Double Wells Research Articles

Resonant-State Expansion Applied to Non-Relativistic Wave Equation in One-Dimension

Study’s Excerpt The rigorous resonant-state expansion (RSE) method is extended to the non-relativistic one-dimensional wave equation. Resonant states (RSs) wave numbers as the unperturbed basis were employed to confirm the RSE's convergence to exact solutions. RSE's has potentials for systematically calculating RSs in complex quantum systems with multi-well potentials. Full Abstract The resonant-state expansion (RSE), a rigorous perturbation theory recently developed in electrodynamics, is here applied to the non-relativistic wave equation in one-dimension. The resonant states (RSs) wave numbers for the double well system are analytically calculated and used as the unperturbed basis for calculating the RSE. We demonstrate the efficiency of the RSE by verifying its convergence to the exact solution for a triple well potential. We show that for the chosen perturbations (i.e., for and ), the method is particularly suitable for calculating all the RSs within the spectrum.

Ultra-wide Bandgap AlGaN Channel HEMTs for Portable Power Electronics Applications

AlGaN channel (Eg>3.4 eV) is the most effective method for enhancing the breakdown field of the group III-nitride based HEMTs. This work demonstrates the potential of AlGaN double channel HEMTs on Silicon carbide substrate. The device DC characteristics are investigated using numerical simulator by using drift-diffusion transport model. The AlGaN double channel HEMTs enhances the total 2DEG density due to double potential well and shows better current driving capability (IDS) of 0.714 A/mm, transconductance (gm) of 116 mS/mm, and low specific ON-resistance (Ron) of 3.262 Ω.mm. The AlGaN double channel HEMT on Silicon carbide substrate exhibited 680 V blocking voltage (VBR) and gate field plate HEMT shows 532 V. The effective reduction in electric field at the gate edge is the major source for elevated breakdown voltage in field plate HEMTs. The superior DC characteristics indicates the proposed wide bandgap channel HEMT is suitable device for future portable power converters.

Assessing the electrode configuration in a sandbox system for the removal of sulfanilamide: A pilot study

Electrochemical oxidation has emerged as an effective and straightforward technology for groundwater remediation. While recent studies have investigated parameters such as current, electrolyte composition, and electrode materials, most have been conducted using small-scale batch or flow reactors, limiting their applicability to real-world conditions. In this study, a pilot-scale sandbox reactor was employed to simulate realistic groundwater conditions and assess the removal of sulfanilamide, a model organic contaminant. Various electrode configurations were systematically evaluated to identify the key operational parameters influencing pollutant removal efficiency, providing insights for practical applications in groundwater treatment. This study proposes three configurations, including a single well with the anode and cathode, a double well with the separated anode and cathode, and an e-barrier with electrodes separately mounted inside a permeable barrier. Single well had the lowest removal efficiency (60%) because cathodic reaction inhibited the anodic oxidation. A double well with a separate anode and cathode can achieve 80% removal efficiency. However, effluent pH can reach up to 13.2, which can adversely impact groundwater. Meanwhile, the e-barrier not only achieved complete removal, but also maintained a neutral pH of 7.0 over 30 days. The e-barriers proved to be the most effective configuration based on their removal efficiency (100%) while yielding an effluent with neutral pH. The energy consumption of the e-barrier was most effective at 1.54 kWh/m3, while the other configurations were 5.40 and 22.18 kWh/m3. E-barriers are deemed a very reasonable configuration, both in terms of removal efficiency and practical application in groundwater.

Quantum Dynamical Interpretation of the Mean Strategy.

The method of quantum dynamics is employed to investigate the mean strategy in the swarm intelligence algorithm. The physical significance of the population mean point is explained as the location where the optimal solution with the highest likelihood can be found once a quantum system has reached a ground state. Through the use of the double well function and the CEC2013 test suite, controlled experiments are conducted to perform a comprehensive performance analysis of the mean strategy. The empirical results indicate that implementing the mean strategy not only enhances solution diversity but also yields accurate, efficient, stable, and effective outcomes for finding the optimal solution.

