Square-well Research Articles

Interfacial properties of square-well chains from molecular dynamics simulation

ABSTRACT Square-well (SW) potential is likely the simplest potential describing attractive and repulsive interactions. However, its discontinuous functional form makes it difficult to be used in Molecular Dynamics (MD) simulation, particularly with commercial MD packages. Recently, Zerón and collaborators [Mol. Phys. 116, 3355 (2018)] have presented a parameterisation of the SW potential that allows its use for simulation packages since the intermolecular potential and force are described by continuous mathematical functions. It was validated for SW spheres. In this work, we use this reported continuous SW potential to describe for the first time the equilibrium and interfacial properties of SW chains, with potential ranges of and 1.75. Simulations for tetramers interacting with are compared with available computational data in the literature, which has allowed to validate the method for molecular chain systems. Besides, a systematic study for the potential range of has not been addressed so far, which represents valuable information for instance to discern whether different microscopic theories are capable of describing this type of system. In particular, we assess the effect of temperature, chain length, and potential range on the calculated properties, namely density profiles, coexistence densities, vapour pressures, surface tensions and critical points. Overall, with increasing the chain length, the width of the envelope of the coexistence phase increases, which results in an increase of the surface tension as well as the critical temperature at the same time that the vapour pressure and the interfacial width decrease.

Chirality-induced directional rotation of a symmetric gear in a bath of chiral active particles

We conduct a numerical study exploring the rotation of a symmetric gear driven by chiral particles in a two-dimensional box with periodic boundary conditions. The symmetric gear is submerged in a sea of chiral active particles. Surprisingly, even though the gear is perfectly symmetric, the microscopic random motion of chiral active particles can be converted into macroscopic directional rotation of the gear. (i) In the case of zero alignment interaction, the direction of rotation of the gear is determined by the chirality of active particles. Optimal parameters (the chirality, self-propelled speed, and packing traction) exist, at which the rotational speed reaches its maximum value. (ii) When considering a finite alignment interaction, alignment interactions between particles play an important role in driving the gear to rotate. The direction of rotation is dictated by the competition between the chirality of active particles and the alignment interactions between them. By tuning the system parameters, we can observe multiple rotation reversals. Our findings are relevant to understanding how the macroscopic rotation of a gear connects to the microscopic random motion of active particles.

Intrinsic quantum dynamics of particles in brane gravity

The Newtonian dynamics of particles in brane gravity is investigated. Due to the coupling of the particles’ energy–momentum tensor to the tension of the brane, the particle is semi-confined and oscillates along the extra dimension. We demonstrate that the frequency of these oscillations is proportional to the kinetic energy of the particle in the brane. We show that the classical stability of particle trajectories on the brane gives us the Bohr–Sommerfeld quantization condition. The particle’s motion along the extra dimension allows us to formulate a geometrical version of the uncertainty principle. Furthermore, we exhibited that the particle’s motion along the extra dimension is identical to the time-independent Schrödinger equation. The dynamics of a free particle, particles in a box, a harmonic oscillator, a bouncing particle, and tunneling are re-examined. We show that the particle’s motion along the extra dimension yields a quantized energy spectrum for bound states.

Bouncing wave packets, Ehrenfest theorem, and uncertainty relation based upon a new concept for the momentum of a particle in a box

For a particle in a box, the operator −i∂x is not self-adjoint and thus does not qualify as the physical momentum. As a result, in general the Ehrenfest theorem is violated. Based upon a recently developed new concept for a self-adjoint momentum operator, we reconsider the theorem and find that it is now indeed satisfied for all physically admissible boundary conditions. We illustrate these results for bouncing wave packets which first spread, then shrink, and return to their original form after a certain revival time. We derive a very simple form of the general Heisenberg–Robertson–Schrödinger uncertainty relation and show that our construction also provides a physical interpretation for it.

