The effect of parabolic electrostatic confinement on the shear viscosity of two-dimensional dusty plasmas was studied using molecular dynamics simulations. The key findings are as follows: (1) the shear viscosity in the inner region of the system is larger than that in the outer region, particularly at low temperatures; and (2) the role of the gradient electrostatic field in reducing the shear viscosity of the system is discussed, based on the high-order corrections to pressure tensor. These simulations reveal the local momentum transport of two-dimensional dusty plasmas when the confinement-induced inhomogeneity of number density is considered.

Abstract We show that numerical simulations of particular solutions of the Gross–Pitaevskii equation with parabolic potential can have features of both regular and chaotic dynamics, depending on initial conditions. Such behavior is a characteristic feature of systems with Kolmogorov–Arnold–Moser chaos. We also report analytical arguments that could support such interpretation.

Abstract A continuous and explicit compact model is developed for the junctionless square-gate field-effect transistor (JLSG-FET), addressing key electrical parameters: drain current, terminal charges, and intrinsic capacitances.. The modeling begins with an implicit unified charge-based control model (UCCM), derived from the one-dimensional Poisson equation under a parabolic potential profile and uniform mobile charge approximation in a junctionless nanowire transistor (JNT). To suit the JLSG-FET structure, the model transitions from cylindrical to Cartesian coordinates. The mobile charge at the source and drain is reformulated using a decoupled UCCM comprising depletion and complementary charge components. By applying the Lambert W function, the implicit model is transformed into a continuous, explicit form by eliminating the need for smoothing functions and improving computational efficiency. From this explicit charge formulation, a unified drain current expression is developed using Pao-Sah's double integral approach. Terminal charges are then derived, enabling the extraction of independent intrinsic capacitances. The proposed model achieves excellent agreement with TCAD simulations with minimum error of < 10% across various biasing and geometric conditions, offering a compact, accurate, and simulation-ready solution for advanced nanoscale device modeling.

In this article, we introduce and analyze some statistical properties of a class of models of random landscapes of the form H(x)=μ2x2+∑l=1Mϕl(kl⋅x),x∈RN,μ>0 where both the functions ϕl(z) and vectors kl are random. An important example of such landscape describes superposition of M plane waves with random amplitudes, directions of the wavevectors, and phases, further confined by a parabolic potential of curvature μ. Our main efforts are directed toward analyzing the landscape features in the limit N → ∞, M → ∞ keeping α = M/N finite. In such a limit we find (i) the rates of asymptotic exponential growth with N of the mean number of all critical points and of local minima known as the annealed complexities and (ii) the expression for the mean value of the deepest landscape minimum (the ground-state energy). In particular, for the latter we derive the Parisi-like optimization functional and analyze conditions for the optimiser to reflect various phases for different values of μ and α: replica-symmetric, one-step and full replica symmetry broken, as well as criteria for continuous, Gardner and random first order transitions between different phases.

Abstract We have theoretically investigated effects of hill-like parabolic and inverse parabolic electric confining potentials on the photoionization cross-section (PCS), diamagnetic susceptibility (DMS), and binding energies of donor impurity-bound electron states located at the center of spherical GaAs quantum dots (SQDs). The results reveal that the inverse parabolic potential draws electron density toward the quantum dot boundaries, thereby reducing binding energies and increasing the magnitude of the DMS, while the hill-like potential enhances ground-state binding energies, decreases excited-state binding energies, and modulates DMS in a state-dependent manner. Additionally, the hill-like potential causes blueshifts in resonance peaks of PCS for $$1s\rightarrow 2p$$ transitions and redshifts for $$2p \rightarrow 3d$$ , whereas the inverse potential consistently causes redshifts for all transitions. A linear combination of the two potentials allows tunable control of electronic, magnetic and optical properties. These findings underscore a novel pathway for tailoring SQD responses through careful design of the geometry of confining potential, offering promising applications in advanced optoelectronic and quantum information devices.

Laguerre-Gaussian vortex beams in the nonlinear fractional Schrödinger equation with parabolic potential

In this paper, we introduce new integral wavelet-type transforms generated by the generalized (Bessel) shift operator and so-called β-kernel. These wavelet-type transforms have close connection with a generalization of the singular parabolic potentials associated with the Laplace-Bessel differential operator. We prove Calderon-type reproducing formulas in the framework of special weighted L p -spaces.

In this study, we explore the thermodynamic and magnetic properties of a non-interacting, spinless charged particle confined by a parabolic potential within a polar quantum disc featuring a conical disclination, subject to a uniform magnetic fieldB. The central theme of this investigation is to explore the impact of a topological defect, namely the conical disclination, on the system's thermodynamic and magnetic properties. The disclination of the system is characterized by kink parameterκ. The thermodynamic and magnetic characteristics of the system are assessed using the canonical formalism. The energy spectrum of the system consisting of non-interacting spinless charged particles is derived by solving the Schrödinger equation using the effective mass approximation. It is found that the energy of the system decreases with an increase in theκ, owing to the weakening of confinement. Increasing the value of theκincreases the internal energy (U), entropy (S) while decreasing the heat capacity (Cv). Moreover, the increasing value ofκcauses to reduce the magnetization (M) and magnetic susceptibility (χm).