The Current Status and Development Trend of Water Control Technology for Horizontal Wells

In the advancement of bottom water reservoir development, water breakthrough poses a significant challenge to the productivity of oil and gas wells, underscoring the paramount importance of effective water control strategies. Given the intricate nature of the factors leading to reservoir water breakthrough, a one-size-fits-all approach to water management is non-existent. Rather, tailored water control techniques are necessary to address the diverse causes of this phenomenon. This paper delves into the evolution and application of water control technologies, particularly focusing on the prevalent horizontal well water control methodologies. Horizontal well variable density water control, segmented water control, double horizontal well oil recovery water control, along with advanced solutions such as ICD (Inflow Control Device), ICV (Inflow Control Valve), AICD (Autonomous Inflow Control Device), and AICV (Autonomous Inflow Control Valve) water control systems are comprehensively introduced. Furthermore, center-controlled, mechanical plugging, and chemical plugging water control technologies are also examined in depth, accompanied by a thorough analysis of their respective strengths, limitations, and adaptability to various scenarios. By keeping abreast of both domestic and international trends in horizontal well water control, the future trajectory of this field is forecasted. Emerging as key technologies are novel composite water control systems, dual-purpose water control and sand prevention techniques, and intelligent water control solutions. These advancements promise to revolutionize the management of water breakthrough in bottom water reservoirs, enhancing oil and gas recovery efficiency and sustainability.

Targeting spectroscopic accuracy for dispersion bound systems from abinitio techniques: Translational eigenstates of Ne@C70.

We investigate the endofullerene system Ne@C70 by constructing a three-dimensional Potential Energy Surface (PES) describing the translational motion of the Ne atom. This is constructed from electronic structure calculations from a plethora of methods, including MP2, SCS-MP2, SOS-MP2, RPA@PBE, and C(HF)-RPA, which were previously used for He@C60 in Panchagnula et al. [J. Chem. Phys. 160, 104303 (2024)], alongside B86bPBE-25X-XDM and B86bPBE-50X-XDM. The reduction in symmetry moving from C60 to C70 introduces a double well potential along the anisotropic direction, which forms a test of the sensitivity and effectiveness of the electronic structure methods. The nuclear Hamiltonian is diagonalized using a symmetrized double minimum basis set outlined in Panchagnula and Thom [J. Chem. Phys. 159, 164308 (2023)], with translational energies having error bars ±1 and ±2 cm-1. We find no consistency between electronic structure methods as they find a range of barrier heights and minima positions of the double well and different translational eigenspectra, which also differ from the Lennard-Jones (LJ) PES given in Mandziuk and Bačić [J. Chem. Phys. 101, 2126-2140 (1994)]. We find that generating effective LJ parameters for each electronic structure method cannot reproduce the full PES nor recreate the eigenstates, and this suggests that the LJ form of the PES, while simple, may not be best suited to describe these systems. Even though MP2 and RPA@PBE performed best for He@C60, due to the lack of concordance between all electronic structure methods, we require more experimental data in order to properly validate the choice.

Model two states dynamics of photo‐detachment [F‐H‐F]− induced by an optimally designed polychromatic field

AbstractPhoto‐detachment of electron from [F‐H‐F] to generate neutral [F‐H‐F] has been studied in this article. Neutral has a linear structure and this is the transition state (T.S.) of F + HF FH + F reaction. The Potential Energy Surface (P.E.S.) of neutral [F‐H‐F] and molecular anion [F‐H‐F] for the asymmetric stretching mode is generated and the dynamics under the influence of an external polychromatic field is followed. The P.E.S. of [F‐H‐F] looks like a “flat‐bed” single well where as for [F‐H‐F] it has a symmetrical double well structure. In absence of any external field these two surfaces are well separated. But in presence of external field transition from molecular anion [F‐H‐F] to neutral molecule [F‐H‐F] takes place which causes the detachment of an electron. We have designed an optimal designed field using Simulated Annealing and studied the dynamics of electron detachment by such external fields. We have achieved detachment probability of by applying the optically designed field.

A note on vibrational perturbation theory for tunneling splitting in a symmetric double well potential.

The modified version of second and fourth order vibrational perturbation theory, whereby the Euclidean action for tunneling is computed on the inverted potential at a shifted energy that is ℏ2 dependent, is applied to a symmetric double well quartic potential. The mean energies of the doublets in each well are also computed using vibrational perturbation theory. Results show that the modified vibrational perturbation theory significantly improves the estimates of tunneling splitting energies both for the ground state and for excited state doublets.