General pseudo self-adjoint boundary conditions for a 1D KFG particle in a box

We consider a 1D Klein–Fock–Gordon particle in a finite interval, or box. We construct for the first time the most general set of pseudo self-adjoint boundary conditions for the Hamiltonian operator that is present in the first order in time 1D Klein–Fock–Gordon wave equation, or the 1D Feshbach–Villars wave equation. We show that this set depends on four real parameters and can be written in terms of the one-component wavefunction for the second order in time 1D Klein–Fock–Gordon wave equation and its spatial derivative, both evaluated at the endpoints of the box. Certainly, we write the general set of pseudo self-adjoint boundary conditions also in terms of the two-component wavefunction for the 1D Feshbach–Villars wave equation and its spatial derivative, evaluated at the ends of the box; however, the set actually depends on these two column vectors each multiplied by the singular matrix that is present in the kinetic energy term of the Hamiltonian. As a consequence, we found that the two-component wavefunction for the 1D Feshbach–Villars equation and its spatial derivative do not necessarily satisfy the same boundary condition that these quantities satisfy when multiplied by the singular matrix. In any case, given a particular boundary condition for the one-component wavefunction of the standard 1D Klein–Fock–Gordon equation and using the pair of relations that arise from the very definition of the two-component wavefunction for the 1D Feshbach–Villars equation, the respective boundary condition for the latter wavefunction and its derivative can be obtained. Our results can be extended to the problem of a 1D Klein–Fock–Gordon particle moving on a real line with a point interaction (or a hole) at one point.

CryoEM single particle reconstruction with a complex-valued particle stack

Single particle reconstruction (SPR) in cryoEM is an image processing task with an elaborate hierarchy that starts with many very noisy multi-frame images. Efficient representation of the intermediary image structures is critical for keeping the calculations manageable. One such intermediary structure is called a particle stack and contains cut-out images of particles in square boxes of predefined size. The micrograph that is the source of the boxed images is usually corrected for motion between frames prior to particle stack creation. However, the contrast transfer function (CTF) or its Fourier Transform point spread function (PSF) are not considered at this step. Historically, the particle stack was intended for large particles and for a tighter PSF, which is characteristic of lower resolution data. The field now performs analyses of smaller particles and to higher resolution, and these conditions result in a broader PSF that requires larger padding and slower calculations to integrate information for each particle. Consequently, the approach to handling structures such as the particle stack should be reexamined to optimize data processing.Here we propose to use as a source image for the particle stack a complex-valued image, in which CTF correction is implicitly applied as a real component of the image. We can achieve it by applying an initial CTF correction to the entire micrograph first and perform box cutouts as a subsequent step. The final CTF correction that we refine and apply later has a very narrow PSF, and so cutting out particles from micrographs that were approximately corrected for CTF does not require extended buffering, i.e. the boxes during the analysis only have to be large enough to encompass the particle. The Fourier Transform of an exit-wave reconstruction creates an image that has complex values. This is a complex value image considered in real space, opposed to standard SPR data processing where complex numbers appear only in Fourier space. This extension of the micrograph concept provides multiple advantages because the particle box size can be small and calculations crucial for high resolution reconstruction such as Ewald sphere correction, aberration refinement, and particle-specific defocus refinement can be performed on the small box data.

Quantum Lenoir engine in the presence of minimal length

The effect of minimal length for quantum heat engine systems is proposed. We use a system of trapped Fermi particles in an infinite potential well. The thermodynamic cycle chosen is the reversible Lenoir cycle. We use both a single particle case and a multiparticle case. The result is that the minimum length increases the efficiency of the engine if the width of the potential well is infinitely small, and the maximum value is obtained when the width of the potential well is close to zero.

Quantum states of H2+ and H2 in an icosahedral potential well

We investigate the potential energy surfaces (PESs) of the hydrogen-based cation H2+ and the neutral molecule H2 confined inside an infinite potential well in the shape of a regular icosahedron. The numerical computations are performed using the diffusion Monte Carlo method and are based on an analytical technique for obtaining simple equations of the surfaces of convex polyhedra proposed by S. Onaka. Different states and different orientations of the molecules inside the confining potential well, as well as various sizes of the latter, are studied. We provide a detailed symmetry analysis and consistent labeling of the H2+ states considered. The results show that the icosahedral confinement is closely isotropic in its inner region, leading to PESs that develop pronounced minima, as in the case of simpler confinement geometries. Shape-specific effects can be evidenced when the nuclei are in contact with the confining wall.

Entropy production of active particles formulated for underdamped dynamics.

The present work investigates the effect of inertia on the entropy production rate Π for all canonical models of active particles for different dimensions and the type of confinement. To calculate Π, the link between the entropy production and dissipation of heat rate is explored, resulting in a simple and intuitive expression. By analyzing the Kramers equation, alternative formulations of Π are obtained and the virial theorem for active particles is derived. Exact results are obtained for particles in an unconfined environment and in a harmonic trap. In both cases, Π is independent of temperature. For the case of a harmonic trap, Π attains a maximal value for τ=ω^{-1}, where τ is the persistence time and ω is the natural frequency of an oscillator. For active particles in one-dimensional box, or other nonharmonic potentials, thermal fluctuations are found to reduce Π.

