates, and then for the isotropic harmonic potential interaction, its solutions are given. Subsequently, using polar coordinates the angular and radial parts of the Dunkl-Schrödinger equation are obtained. It is demonstrated that the system permits the separation of variables in both coordinate systems, with the resulting separated solutions expressed through Laguerre and Jacobi polynomials. Then, the radial Dunkl-Schrödinger equation is solved using the isotropic harmonic, pseudoharmonic, and Coulomb potentials. The eigenstates and eigenvalues are obtained for each case and the behavior of the energy eigenvalue functions are illustrated graphically with the reduced probability densities.

SIMP dark matter during reheating

Strongly interacting massive particle (SIMP) has become one of the promising dark matter (DM) candidates due to its capability of addressing the small-scale anomaly, where the final DM abundance is set via the freeze-out of 3→ 2 or 4→ 2 annihilation process involving solely the dark sector particles. In this work, we explore the freeze-out of SIMP DM during the inflationary reheating epoch. During reheating, the radiation energy density evolves differently based on the shape of inflaton potential and spin of its decay products than the standard radiation-dominated picture; as a result, in this scenario, the freeze-out temperature varies distinctly with DM mass compared to the standard case. Large entropy injection due to inflaton decay demands a smaller cross-section to satisfy the observed relic than the standard radiation-dominated freeze-out case. The required cross-section, satisfying the relic density constraint and the maximum allowed thermally averaged cross-section by the unitarity of the S-matrix, set an upper limit on the DM mass. The upper bound on the mass of the dark matter for 3→2 (4→2) is 1 GeV (7 MeV), assuming a radiation-dominated background. Interstingly, these limits get relaxed to 106 (104) GeV for 3→2 (4→2) SIMP dark matter for quadratic inflaton potential. We find that a small amount of DM parameter space survives for reheating with quadratic inflaton potential after considering the lower bound of reheating temperature, put by the latest CMB observation depending on the inflationary models. In the case of the quartic inflaton potential, the allowed DM parameter space gets reduced compared to the quadratic case.

A New Paradigm in Quantum Fields: The Quantum Oscillator with Semi-Quanta (IQuO) (Part Two)

A New Paradigm in Quantum Fields: The Quantum Oscillator with Semi-Quanta (IQuO) (Part Two)

A New Paradigm in Quantum Fields: The Quantum Oscillator with Semi-Quanta (IQuO) (Part One)

A New Paradigm in Quantum Fields: The Quantum Oscillator with Semi-Quanta (IQuO) (Part One)

A glimpse of matrix mechanics via the harmonic oscillator

In this paper, we provide a glimpse of the original formulation of quantum mechanics (a.k.a. matrix mechanics), as proposed by Heisenberg, Born, and Jordan in 1925, by showing how it solves the quantum harmonic oscillator. This presentation can shed light on the relationship between different formulations and give students a deeper understanding of quantum mechanics.

On the mathematical foundations of diffusion Monte Carlo

The Diffusion Monte Carlo method with constant number of walkers, also called Stochastic Reconfiguration as well as Sequential Monte Carlo, is a widely used Monte Carlo methodology for computing the ground-state energy and wave function of quantum systems. In this study, we present the first mathematically rigorous analysis of this class of stochastic methods on non necessarily compact state spaces, including linear diffusions evolving in quadratic absorbing potentials, yielding what seems to be the first result of this type for this class of models. We present a novel and general mathematical framework with easily checked Lyapunov stability conditions that ensure the uniform-in-time convergence of Diffusion Monte Carlo estimates towards the top of the spectrum of Schrödinger operators. For transient free evolutions, we also present a divergence blow up of the estimates with respect to the time horizon even when the asymptotic fluctuation variances are uniformly bounded. We also illustrate the impact of these results in the context of generalized coupled quantum harmonic oscillators with non necessarily reversible nor stable diffusive particle and a quadratic energy absorbing well associated with a semi-definite positive matrix force.

Superconductivity and its Properties: Cooper Pairs, Meissner Effect, London Moment, Gravitomagnetic and Gravitoelectric Processes

The following properties of superconductivity are considered in this work: the creation and destruction of Cooper pairs, “mass defect”, Meissner effect, London moment, gravitomagnetic and gravitoelectric processes. The conducted research has shown that for explanation of the above-mentioned properties of superconductivity it is necessary to investigate the characteristics of physical vacuum. With this aim, the following physical models of physical vacuum are analyzed in the work. The Feynman model of creating of virtual photons by quantum objects, explaining the creation and destruction of Cooper pairs, “mass defect” and partly Meissner effect. The model of physical vacuum consisting of quantum oscillators by A. Einstein and O. Stern and the model of magnetic field by L. I. Sedov. The latter two models are basic for interpretation of Meissner effect, London moment, gravitomagnetic and gravitoelectric processes.