Nonlinear energy harvesting system with multiple stability

The nonlinear energy harvesting systems of the forced vibration with an electron-mechanical coupling are widely used to capture ambient vibration energy and convert mechanical energy into electrical energy. However, the nonlinear response mechanism of the friction induced vibration (FIV) energy harvesting system with multiple stability and stick-slip motion is still unclear. In the current paper, a novel nonlinear energy harvesting model with multiple stability of single-, double- and triple-well potential is proposed based on V-shaped structure spring and the belt conveying system. The dynamic equations for the energy harvesting system with multiple stability and self-excited friction are established by using Euler-Lagrangian equations. Secondly, the static characteristics of the nonlinear restoring force, the friction force, and the potential energy surfaces are obtained to show the nonlinear stiffness, multiple equilibrium points, discontinuous behaviors and multiple well responses. Then, the equilibrium surface of bifurcation sets for the autonomous system is given to show the third-order quasi zero stiffness (QZS3), fifth-order quasi zero stiffness (QZS5), double well (DW) and triple well (TW). The co-dimension bifurcation sets of the self-excited vibration system are analyzed and the corresponding phase portraits for the coexistent of multiple limit cycles are obtained. Furthermore, the analytical formula of amplitude frequency response of the approximated system are obtained by the complex harmonic method. The response amplitudes of charge, current, voltage and power of the forced electron-mechanical coupled vibration system for QZS3, QZS5, DW and TW are analyzed by using the numerically solution. Finally, a prototype of FIV energy harvesting system is manufactured and the experimental system is setup. The experimental works of static restoring forces, damping forcse and the electrical outputs are well agreeable with the numerical results, which testified the proposed FIV energy harvesting model.

Reconfigurable stochastic neurons based on strain engineered low barrier nanomagnets

Stochastic neurons are efficient hardware accelerators for solving a large variety of combinatorial optimization problems. ‘Binary’ stochastic neurons (BSN) are those whose states fluctuate randomly between two levels +1 and −1, with the probability of being in either level determined by an external bias. ‘Analog’ stochastic neurons (ASNs), in contrast, can assume any state between the two levels randomly (hence ‘analog’) and can perform analog signal processing. They may be leveraged for such tasks as temporal sequence learning, processing and prediction. Both BSNs and ASNs can be used to build efficient and scalable neural networks. Both can be implemented with low (potential energy) barrier nanomagnets (LBMs) whose random magnetization orientations encode the binary or analog state variables. The difference between them is that the potential energy barrier in a BSN LBM, albeit low, is much higher than that in an ASN LBM. As a result, a BSN LBM has a clear double well potential profile, which makes its magnetization orientation assume one of two orientations at any time, resulting in the binary behavior. ASN nanomagnets, on the other hand, hardly have any energy barrier at all and hence lack the double well feature. That makes their magnetizations fluctuate in an analog fashion. Hence, one can reconfigure an ASN to a BSN, and vice-versa, by simply raising and lowering the energy barrier. If the LBM is magnetostrictive, then this can be done with local (electrically generated) strain. Such a reconfiguration capability heralds a powerful field programmable architecture for a p-computer whereby hardware for very different functionalities such as combinatorial optimization and temporal sequence learning can be integrated in the same substrate in the same processing run. This is somewhat reminiscent of heterogeneous integration, except this is integration of functionalities or computational fabrics rather than components. The energy cost of reconfiguration is miniscule. There are also other applications of strain mediated barrier control that do not involve reconfiguring a BSN to an ASN or vice versa, e.g. adaptive annealing in energy minimization computing (Boltzmann or Ising machines), emulating memory hierarchy in a dynamically reconfigurable fashion, and control over belief uncertainty in analog stochastic neurons. Here, we present a study of strain engineered barrier control in unconventional computing.

Tunneling Probability of Quantum Wavepacket in Time-Dependent Potential Well

Quantum tunneling of particles plays an important role in many chemical reactions. Studying quantum tunneling in time-dependent potential wells is tricky since most of the available solutions of time-dependent potential wells are coupled to specific properties of the Hamiltonian. Here, we investigate the tunneling probability of a quantum wavepacket in time-dependent potential well by using the split operator method. This numerical method can give us an overview of the tunneling probability of a quantum wavepacket for any temporal change in the shape of the potential well. We study a time-dependent potential well model evolving from symmetric to asymmetric quartic double well since quartic potential wells resemble certain practically available potential well models.Quanta 2024; 13: 11–19.