Operator associated to the index of degeneration of Landau’s levels

We determine the operators associated to the index of degeneration of Landau's levels for the Landau's gauge and symmetric gauge of the magnetic field, with the non separable eigenvalue solution obtained for a charged particle in a flat box under a magnetic field perpendicular to flat motion.

Numerical Calculations of Energies for an Infinite Potential Well with Sinusoidal Bottom

Abstract: We present an investigation for a particle confined in an infinite well with sinusoidal bottom, using the perturbation theory and numerical solution for the Schrödinger equation to obtain the eigen energies and wavefunctions. Potential strength and potential oscillation dependence of the state are examined and analyzed. It is shown that the particle in a box with sinusoidal bottom does not show up the Klauder phenomenon when the perturbations are gradually reduced to zero. The research results show that the potential oscillation significantly affects certain quantum states and, therefore, the ability to manipulate the energy difference between the states. In addition, our results for the present system converge to their corresponding values for the unperturbed one in the high-potential oscillation limit. Keywords: Infinite well, Perturbation theory, Sinusoidal potential, Numerical calculations, Klauder phenomenon.

基于离散元法的荞麦三级振动筛分试验研究

To improve the operating effect of buckwheat classifying equipment and meanwhile reduce the dependence on tests in the process of operating parameter optimization of the equipment, this paper designed a three-level classifying screen for buckwheat, confirmed the structure and parameters of upper and lower sieves, established a three-level screening discrete element model for buckwheat with the EDEM software, and conducted the numerical simulation for the sieving processes at an amplitude of 24 mm, 28 mm and 32 mm, respectively. The results indicated that when the inclination angle of screen surface was 3°, the vibrational direction angle was 30° and the vibrational frequency was 4.5 HZ, as the amplitude increased, the conveying capacity of the classifying screen increased and at the same time the seed loss rate also increased, of which at 16 s, the loss rate was 0.03%, 0.37% and 1.42%, respectively; the proportion of medium particles in the collecting box of screen overflow was 2.88%, 8.65% and 17.65%, respectively; and the proportion of small particles in the collecting box of screen residue was 0.58%, 6.06% and 19.14%, respectively. Through comprehensive analysis of conveying capacity, screening loss and classifying effect, when the amplitude of the classifying screen was 28 mm, the classifying operating effect was good. This study can provide reference for the design and operating parameter optimization of buckwheat classifying equipment.

Enabling multiple intercavity polariton coherences by adding quantum confinement to cavity molecular polaritons

In this study, the "particle in a box" idea, which was broadly developed in semiconductor quantum dot research, was extended into mid-infrared (IR) cavity modes by applying lateral confinement in an optical cavity. The discrete cavity modes hybridized with molecular vibrational modes, resulting in a quartet of polariton states that can support multiple coherence states in the IR regime. We applied tailored pump pulse sequences to selectively prepare these coherences and verified the multi-coherence existence. The simulation based on Lindblad equation showed that because the quartet of polariton states resided in the same cavity, they were specifically robust toward decoherence caused by fluctuations in space. The multiple robust coherences paved the way for entangled states and coherent interactions between cavity polaritons, which would be critical for advancing polariton-based quantum information technology.

The effects of the covariant generalized uncertainty principle on quantum mechanics

One can use the generalized uncertainty principle (GUP) to incorporate the minimum measurable length in quantum gravity. It may be interesting to have a minimal time interval as well as the minimal length in the relativistic version of quantum mechanics in the presence of the gravitational effects. In this paper, we considered a covariant version of the GUP to investigate the effects of both the minimal time and the minimal length. Using the covariant GUP, the energy–momentum dispersion relation was modified. Starting with the modified dispersion relation, the corrections to the wave function were obtained and the problems of the particle in a box and the hydrogen atom were revisited. Considering the minimal time may be an interesting new topic, which is not widely studied before. It may lead to new results that can open a new window into quantum gravity.

Nonlinear dynamics of positron resonances in a carbon nanotube

We have investigated long-time dynamics of the transverse resonant states occurring in positron transmission through a chiral single-wall carbon nanotube in the channeling mode. This was done by a detailed analysis of quantum carpet, generated by the interference of the resonant states. We found that structure of the carpet depends strongly on the width of the initial wave packet. In the case of the narrow wave packet obtained carpet is periodic and very regular, woven by full and fractional wave packet revivals. Close to every fractional revival additional repeated and inverted reconstructed patterns were observed which do not exist in carpets for a particle in a sealed box. In the case of the wide wave packet, we were able to recognize motifs that repeat approximately, and conclude that dynamics, in this case, is quasi-periodic. This peculiar behavior was traced back to the level of coordination between fluctuations of resonances amplitude and phase functions.

