Hard-wall Potential Research Articles

Modification of Landau Levels in a 2D Ring Due to Rotation Effects and Edge States

AbstractThe properties of a 2D quantum ring under rotating and external magnetic field effects are investigated. The Landau levels and their inertial effects on them are initially analyzed. Among the results obtained, it is emphasized that the rotation lifted the degeneracy of Landau levels. The second part deals with the electronic confinement in a 2D ring modeled by a hard wall potential. The eigenstates are described by Landau states as long as they are not too close to the ring edges. On the other hand, near the ring edges, the energies increase monotonically. These states are known as edge states. Edge states have a significant role in the physical properties of the ring. Thus, the Fermi energy and magnetization are analyzed. In the specific case of magnetization, two approaches are considered. In the first approach, an analytical result for magnetization is obtained but without considering rotation. Numerical results show the de Haas‐Van Alphen (dHvA) oscillations. In the second approach, rotating effects are considered. In addition to the dHvA oscillations, the Aharonov–Bohm‐type (AB) oscillations are verified, which are associated with the presence of edge states. The effects of rotation on the results are discussed and it is found that rotation is responsible for inducing AB oscillations.

Quantum jamming: Critical properties of a quantum mechanical perceptron

In this Letter, we analyze the quantum dynamics of the perceptron model: a particle is constrained on a $N$-dimensional sphere, with $N\to \infty$, and subjected to a set of randomly placed hard-wall potentials. This model has several applications, ranging from learning protocols to the effective description of the dynamics of an ensemble of infinite-dimensional hard spheres in Euclidean space. We find that the jamming transition with quantum dynamics shows critical exponents different from the classical case. We also find that the quantum jamming transition, unlike the typical quantum critical points, is not confined to the zero-temperature axis, and the classical results are recovered only at $T=\infty$. Our findings have implications for the theory of glasses at ultra-low temperatures and for the study of quantum machine-learning algorithms.

Shannon information entropy sum of the confined hydrogenic atom under the influence of an electric field

In this work, we present the effects of an external electric field on the Shannon entropy sum of a spherically confined hydrogenic atom. The confinement considered is of the impenetrable hard wall type. The electric field modifies the spectrum of the confined hydrogenic system, which results in avoided crossings among the energy levels of the system, with strong competition between the Coulombic and hard wall potential. The results presented indicate that the electric field is a strong candidate to modify information theoretic measures. In addition, we examine the effects of field strength, nuclear charge and hard walls on the minima/maxima structure of the entropic sum. Shannon entropy sum, $$S_t$$ , versus confinement radius, $$R_c$$ , of the 2p level of confined hydrogenic atoms, with field strength $$\epsilon = 0$$ (black), $$\epsilon = 0.001$$ (red), $$\epsilon = 0.01$$ (green) and $$\epsilon = 0.05$$ (blue). The intensity of the field modifies the structure in $$S_t$$ .

Aspects of arbitrarily oriented dipoles scattering in a plane: Short-range interaction influence

The impact of the short-range interaction on the resonances occurrence in the anisotropic dipolar scattering in a plane was numerically investigated for the arbitrarily oriented dipoles and for a wide range of collision energies. We revealed the strong dependence of the cross section of the 2D dipolar scattering on the radius of short-range interaction, which is modeled by a hard wall potential and by the more realistic Lennard-Jones potential, and on the mutual orientations of the dipoles. We defined the critical (magic) tilt angle of one of the dipoles, depending on the direction of the second dipole for arbitrarily oriented dipoles. It was found that resonances arise only when this angle is exceeded. In contrast to the 3D case, the energy dependencies of the boson (fermion) 2D scattering cross section grows (is reduced) with an energy decrease in the absence of the resonances. We showed that the mutual orientation of dipoles strongly impacts the form of the energy dependencies, which begin to oscillate with the tilt angle increase, unlike the 3D dipolar scattering. The angular distributions of the differential cross section in the 2D dipolar scattering of both bosons and fermions are highly anisotropic at non-resonant points. The results of the accurate numerical calculations of the cross section agree well with the results obtained within the Born and eikonal approximations.