Effect of spin-orbit coupling and impurities on the optical properties of double quantum rings under magnetic fields

In this paper, the energy spectrum of concentric double quantum rings (CDQRs) with double well confinement under the influence of spin-orbit interactions (SOIs), magnetic fields, and hydrogen donor impurities is studied by using diagonalization. The light absorption coefficient is then calculated in the form of a compactness density-matrix. Key findings from this study include the ability to manipulate fine energy level splitting and optical absorption coefficients by tuning the magnetic field, impurity position, spin-orbit coupling, and inner rings size. Furthermore, this study reveals the bleaching effect of the optical absorption coefficient under certain conditions and demonstrates the anisotropic nature of the system through changes in the optical absorption coefficients (OACs) for different incident light polarization angles.

Tunable on-chip optical traps for levitating particles based on single-layer metasurface

Abstract Optically levitated multiple nanoparticles have emerged as a platform for studying complex fundamental physics such as non-equilibrium phenomena, quantum entanglement, and light–matter interaction, which could be applied for sensing weak forces and torques with high sensitivity and accuracy. An optical trapping landscape of increased complexity is needed to engineer the interaction between levitated particles beyond the single harmonic trap. However, existing platforms based on spatial light modulators for studying interactions between levitated particles suffered from low efficiency, instability at focal points, the complexity of optical systems, and the scalability for sensing applications. Here, we experimentally demonstrated that a metasurface which forms two diffraction-limited focal points with a high numerical aperture (∼0.9) and high efficiency (31 %) can generate tunable optical potential wells without any intensity fluctuations. A bistable potential and double potential wells were observed in the experiment by varying the focal points’ distance, and two nanoparticles were levitated in double potential wells for hours, which could be used for investigating the levitated particles’ nonlinear dynamics, thermal dynamics and optical binding. This would pave the way for scaling the number of levitated optomechanical devices or realizing paralleled levitated sensors.

Exact instanton transseries for quantum mechanics

We calculate the instanton corrections to energy spectra of one-dimensional quantum mechanical oscillators to all orders and unify them in a closed form transseries description. Using alien calculus, we clarify the resurgent structure of these transseries and demonstrate two approaches in which the Stokes constants can be derived. As a result, we formulate a minimal one-parameter transseries for the natural nonperturbative extension to the perturbative energy, which captures the Stokes phenomenon in a single stroke. We derive these results in three models: quantum oscillators with cubic, symmetric double well and cosine potentials. In the latter two examples, we find that the resulting full transseries for the energy has a more convoluted structure that we can factorise in terms of a minimal and a median transseries. For the cosine potential we briefly discuss this more complicated transseries structure in conjunction with topology and the concept of the resurgence triangle.

Resonance response and chaotic analysis for an irrational pendulum system

We propose a novel rotating pendulum system with irrational nonlinearity, bi-stable phenomenon and quasi-zero stiffness characteristic, which bears a transition from standard double well dynamics to discontinuous double well dynamics by adjusting a geometric parameter. Nonlinear dynamical behaviors of the proposed irrational pendulum system subjected to viscus damping and periodic excitation are studied. To analytically demonstrate the primary resonance response for this perturbed irrational pendulum system, we introduce an approximate irrational system which is significant parallels with the original pendulum system from the perspective of qualitative analysis and quantitative calculation. Averaging method is applied to investigate the dynamic response of the perturbed irrational pendulum system with quasi-zero stiffness at origin. The effect of the internal and external parameters on the response curves are discussed. Numerical fitting technique and semi-analytical Melnikov method are used to detect the chaotic boundaries of the perturbed irrational pendulum system with two types of homoclinic orbits. Different types of periodic solutions and chaos are clarified in the perturbed irrational pendulum system by using numerical simulations. It is found that a class of chaos with oscillatory and rotational motions bears significant similarities to paroxysmal chaos due to sudden rotational motion and two chaotic motions formed by period-doubling bifurcation merge into one chaos.

Comparisons for Global Dynamics of a Geometrically Nonlinear Oscillator among Single-, Double- and Quadruple-Well Configurations

This paper conducts a comparative analysis of the global dynamics of a harmonically excited oscillator with geometrical nonlinearities. Static analysis of the oscillatory system shows that adjusting the horizontal distance ratio from 1 to 0 can lead to single, double and quadruple well configurations successively. Intra-well and inter-well resonant responses are deduced analytically. Qualitative and quantitative results both reveal that the oscillator displays the stiffness–softening characteristic in cases of double and quadruple wells and the stiffness–hardening characteristic in the case of a single well. The initial-sensitive phenomenon jump is performed via fractal basins of attraction. Complex dynamical behaviors, including higher-order periodic responses and chaos, are also exhibited. The results demonstrate that the oscillator with a double or quadruple well configuration can achieve the inter-well response with large displacement, thus confirming its desirability in engineering applications of geometrically nonlinear oscillators.

