Hard-wall Potential Research Articles

Effect of electric field on thermodynamic properties of confined molecules

A detailed study of electric field effect on the thermodynamic properties namely: partition function, free energy, internal energy, entropy and specific heat of a spatially confined diatomic molecule has been presented. The molecule undertaken for study is LiH, as this molecule under confinement has recently received a lot of attention. The confinement is spherical hard wall potential. The rotational spectra for ground vibrational level and matrix elements of the form ψi(r)r-rereψj(r) have been evaluated using accurate finite difference method. Orientation and alignment of confined LiH in the presence of an applied static electric field has also been investigated.

Anchoring transition of confined prolate hard spherocylinder liquid crystals: hard needle-wall potential

ABSTRACTIn the present work, the effects of confinement on a system of hard spherocylinder (HSC) particles interacting with planar substrates through the hard needle-wall potential are studied via Monte Carlo simulation. The molecular volume absorbed at the substrates for the spherocylinder particles are calculated analytically and predicted the critical values of transition parameter from planar to homeotropic anchoring. The transition parameters are achieved from simulations for three particle’s elongations: , , and . The results are in agreement with the predicted values. In the range of small needle length , HSC particles at the first layer near the walls are perpendicular to the walls but in the second layer, are parallel to the walls. To describe this behaviour of HSC particles, we used a system of HSCs consists of two types of molecules: free liquid crystal molecules and fixed perpendicular substrate molecules. We show that the particles near the perpendicular HSCs substrates have parallel alignment. The results of HSCs with and are compared with the hard particle-wall potential. This long needle length interaction is similar to the hard wall potential. Also our results are corresponded to Barmes and Cleaver results on hard Gaussian overlap particles with and , qualitatively.

Aharonov–Bohm effect for bound states in relativistic scalar particle systems in a spacetime with a spacelike dislocation

We investigate the analog effect of the Aharonov–Bohm effect for bound states in two relativistic quantum systems in a spacetime with a spacelike dislocation. We assume that the topological defect has an internal magnetic flux. Then, we analyze the interaction of a charged particle with a uniform magnetic field in this topological defect spacetime, and thus, we extend this analysis to the confinement of a hard-wall potential and a linear scalar potential. Later, the interaction of the Klein–Gordon oscillator with a uniform magnetic field is analyzed. We first focus on the effects of torsion that stem from the spacetime with a spacelike dislocation and the geometric quantum phase. Then, we analyze the effects of torsion and the geometric quantum phase under the presence of a hard-wall potential and a linear scalar potential.

Ionization probability of the hydrogen atom suddenly released from confinement

AbstractThe problem of the stability of a confined atom when it is extracted from the confining cavity has been investigated, modeled by a spherical hard wall potential. The ionization probability when the atom is released from confinement has been obtained. The dependence of the ionization probability on the confinement radius and on the quantum numbers of the initial confined state has been studied. The probability density function of the ionization energy of the ejected electron has been obtained for the different cases considered. The oscillatory structure of this distribution function, with a principal maximum located in the neighborhood of the energy of the initial state and minima very close to zero has been elucidated. The sudden approximation has been applied and the analytic continuation method has been used to calculate the different stationary states.

Hard-wall confinement of a fractional quantum Hall liquid

We make use of numerical exact diagonalization calculations to explore the physics of $\nu = 1/2$ bosonic fractional quantum Hall (FQH) droplets in the presence of experimentally realistic cylindrically symmetric hard-wall potentials. This kind of confinement is found to produce very different many-body spectra compared to a harmonic trap or the so-called extremely steep limit. For a relatively weak confinement, the degeneracies are lifted and the low-lying excited states organize themselves in energy branches that can be explained in terms of their Jack polynomial representation. For a strong confinement, a strong spatial deformation of the droplet is found, with an unexpected depletion of its central density.

Statistics of fermions in a d-dimensional box near a hard wall

We study N noninteracting fermions in a domain bounded by a hard-wall potential in dimensions. We show that for large N, the correlations at the edge of the Fermi gas (near the wall) at zero temperature are described by a universal kernel, different from the universal edge kernel valid for smooth confining potentials. We compute this d-dimensional hard edge kernel exactly for a spherical domain and argue, using a generalized method of images, that it holds close to any sufficiently smooth boundary. As an application we compute the quantum statistics of the position of the fermion closest to the hard wall. Our results are then extended in several directions, including non-smooth boundaries such as a wedge, and also to finite temperature.