Hartree-Fock-Bogoliubov theory of trapped one-dimensional imbalanced Fermi systems

Ground state Hartree-Fock-Bogoliubov (HFB) theory is applied to imbalanced spin-1/2 one-dimensional Fermi systems that are spatially confined by either a harmonic or a hard-wall trapping potential. It has been hoped that such systems, which can be realized using ultracold atomic gases, would exhibit the long-sought-after Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase. The HFB formalism generalizes the standard Bogoliubov quasi-particle transformation, by allowing for Cooper pairing to exist between all possible single-particle states, and accounts for the effects of the inhomogeneous trapping potential as well as the mean-field Hartree potential. This provides an unbiased framework to describe inhomgenous densities and pairing correlations in the FFLO state of a confined 1D gas. In a harmonic trap, numerical minimization of the HFB ground state energy yields a spatially oscillating order parameter reminiscent of the FFLO state. However, we find that this state has almost no imprint in the local fermion densities (consistent with experiments that found no evidence of the FFLO phase). In contrast, for a hard-wall geometry, we find a strong signature of the spatial oscillations of the FFLO pairing amplitude reflected in the local in situ densities. In the hard wall case, the excess spins are strongly localized near regions where there is a node in the pairing amplitude, creating an unmistakeable crystalline modulation of the density.

Electrostatic potential shape of gate-defined quantum point contacts

Quantum point contacts (QPC) are fundamental building blocks of nanoelectronic circuits. For their emission dynamics as well as for interaction effects such as the 0.7-anomaly the details of the electrostatic potential are important, but the precise potential shapes are usually unknown. Here, we measure the one-dimensional subband spacings of various QPCs as a function of their conductance and compare our findings with models of lateral parabolic versus hard wall confinement. We find that a gate-defined QPC near pinch-off is compatible with the parabolic saddle point scenario. However, as the number of populated subbands is increased Coulomb screening flattens the potential bottom and a description in terms of a finite hard wall potential becomes more realistic.

Stretching DNA in hard-wall potential channels

A three-dimensional mesoscopic model is applied to study the properties of short DNA chains in a confining environment. The cylindrical channel is represented by a hard-wall repulsive potential incorporated in the system Hamiltonian. The macroscopic helical parameters are computed performing statistical averages over the ensemble of microscopic base pair fluctuations. The average molecule elongation, measured by the end-to-end distance, is derived as a function of the channel potential parameters both for a homogeneous and a heterogeneous chain. The overall results suggest that the mesoscopic model, with the channel potential term, yields consistent quantitative estimates for the stretching and twisting of short chains.

Relativistic quantum oscillators in the global monopole spacetime

We investigated the effects of the global monopole spacetime on the Dirac and Klein–Gordon relativistic quantum oscillators. In order to do this, we solve the Dirac and Klein–Gordon equations analytically and discuss the influence of this background, which is characterised by the curvature of the spacetime, on the energy profiles of these oscillators. In addition, we introduce a hard-wall potential and, for a particular case, determine the energy spectrum for relativistic quantum oscillators in this background.

Effects of a Landau-Type Quantization Induced by the Lorentz Symmetry Violation on a Dirac Field

Inspired by the extension of the Standard Model, we analyzed the effects of the spacetime anisotropies on a massive Dirac field through a nonminimal CPT-odd coupling in the Dirac equation, where we proposed a possible scenario that characterizes the breaking of the Lorentz symmetry which is governed by a background vector field and induces a Landau-type quantization. Then, in order to generalize our system, we introduce a hard-wall potential and, for a particular case, we determine the energy levels in this background. In addition, at the nonrelativistic limit of the system, we investigate the effects of the Lorentz symmetry violation on thermodynamic aspects of the system.

On the number of isolated eigenvalues of a pair of particles on the half-line

In this note we consider a pair of particles moving on the positive half-line with the pairing generated by a hard-wall potential. This model was first introduced in [arXiv:1604.06693] and later applied to investigate condensation of pairs of electrons in a quantum wire [arXiv:1708.03753,arXiv:1801.00696]. For this, a detailed spectral analysis proved necessary and as a part of this it was shown in [arXiv:1708.03753] that, in a special case, the discrete spectrum of the Hamiltonian consists of a single eigenvalue only. It is the aim of this note to prove that this is generally the case.

On a massive scalar field subject to the relativistic Landau quantization in an environment of aether-like Lorentz symmetry violation

We analyze the effects of the aether-like Lorentz symmetry violation on a massive scalar field subject to a uniform magnetic field, where, analytically, we determine the relativistic Landau levels and note that this background governed by a constant vector field modifies the energy spectrum of the relativistic quantum system. We extend our analysis by including a hard-wall potential in the system, and, under some conditions, we determine the energy spectrum of the scalar field and show that the presence of this confinement potential drastically modifies the relativistic energy levels in this possible scenario of breaking of the Lorentz symmetry.