We theoretically investigate the thermodynamic performance characteristics of an active magneto gyrator taking into account the two-dimensional motion of an inertial charged active particle confined in an asymmetric parabolic potential and in contact with two heat baths kept at two different temperatures. A magnetic field of constant magnitude is applied in a direction perpendicular to the plane of motion. In such a system, the particle exhibits a gyrating motion across the potential minimum and exerts a torque on the confining potential as long as there is a potential asymmetry and temperature gradient. Hence, this system can operate as an active magneto heat engine or pump in the presence of a load force. Interestingly, we observe that the activity or self-propulsion impacts the thermodynamic performance characteristics of the gyrator only in the presence of the magnetic field. We examine two scenarios: first, by applying a load in a direction opposing the torque and, second, by applying a load in the same direction as that of torque. In the first case, for a fixed parameter regime, the gyrator is found to act as a heat engine or a heat pump depending on the strength of the applied load, whereas in the latter case, it can only operate as a heat pump. Moreover, unlike the Brownian gurator or Brownian magneto gyrator, captivatingly, the efficiency is found to have no universal upper bound and can be made 100% by tuning the system parameters. Additionally, when the system is suspended in a viscoelastic medium characterized by the presence of a finite memory, for a short persistence of memory and a fixed duration of activity, the efficiency can be 100% even for more than one value of viscoelastic memory timescale. In the first case, the duration of the activity has a nonmonotonic impact on the system performing either as an engine or a pump, whereas the magnetic field has a similar impact on the performance of an engine, but it degrades the performance of the system as a heat pump. In the latter case, the coefficient of performance has a nonmonotonic dependence on the duration of the activity, whereas the magnetic field favors the system performing as a heat pump. Our analytical results are supported by numerical simulation.

Abstract This study explores the transmission properties of off‐axis chirped Hermite Gaussian cross‐phase (HGCP) beams in fractional systems under cosine modulations and parabolic potentials. Cosine modulation induces periodic transitions in the light field, influenced by modulation frequency, Lévy index, cross‐phase (CP) coefficient, and Hermite Gaussian (HG) order, creating diverse patterns like rugby balls, water waves, and elliptical rings. The cross‐phase effect causes beam rotation, and diffraction enhances with increasing CP coefficient and Lévy index. Beam trajectories exhibit periodic oscillations, with amplitude growing with the Lévy index and chirp coefficients. Under parabolic potentials, the beam demonstrates autofocusing, defocusing, and periodic mode transitions, including HG to Laguerre‐Gaussian (LG) conversions. The beam propagation exhibits “spiral” and “straight line” oscillatory trajectories moving toward the origin, and periodic elliptical spiral trajectories depend on the Lévy index, off‐axis, and chirp parameters. These findings offer insights into beam dynamics in fractional Schrödinger equation (FSE) systems, with implications for optical communications and particle manipulation.

In this work, we calculated the masses of the ground and radial excited states of heavy tetraquarks in the framework of the nonrelativistic quark model for two wave states nS and nP. The potential used is the parabolic potential plus the spin term, and the method we used to solve the Schrödinger equation is the NU method. The Regge trajectories in the (nr,M2) plane are linear and we obtained the parameters β and β0 for each state. The results are in good agreement with the available experimental data and we predicted the structures of tetraquarks X(4.500), X(4.700), X(4.740), X(6.900), X(7.200), Y(4.230), Y(4.660), and Zb(10.650).

A contactless control of mean values and fluctuations of position and velocity of a nanoobject belongs among the key methods needed for ultra-precise nanotechnology and the upcoming quantum technology of macroscopic systems. An analysis of experimental implementations of such a control, including assessments of linearity and the effects of added noise, is required. Here, we present a protocol of linear amplification of mean values and fluctuations along an arbitrary phase space variable and squeezing along the complementary one, referred to as a nanomechanical state amplifier. It utilizes the experimental platform of a single optically levitating nanoparticle and the three-step protocol combines a controlled fast switching of the parabolic trapping potential to an inverted parabolic potential and back to the parabolic potential. The protocol can be sequentially repeated or extended to shape the nanomechanical state appropriately. Experimentally, we achieve amplification of position with a gain of ∣G∣ ≃ 2 and a classical squeezing coefficient above 4 dB in as short a timestep as one period of nanoparticle oscillations (7.6 μs). Amplification in velocity, with the same parameters, squeezes the input noise and enhances force sensing.

In the case of an undegenerated electron gas in quantum dot superlattices with anisotropic parabolic potential, it was found that intraband absorption takes place between adjacent sublevels in the first-order excitation theory of electron-photon interaction in the direction of the limiting potential axis of the polarization vector of the electromagnetic wave.