Pauli structures arising from confined particles interacting via a statistical potential

There have been suggestions that the Pauli exclusion principle alone can lead a non-interacting (free) system of identical fermions to form crystalline structures dubbed Pauli crystals. Single-shot imaging experiments for the case of ultra-cold systems of free spin-polarized fermionic atoms in a two-dimensional harmonic trap appear to show geometric arrangements that cannot be characterized as Wigner crystals. This work explores this idea and considers a well-known approach that enables one to treat a quantum system of free fermions as a system of classical particles interacting with a statistical interaction potential. The model under consideration, though classical in nature, incorporates the quantum statistics by endowing the classical particles with an effective interaction potential. The reasonable expectation is that possible Pauli crystal features seen in experiments may manifest in this model that captures the correct quantum statistics as a first order correction. We use the Monte Carlo simulated annealing method to obtain the most stable configurations of finite two-dimensional systems of confined particles that interact with an appropriate statistical repulsion potential. We consider both an isotropic harmonic and a hard-wall confinement potential. Despite minor differences, the most stable configurations observed in our model correspond to the reported Pauli crystals in single-shot imaging experiments of free spin-polarized fermions in a harmonic trap. The crystalline configurations observed appear to be different from the expected classical Wigner crystal structures that would emerge should the confined classical particles had interacted with a pair-wise Coulomb repulsion.

Double Weyl points and Fermi arcs of topological semimetals in non-Abelian gauge potentials

We study the effect of a non-Abelian SU(2) gauge potential on the topological semimetal induced by a magnetic field having {\pi}-flux per plaquette and acting on fermions in a cubic lattice. The Abelian {\pi}-flux term gives rise to a spectrum characterized by Weyl points. When the non-Abelian part is turned on, due to the presence of a C4 rotation symmetry, the Weyl points assume a quadratic dispersion along two directions and constitute double monopoles for the Berry curvature. We examine both analytically and numerically the main features of this system, focusing on its gapless surface modes, the so-called Fermi arcs. We discuss the stability of the system under confining hard-wall and harmonic potentials, relevant for the implementation in ultracold atom settings, and the effect of rotation symmetry breaking.

Ga–In intermixing, intrinsic doping, and Wigner localization in the emission spectra of self-organized InP/GaInP quantum dots

We present study of structural and optical properties of InP/GaInP quantum (QDs) providing a weak quantum confinement and creating a platform to study Wigner localization (WL) effects using high spatial resolution optical spectroscopy. Self-organized QD structures were grown using metal-organic chemical phase epitaxy by using different substrate misorientations and cap layer deposition temperatures. Using transmission electron microscopy and energy dispersive x-ray spectroscopy, we demonstrated a bimodal height distribution with peaks at ~5 and ~20 nm and a control of both the lateral size distribution, peaked from ~100 to ~160 nm, and the amount of Ga–In intermixing in the QDs (up to 20%). Using photoluminescence (PL) spectroscopy in combination with circular polarization degree and time resolved micro-PL measurements, we demonstrated control of the emission energy, the intrinsic doping, and the emission decay of these In(Ga)P QDs. Using high-spatial-resolution near-field PL spectra and imaging of single dots, we demonstrated WL effects in dots having a population of up to nine electrons and a parabolic confinement down to ħω0 ~ 1 meV. We performed a self-consistent calculation of exciton transitions using an effective mass, mean field theory with an isotropic elasticity model to describe the effect of Ga–In intermixing on the emission properties of these dots; and we used calculations of shell splitting, using mean field Hartree–Fock approach and calculations of electron density distribution using configuration interaction approach, to described effects of enhancement of WL in non-circular dots with hard-wall potentials.

Confinement and inhomogeneous broadening effects in the quantum oscillatory magnetization of quantum dot ensembles

We report on the magnetization of ensembles of etched quantum dots with a lateral diameter of 460 nm, which we prepared from InGaAs/InP heterostructures. The quantum dots exhibit 1/B-periodic de-Haas–van-Alphen-type oscillations in the magnetization M(B) for external magnetic fields B > 2 T, measured by torque magnetometry at 0.3 K. We compare the experimental data to model calculations assuming different confinement potentials and including ensemble broadening effects. The comparison shows that a hard wall potential with an edge depletion width of 100 nm explains the magnetic behavior. Beating patterns induced by Rashba spin–orbit interaction (SOI) as measured in unpatterned and nanopatterned InGaAs/InP heterostructures are not observed for the quantum dots. From our model we predict that signatures of SOI in the magnetization could be observed in larger dots in tilted magnetic fields.