Noninertial effects on a scalar field in a spacetime with a magnetic screw dislocation

We investigate rotating effects on a charged scalar field immersed in spacetime with a magnetic screw dislocation. In addition to the hard-wall potential, which we impose to satisfy a boundary condition from the rotating effect, we insert a Coulomb-type potential and the Klein–Gordon oscillator into this system, where, analytically, we obtain solutions of bound states which are influenced not only by the spacetime topology, but also by the rotating effects, as a Sagnac-type effect modified by the presence of the magnetic screw dislocation.

Gate electrostatics and quantum capacitance in ballistic graphene devices

We experimentally investigate the charge induction mechanism across gated, narrow, ballistic graphene devices with different degrees of edge disorder. By using magnetoconductance measurements as the probing technique, we demonstrate that devices with large edge disorder exhibit a nearly homogeneous capacitance profile across the device channel, close to the case of an infinitely large graphene sheet. In contrast, devices with lower edge disorder (< 1 nm roughness) are strongly influenced by the fringing electrostatic field at graphene boundaries, in quantitative agreement with theoretical calculations for pristine systems. Specifically, devices with low edge disorder present a large effective capacitance variation across the device channel with a nontrivial, inhomogeneous profile due not only to classical electrostatics but also to quantum mechanical effects. We show that such quantum capacitance contribution, occurring due to the low density of states (DOS) across the device in the presence of an external magnetic field, is considerably altered as a result of the gate electrostatics in the ballistic graphene device. Our conclusions can be extended to any two dimensional (2D) electronic system confined by a hard-wall potential and are important for understanding the electronic structure and device applications of conducting 2D materials.

Individually addressable double quantum dots formed with nanowire polytypes and identified by epitaxial markers

Double quantum dots (DQDs) hold great promise as building blocks for quantum technology as they allow for two electronic states to coherently couple. Defining QDs with materials rather than using electrostatic gating allows for QDs with a hard-wall confinement potential and more robust charge and spin states. An unresolved problem is how to individually address these QDs, which is necessary for controlling quantum states. We here report the fabrication of DQD devices defined by the conduction band edge offset at the interface of the wurtzite and zinc blende crystal phases of InAs in nanowires. By using sacrificial epitaxial GaSb markers selectively forming on one crystal phase, we are able to precisely align gate electrodes allowing us to probe and control each QD independently. We hence observe textbooklike charge stability diagrams, a discrete energy spectrum, and electron numbers consistent with theoretical estimates and investigate the tunability of the devices, finding that changing the electron number can be used to tune the tunnel barrier as expected by simple band diagram arguments.

Space-time resolution of size-dispersed suspensions in Deterministic Lateral Displacement microfluidic devices

Deterministic Lateral Displacement (DLD) is a relatively recent microfluidics-assisted technique which allows the size-based separation of a population of micrometric particles suspended in a buffer solution. The core of the device is a shallow channel with rectangular cross-section filled with an array of solid obstacles arranged in a spatially periodic lattice, whose directions are slanted with respect to the channel walls. In practical implementations of DLD, particles are continuously introduced at a localized position of the channel entrance and migrate along different average directions downstream the device according to their size. Thus, at steady state, size-sorted subpopulations can be collected at different positions of the channel outlet. Besides, theoretical predictions of recent models of particle transport in these devices suggest that not only the direction of the average particle velocity, but also its magnitude (i.e. the mobility) depends sensitively on particle size. By exploiting this dependence, a novel use of DLD devices is here proposed, where the size-driven separation is realized over time and space by running the process under transient conditions, thus mimicking a classical chromatographic separation. We show how this approach is particularly effective for particles of specific (critical) dimensions, which are known to impair the efficiency of the steady-state separation process. Numerical predictions based on a hard-wall repulsive potential for the particle-obstacle interaction suggest that unprecedented separation performance for near-critical particle size could be obtained in transient conditions within the same channel length used for the time-continuous separation. The case of cylindrical obstacles and spherically shaped particles is considered in detail as an illustrative example.

Bottom-Up Approach to the Coarse-Grained Surface Model: Effective Solid-Fluid Potentials for Adsorption on Heterogeneous Surfaces.