Hydrostatic pressure and temperature effects on nonlinear optical properties in harmonic-Gaussian asymmetric double quantum wells

The paper examines the linear and non-linear optical characteristics of an electron in harmonic Gaussian asymmetrical double quantum wells, taking into account thermodynamic variables such as temperature and hydrostatic pressure. Numerical calculations by considering the effective mass and parabolic band approximation are performed. The electron contained within an asymmetric double well generated by the sum of a parabolic and Gaussian potential has its eigenvalues and eigenfunctions determined using the diagonalization approach. For nonlinear optical coefficients, the density matrix expansion is used. Wavefunctions and energy levels vary as an effect of the applied fields. In harmonic Gaussian asymmetrical double quantum wells, the total optical absorption coefficient (TOAC), the relative refractive index changes (RRIC), and second harmonic generation (SHG) have all been theoretically investigated. The magnitude and position of the resonant peaks are significantly influenced by the hydrostatic pressure and temperature effects. With controllable coupling and externally applied hydrostatic pressure and temperature, the potential model presented in this study can be used to simulate and manipulate the optical and electronic properties of the asymmetric double-quantum heterostructures, such as double quantum dots and wells.

Analysis of a one-dimensional Hamiltonian with a singular double well consisting of two nonlocal δ′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta '$$\\end{document} interactions

The objective of the present paper is the study of a one-dimensional Hamiltonian with the interaction term given by the sum of two nonlocal attractive δ′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta '$$\\end{document}-interactions of equal strength and symmetrically located with respect to the origin. We use the procedure known as renormalisation of the coupling constant in order to rigorously achieve a self-adjoint determination for this Hamiltonian. This model depends on two parameters, the interaction strength and the distance between the centre of each interaction and the origin. Once we have the self-adjoint determination, we obtain its discrete spectrum showing that it consists of two negative eigenvalues representing the energy levels. We analyse the dependence of these energy levels on the above-mentioned parameters. We investigate the possible resonances of the model. Furthermore, we analyse in detail the limit of our model as the distance between the supports of the two δ′\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\delta '$$\\end{document} interactions vanishes.

Oscillations through a barrier tunneling potential for a particle in a central potential (double potential well)

In some molecules such as ammonia, double vibrations are observed at small energies. These small vibrations are thought to arise from double well potentials. To explain these small energy gaps, double potential wells are investigated, and complex calculations are made. Until recently, since the exact solution of the Schrödinger equation was not known, approximate solutions were always obtained. The exact solution of the Schrödinger equation is now known. In previous studies, a simple procedure for the general solution of the radial Schrödinger Equation has been found for spherical symmetric potentials without making any approximation. In this article, the Schrodinger equation was solved with this new solution method. It has been applied to the oscillations through a barrier tunneling potential for a particle in a central quadratic deformed potential well (double potential well). It is seen that there is no need to look for complex potentials to explain the double wells observed in small vibrations in ammonia and similar molecules, they were compared with experimentally measured energies. The results were found to be fully compatible. It has been seen that there can always be double well potentials at small energies for all molecules, atomic nuclei, and similar particles with angular momentum other than zero.

Global Dynamics and Bifurcations of an Oscillator with Symmetric Irrational Nonlinearities

This study’s objective is an irrationally nonlinear oscillating system, whose bifurcations and consequent multi-stability under the circumstances of single potential well and double potential wells are investigated in detail to further reveal the mechanism of the transition of resonance and its utilization. First, static bifurcations of its nondimensional system are discussed. It is found that variations of two structural parameters can induce different numbers and natures of potential wells. Next, the cases of mono-potential wells and double wells are explored. The forms and stabilities of the resonant responses within each potential well and the inter-well resonant responses are discussed via different theoretical methods. The results show that the natural frequencies and trends of frequency responses in the cases of mono- and double-potential wells are totally different; as a result of the saddle-node bifurcations of resonant solutions, raising the excitation level or frequency can lead to the coexistence of bistable responses within each well and cause an inter-well periodic response. Moreover, in addition to verifying the accuracy of the theoretical prediction, numerical results considering the disturbance of initial conditions are presented to detect complicated dynamical behaviors such as jump between coexisting resonant responses, intra-well period-two responses and chaos. The results herein provide a theoretical foundation for designing and utilizing the multi-stable behaviors of irrationally nonlinear oscillators.