Phase-induced transport in atomic gases: From superfluid to Mott insulator

Recent experimental realizations of artificial gauge fields for cold atoms are promising for generating steady states carrying a mass current in strongly correlated systems, such as the Bose-Hubbard model. Moreover, a homogeneous condensate confined by hard-wall potentials from laser sheets has been demonstrated, which provides opportunities for probing the intrinsic transport properties of isolated quantum systems. Using the time-dependent Density Matrix Renormalization Group (TDMRG), we analyze the effect of the lattice and interaction strength on the current generated by a quench in the artificial vector potential when the density varies from low values (continuum limit) up to integer filling in the Mott-insulator regime. There is no observable mass current deep in the Mott-insulator state as one may expect. Other observable quantities used to characterize the quasi-steady state in the bulk of the system are the Drude weight and entanglement entropy production rate. The latter in particular provides a striking signature of the superfluid-Mott insulator transition. Furthermore, an interesting property of the superfluid state is the formation of shock and rarefaction waves at the boundaries due to the hard-wall confining potentials. We provide results for the height and the speed of the shock front that propagates from the boundary toward the center of the lattice. Our results should be verifiable with current experimental capabilities.

Generic ordering of structural transitions in quasi-one-dimensional Wigner crystals

We investigate the dependence of the structural phase transitions in an infinite quasi-one-dimensional system of repulsively interacting particles on the profile of the confining channel. Three different functional expressions for the confinement potential related to real experimental systems are used that can be tuned continuously from a parabolic to a hard-wall potential in order to find a thorough understanding of the ordering of the chainlike structure transitions. We resolve the long-standing issue why the most theories predicted a 1-2-4-3-4 sequence of chain configurations with increasing density, while some experiments found the 1-2-3-4 sequence.

Determination of the thermodynamic correction factor of fluids confined in nano-metric slit pores from molecular simulation.

The multi-component diffusive mass transport is generally quantified by means of the Maxwell-Stefan diffusion coefficients when using molecular simulations. These coefficients can be related to the Fick diffusion coefficients using the thermodynamic correction factor matrix, which requires to run several simulations to estimate all the elements of the matrix. In a recent work, Schnell et al. ["Thermodynamics of small systems embedded in a reservoir: A detailed analysis of finite size effects," Mol. Phys. 110, 1069-1079 (2012)] developed an approach to determine the full matrix of thermodynamic factors from a single simulation in bulk. This approach relies on finite size effects of small systems on the density fluctuations. We present here an extension of their work for inhomogeneous Lennard Jones fluids confined in slit pores. We first verified this extension by cross validating the results obtained from this approach with the results obtained from the simulated adsorption isotherms, which allows to determine the thermodynamic factor in porous medium. We then studied the effects of the pore width (from 1 to 15 molecular sizes), of the solid-fluid interaction potential (Lennard Jones 9-3, hard wall potential) and of the reduced fluid density (from 0.1 to 0.7 at a reduced temperature T* = 2) on the thermodynamic factor. The deviation of the thermodynamic factor compared to its equivalent bulk value decreases when increasing the pore width and becomes insignificant for reduced pore width above 15. We also found that the thermodynamic factor is sensitive to the magnitude of the fluid-fluid and solid-fluid interactions, which softens or exacerbates the density fluctuations.

Torsion and noninertial effects on a nonrelativistic Dirac particle

We investigate torsion and noninertial effects on a spin-1/2 quantum particle in the nonrelativistic limit of the Dirac equation. We consider the cosmic dislocation spacetime as a background and show that a rotating system of reference can be used out to distances which depend on the parameter related to the torsion of the defect. Therefore, we analyse torsion effects on the spectrum of energy of a nonrelativistic Dirac particle confined to a hard-wall potential in a Fermi–Walker reference frame.

30-bandk·pmodel of electron and hole states in silicon quantum wells

We modeled the electron and hole states in Si/SiO2 quantum wells within a basis of standing waves using the 30-band k.p theory. The hard-wall confinement potential is assumed, and the influence of the peculiar band structure of bulk silicon on the quantum-well sub-bands is explored. Numerous spurious solutions in the conduction-band and valence-band energy spectra are found and are identified to be of two types: (1) spurious states which have large contributions of the bulk solutions with large wave-vectors (the high-k spurious solutions) and (2) states which originate mainly from the spurious valley outside the Brillouin zone (the extra-valley spurious solutions). An algorithm to remove all those nonphysical solutions from the electron and hole energy spectra is proposed. Furthermore, slow and oscillatory convergence of the hole energy levels with the number of basis functions is found and is explained by the peculiar band mixing and the confinement in the considered quantum well. We discovered that assuming the hard-wall potential leads to numerical instability of the hole states computation. Nonetheless, allowing the envelope functions to exponentially decay in a barrier of finite height is found to improve the accuracy of the computed hole states.