Coarse-grained surface models with a low-dimension positional dependence have great advantages in simplifying the theoretical adsorption model and speeding up molecular simulations. In this work, we present a bottom-up strategy, developing a new two-dimensional (2D) coarse-grained surface model from the "bottom-level" atomistic model, for adsorption on highly heterogeneous surfaces with various types of defects. The corresponding effective solid-fluid potential consists of a 2D hard wall potential representing the structure of the surface and a one-dimensional (1D) effective area-weighted free-energy-averaged (AW-FEA) potential representing the energetic strength of the substrate-adsorbate interaction. Within the conventional free-energy-averaged (FEA) framework, an accessible-area-related parameter is introduced into the equation of the 1D effective solid-fluid potential, which allows us not only to obtain the energy information from the fully atomistic system but also to get the structural dependence of the potential on any geometric defect on the surface. Grand canonical Monte Carlo simulations are carried out for argon adsorption at 87.3 K to test the validity of the new 2D surface model against the fully atomistic system. We test four graphitic substrates with different levels of geometric roughness for the top layer, including the widely used reference solid substrate Cabot BP-280. The simulation results show that adding one more dimension to the traditional 1D surface model is essential for adsorption on the geometrically heterogeneous surfaces. In particular, the 2D surface model with the AW-FEA solid-fluid potential significantly improves the adsorption isotherm and density profile over the 1D surface model with the FEA solid-fluid potential over a wide range of pressure. The method to construct an effective solid-fluid potential for an energetically heterogeneous surface is also discussed.

Semiclassical trace formula for truncated spherical well potentials: Toward the analyses of shell structures in nuclear fission processes

Trace formulas for the contributions of degenerate periodic-orbit families to the semiclassical level density in truncated spherical hard-wall potentials are derived. In addition to the portion of the continuous periodic-orbit family contribution which persists after truncation, end-point corrections to the truncated family should be taken into account. I propose a formula to evaluate these end-point corrections as separate contributions of what I call marginal orbits. Applications to the two-dimensional billiard and three-dimensional cavity systems with the three-quadratic-surfaces shape parametrization, initiated to describe the nuclear fission processes, reveal unexpectedly large effects of the marginal orbits.

Two-dimensional Rutherford-like scattering in ballistic nanodevices

Ballistic injection in a nanodevice is a complex process where electrons can either be transmitted or reflected, thereby introducing deviations from the otherwise quantized conductance. In this context, quantum rings (QRs) appear as model geometries: in a semiclassical view, most electrons bounce against the central QR antidot, which strongly reduces injection efficiency. Thanks to an analogy with Rutherford scattering, we show that a local partial depletion of the QR close to the edge of the antidot can counter-intuitively ease ballistic electron injection. On the contrary, local charge accumulation can focus the semi-classical trajectories on the hard-wall potential and strongly enhance reflection back to the lead. Scanning gate experiments on a ballistic QR, and simulations of the conductance of the same device are consistent, and agree to show that the effect is directly proportional to the ratio between the strength of the perturbation and the Fermi energy. Our observation surprisingly fits the simple Rutherford formalism in two-dimensions in the classical limit.

Many-body stabilization of a resonant p -wave Fermi gas in one dimension

Using the asymptotic Bethe Ansatz, we study the stabilization problem of the one-dimensional spin-polarized Fermi gas confined in a hard-wall potential with tunable p-wave scattering length and finite effective range. We find that the interplay of two factors, i.e., the finite interaction range and the hard-wall potential, will stabilize the system near resonance. The stabilization occurs even in the positive scattering length side, where the system undergoes a many-body collapse if any of the factors is absent. At p-wave resonance, the fermion system is found to feature the "quasi-particle condensation" for any value of effective range, which is stabilized if the range is above twice the mean particle distance. Slightly away from resonance, the correction to the stability condition linearly depends on the inverse scattering length. Finally, a global picture is presented for the energetics and stability properties of fermions from weakly attractive to deep bound state regime. Our results raise the possibility for achieving stable p-wave superfluidity in quasi-1D atomic systems, and meanwhile, shed light on the intriguing s- and p-wave physics in 1D that violate the Bose-Fermi duality.

Ring-shaped fractional quantum Hall liquids with hard-wall potentials

We study the physics of $\nu=1/2$ bosonic fractional quantum Hall droplets confined in a ring-shaped region delimited by two concentric cylindrically symmetric hard-wall potentials. Trial wave functions based on an extension of the Jack polynomial formalism including two different chiral edges are proposed and validated for a wide range of confinement potentials in terms of their excellent overlap with the eigenstates numerically found by exact diagonalization. In the presence of a single repulsive potential centered in the origin, a recursive structure in the many-body spectra and a massively degenerate ground state manifold are found. The addition of a second hard-wall potential confining the fractional quantum Hall droplet from the outside leads to a non-degenerate ground state containing a well defined number of quasiholes at the center and, for suitable potential parameters, to a clear organization of the excitations on the two edges. The utility of this ring-shaped configuration in view of theoretical and experimental studies of subtle aspects of fractional quantum Hall physics is outlined.