Non-Archimedean quantum mechanics via quantum groups

We present a new non-Archimedean realization of the Fock representation of the q-oscillator algebras where the creation and annihilation operators act on complex-valued functions, which are defined on a non-Archimedean local field of arbitrary characteristic, for instance, the field of p-adic numbers. This new realization implies that many quantum models constructed using q-oscillator algebras are non-Archimedean models, in particular, p-adic quantum models. In this framework, we select a q-deformation of the Heisenberg uncertainty relation and construct the corresponding q-deformed Schrödinger equations. In this way we construct a p-adic quantum mechanics which is a p-deformed quantum mechanics. We also solve the time-independent Schrödinger equations for the free particle, and a particle in a non-Archimedean box. In the last case, we show the existence of a discrete sequence of energy levels. We determine the eigenvalues of Schrödinger operator for a general radial potential. By choosing the potential in a suitable form we recover the energy levels of the q-hydrogen atom.

Impurity reveals distinct operational phases in quantum thermodynamic cycles.

We analyze the effect of impurity on the work output and efficiency of quantum Otto and quantum Carnot heat cycles, modeled as a single quantum particle in an infinite square well potential, which is the working substance. We solve this quantum mechanical system perturbatively up to first and second order in strength of the impurity for strong- and weak-coupling regimes, respectively. We derive the analytical expressions of work and efficiency for the strong-coupling regime to the first order in the strength parameter. The threshold value of the strength parameter in weak coupling is obtained up to which the numerical result agrees with the perturbative result for a repulsive and attractive impurity. To our surprise, an embedded impurity unlocks new operational phases in the system, such as a quantum heat engine, quantum refrigerator, and quantum cold pump. In addition, the efficiency of the quantum Otto heat engine is seen to reach Carnot efficiency for some parameter regimes. The cooling power and coefficient of performance of the quantum refrigerator and quantum cold pump are nontrivially affected by the impurity.

Numerical Investigation of the Radial Ore‐to‐Coke Ratio in the Blast Furnace Throat during Nonuniform Burden Descent

The burden descent in the blast furnace throat affects the radial ore‐to‐coke ratio, which is directly related to the gas distribution and chemical reactions in the furnace. Herein, the layer structure and the radial ore‐to‐coke ratio of the burden bed under uniform and nonuniform burden descent are studied numerically by the discrete element method. Two kinds of nonuniform descent are considered, where the descent rate in the furnace center is greater than the descent rate at the wall or vice versa. The descent is realized by deleting particles in virtual boxes of different sizes at the lower end of the simulated domain. The results show that the ore‐to‐coke ratio decreases where the descent rate is low and increases where the descent rate is high. For a burden profile of the “platform + hopper” type, a faster burden descent in the center has a much stronger influence on the radial ore‐to‐coke ratio distribution than the case with faster descent at the wall. The size difference between the ore and coke particles and the charging matrix are also found to play a role in the influence of the burden descent on the distribution of the ore‐to‐coke ratio.

A Valid Quantization of the Particle in a Box Field Theory, and Well Beyond

The usual particle in a box is turned into a field theory, and its behavior is examined using canonical and affine quantizations. The result leads to a valid affine quantization of the particle in a box field theory, which points toward further valid quantizations of more realistic field theory models.

Quantum Level Instability of Transverse Excitation in Electron Flow

In current research, we use the effective Schrödinger-Poisson model to study a new kind of quantum-level instability in an infinite-wall slab electron flow. We use the Madelung fluid representation along with the conventional eigenvalue problem techniques in order to solve the linearized coupled differential equations representing the linear transverse collective excitations in the electron gas of arbitrary degree of degeneracy having a constant perpendicular drift. It is shown that the energy levels of collective electrostatic excitations are doubly quantized due to mutual interactions between single electron oscillations, analogous to the problem of a particle in a box, and collective Langmuir oscillations, which are modulated over single electron quantum state. We also report the transverse excitation instability of plasmon energy level in electron slab flow due to the interplay between the wave-like dispersion and the destabilizing perpendicular electron drift momentum. We further study in detail the parametric dependence of such instability in terms of different aspects of the many-electron system. Such a quantum-level instability may have important applications in characteristic behavior of plasmonic devices and their frequency response. Parametric quantization of drifting electron fluid may also have broad applications in nanoscale quantum device calibration and quantum measurements.