Different particle-accumulation structures arising from particle–boundary interactions in a liquid bridge

The formation of particle-accumulation structures in the flow in a cylindrical liquid bridge driven by the thermocapillary effect is studied. The problem is modeled as an incompressible fluid seeded with a low concentration of small spherical particles which are assumed to have a negligible effect on the flow. The particle motion is modeled by pure advection except for small regions at the free surface and walls where the particle interaction with the free surface and walls is modeled by a hard-wall potential which restricts the motion of the particle within some interaction length from the boundaries. The model yields a wide range of particle-accumulation structures when varying the relative interaction length from 5×10-3 to 3×10-2. It is found that in many cases each particle need undergo no more than a handful of returns to the free surface for particle-accumulation structures to arise. It is also found that the shape of the particle-accumulation structures changes qualitatively at certain critical interaction lengths.

Critical dispersion of advecting-diffusing tracers in periodic landscapes of hard-wall symmetric potentials

Large-scale, time-asymptotic dispersion properties of diffusing tracers dragged by a uniform drive through a two-dimensional periodic lattice of hard-wall symmetric potentials are investigated. Dispersion is quantified by a typically anisotropic effective diffusivity tensor D, whose eigenvalues and eigenvectors depend on the dimensionless bare diffusivity 1/Pe for each given lattice geometry. Attention is focused on critical lattice geometries yielding sustained macroscale dispersion D([perpendicular]) along the direction orthogonal to the uniform drive in the limit where Pe→∞. A simple one-dimensional model is proposed, which predicts the anomalous scaling D([perpendicular])~1/[A(1)+A(2)log(Pe)].

Considerations on Hund's first rule in a planar two-electron quantum dot

We give a detailed analysis of the applicability of Hund's first rule for harmonic planar two-electron quantum dots by means of entanglement witnesses. We find that for purely harmonic confinement there is only one pair of singlet and triplet states for which it can be applied. We also discuss the origin and validity for this case and extend the discussion to a quartic confining potential, a hard-wall potential, and a combination of harmonic confinement with quartic perturbation. A generalized rule, the alternating rule, is found to be applicable and valid for vanishing angular momentum states in all these cases. Furthermore, we are able to clarify the role of entanglement in general harmonic two-electron models for vanishing interaction strength. This behavior can be attributed to the special separability properties of these models.

Pseudostate description of diatomic-molecule scattering from a hard-wall potential

A collinear scattering of a structured particle from a hard wall is studied with consideration of vibrational transitions initiated by the collision. It is shown that this problem can be solved analytically in the framework of the source-function method. With the use of the continuum discretization technique we are able to take into account both discrete and continuum states. No approximations of the interatomic potential is required. We illustrate our approach for the case of a hydrogen molecule bound by the realistic Morse potential. simple systems. The results by Sato and Kayanuma (13) indicate that the initial molecule ground state cannot survive after the collision when the energy difference between this state and the first-excited state goes to zero. Contrarily, Kavka et al. (9) show that an arbitrarily weakly bound molecule scattering from an arbitrarily high step potential remains in the ground state with probability equal to unity. Moreover, the molecule center of mass cannot get closer to the hard wall than ξ0 ln(V0/Ein) where ξ0 is a constant of order of the mean distance between the atoms, V0 is the potential barrier heights and Ein is the molecule impact energy. The case where the hard wall is infinitely high is particularly interesting because the molecule reflects from the surface at an infinitely large distance from the surface. In the next section we present the general analytical solution to the problem of interest for case where V0 is infinite. Our approach requires no approximations on the form of the interparticle interaction. To illustrate our theory we give a numerical example in Sec. III. In the conclusion we present the summary of the results.

Transition from single-file to two-dimensional diffusion of interacting particles in a quasi-one-dimensional channel

Diffusive properties of a monodisperse system of interacting particles confined to a quasi-one-dimensional channel are studied using molecular dynamics simulations. We calculate numerically the mean-squared displacement (MSD) and investigate the influence of the width of the channel (or the strength of the confinement potential) on diffusion in finite-size channels of different shapes (i.e., straight and circular). The transition from single-file diffusion to the two-dimensional diffusion regime is investigated. This transition [regarding the calculation of the scaling exponent (α) of the MSD (Δx(2)(t) ∝ t(α)] as a function of the width of the channel is shown to change depending on the channel's confinement profile. In particular, the transition can be either smooth (i.e., for a parabolic confinement potential) or rather sharp (i.e., for a hard-wall potential), as distinct from infinite channels where this transition is abrupt. This result can be explained by qualitatively different distributions of the particle density for the different confinement potentials.