Active matter composed of self-propelled particles features fascinating self-organization phenomena, spanning from motility-induced phase separation to phototaxis to topological excitations depending on the nature and parameters of the system. In the present paper, we consider micelle formation by active particles with a broken symmetry having a circular back and a sharpened nose toward which the particles accelerate. As we demonstrate in experiments with robotic swarms, such particles can either remain in the isotropic phase or form micelles depending on the location of their center of inertia, in accordance with a recent theoretical proposal [T. Kruglov and A. Borisov, Presentations and Videos to 7th Edition of the International Conference on Particle-based Methods (2021), Vol. CT07, p. 2]. Such a behavior is observed for both nonchiral particles moving linearly and placed in a parabolic potential and for chiral particles moving along circular trajectories on a flat surface. By performing experiments with single robots and two-robot collisions, we unveil that the observed emergence of micellization associated with shifting robots' center of inertia towards their noses is governed by at least two-particle effects, in particular, by a difference in the formation of stable two-robot clusters. Finally, we consider the dependence of micelle lifetime and formation probability as well as two-robot collisions on friction between the lateral surfaces of the robots. Crucially, the predicted micellization does not involve any solvation shells that give rise to the micellization of surfactants but is instead driven by an interplay of activity and particle shape asymmetry.

Hydrogenic and non-hydrogenic donor impurity in quantum dot with an inverse parabolic plus a parabolic potential under magnetic field effect

We study the lower bound of the entropy production in a one-dimensional underdamped Langevin system constrained by a time-dependent parabolic potential. We focus on minimizing the entropy production during transitions from a given initial distribution to a given final distribution taking a given finite time. We derive the conditions for achieving the minimum entropy production for the processes with normal distributions, using the evolution equationsof the mean and covariance matrix to determine the optimal control protocols for stiffness and center of the potential. Our findings reveal that not all covariance matrices can be given as the initial and final conditions due to the limitations of the control protocol. This study extends existing knowledge of the overdamped systems to the underdamped systems.

In CdSe nanoplatelet, interband transitions in the presence of an axial electric field are considered. It is shown that at certain nanoplatelet thicknesses, the combined effect of polarization and confining potentials forms an effective parabolic potential in the axial direction. As a consequence, the influence of the electric field in this direction can be described within the framework of the one-dimensional mixed oscillator model. Analytical formulas for the energy spectrum and wave function are obtained, threshold frequencies are determined for different monolayer thicknesses.

Periodic focusing properties of circular Butterfly Vortex beams in the fractional Schrödinger equation with parabolic potential

Abstract In this paper, we have theoretically investigated effects of certain electric confining potentials, hydrostatic pressure, and temperature on binding energies, photoionization cross-sections (PCS) and associated diamagnetic susceptibilities (DMS) in a GaAs spherical quantum dot. The potential profile considered here is the linear combination of the inverse lateral shifted parabolic potential and the inverse parabolic potential. Results show that the inverse lateral shifted parabolic potential enhances both binding energies and transition energies, while the inverse parabolic potential decreases the binding energies and transition energies. Photoionization occurs whenever the energy of incident electromagnetic radiation equals the transition energies. This implies that the two potentials can be used to tune PCS in SQDs, the inverse lateral shifted parabolic potential blueshifting the peaks of the PCS, while the inverse parabolic potential redshifting the peaks. The results also reveal that rise in temperature increases transition energies while it decreases binding energies. On the other hand, increase in pressure decreases transition energies while it enhances binding energies. This implies that, in the event that SQDs are incorporated in nanodevices, increase in temperature (possibly due to Joule heating) may detune SQDs. Thus, pressure of precise magnitude can be applied to counter the effects of temperature on transition energies, thereby ameliorating the temperature-induced detuning.

Abstract The autofocusing properties of Hermite-Gaussian vortex beams (HGVBs) with quadratic phase modulation (QPM) are studied using a split-step Fourier transform algorithm within fractional systems characterized by variable coefficients and potentials. Initially, the autofocusing behavior of HGVBs in free space driven by QPM is analyzed, revealing that the focusing characteristics are influenced by the Lévy index, topological charge, and QPM coefficient. The propagation dynamics are then examined under varying diffraction modulations. Cosine modulation induces phenomena such as oscillation, periodic evolution with single or dual focusing, with the focusing ability and period decreasing as modulation frequency rises. Under power function modulation, the beam stabilizes after focusing, with the focusing time and stabilization structure width governed by the modulation coefficient. The influence of external potentials is explored, where a parabolic potential induces self-focusing and defocusing, with the focusing effect being dependent on both the Lévy index and parabolic coefficient. The focusing characteristics of the beam in the frequency domain are opposite to those in the spatial domain. In an annular potential, the beam exhibits periodic reflection, ultimately evolving into chaos at higher Lévy indices. The focusing dynamics is also investigated when the Lévy index is less than 1. These findings highlight new opportunities for optical switching and manipulation.