Variation in (Hyper)Polarizability of H2 Molecule in Bond Dissociation Processes Under Spatial Confinement.

We report the results of calculations of the linear polarizability and second hyperpolarizability of the H2 molecule in the bond dissociation process. These calculations were performed for isolated molecules, as well as molecules under spatial confinement. The spatial confinement was modeled using the external two-dimensional (cylindrical) harmonic oscillator potential. In contrast to the recently investigated polar LiH molecule, it was shown that the spatial confinement significantly diminishes the linear and nonlinear response of H2 for each interatomic (H-H) distance.

Solutions of the Generalized Dunkl-Schrödinger Equation for Harmonic and Coulomb Potentials in two Dimensions

Solutions of the Generalized Dunkl-Schrödinger Equation for Harmonic and Coulomb Potentials in two Dimensions

Modeling the tail risk of crude oil futures using a quantum approach

This study proposes a quantum approach to measure the tail risk of crude oil futures. Based on the quantum harmonic oscillator (QHO) model, we first model the log return process of crude oil futures. From the equilibrium distribution of QHO model, we calculate the well-known tail risk measures such as Value-at-Risk (VaR) and Expected Shortfall (ES); we confirm that this quantum approach provides precise estimates of in-sample and out-of-sample VaR and ES for crude oil futures. The findings suggest the QHO model for log return process outperforms the geometric Brownian motion for price process and the historical simulation approach. The excellence of QHO model in explaining the tail risk of crude oil futures can be attributed to its fast angular frequency and high probability allocation in excited states. Crude oil market participants can use this study’s analytical framework to precisely measure and manage potential risks in the marketplace. Regulatory authorities can evaluate the degree of crude oil market instability through the current market state of crude oil futures characterized by the QHO model parameters while devising and revising crude oil market regulations. Future research can examine quantum models with (1) different assumptions, e.g., position-dependent diffusion and time-varying equilibrium return, and (2) different potential functions, e.g., infinite and finite square well.

Fringing effects in the operation of harmonic backing potential Kelvin probes

In this paper we present the effects of fringing on the measurement of the tip-sample capacitance for Kelvin probes driven by a harmonic backing potential. Moreover, we show that in this case it is still possible to obtain good estimations of operational parameters that allow for the fully controlled operation of harmonically driven Kelvin probes.

Many-body Stark resonances by the complex absorbing potential method

The resonances of many-body Stark Hamiltonians are characterized by the complex absorbing potential method. Namely, the resonances are shown to be the limit points of complex discrete eigenvalues of many-body Stark Hamiltonians with quadratic complex potential when the coefficient of the complex potential tends to zero. The proof is based on the complex distortion outside a cone. Pseudodifferential operators are used in the proof of the main estimate.

Impurity-induced vortex lattice melting and turbulence in rotating Bose–Einstein condensates

Abstract We numerically investigate the impact of various impurities on rotating Bose–Einstein condensates confined within two-dimensional harmonic and Gaussian distributed square lattice potentials. Without impurities, the rotating condensates display an organized square lattice pattern of vortices due to the influence of Gaussian distributed square lattice potential. The introduction of impurity potentials disrupts this lattice structure, inducing a phase transition from an ordered state to a disordered state. Our analysis encompasses both static and dynamic types of impurities. The static impurities are implemented using a randomly varying potential with a spatially random amplitude. The transformation of the vortex lattice structure, in this case, relies on the strength and lattice constant of the impurity potential. For dynamical impurities, we employ a Gaussian obstacle that orbits around the condensate at a specific distance from its center. In this scenario, the vortex lattice melting occurs beyond a certain threshold radius and frequency of oscillation of the rotating obstacle. We characterize the melting of the vortex lattice due to impurities using various quantities, such as the structure factor and angular momentum. Notably, in the vortex-melted state, the angular momentum follows a power-law dependence with an exponent of approximately 1.73, regardless of the type of impurity. Finally, we demonstrate the signature of the presence of a turbulent state within the vortex-melted state generated by both static and dynamical impurities.