Single-particle Parameters Research Articles

Correlations and Signaling in the Schrödinger-Newton Model

Abstract The Schrödinger-Newton model is a semi-classical theory in which, in addition to mutual attraction, massive quantum particles interact with their own gravitational fields. While there are many studies on the phenomenology of single particles, correlation dynamics in multipartite systems is largely unexplored. Here, we show that the Schrödinger-Newton interactions preserve the product form of the initial state of a many-body system, yet on average agreeing with classical mechanics of continuous mass distributions. This leads to a simple test of the model, based on verifying bipartite gravitational evolution towards non-product states. We show using standard quantum mechanics that, with currently accessible single-particle parameters, two masses released from harmonic traps get correlated well before any observable entanglement is accumulated. Therefore, the Schrödinger-Newton model can be tested with setups aimed at observation of gravitational entanglement with significantly relaxed requirements on coherence time. We also present a mixed-state extension of the model that avoids superluminal signaling.

Quantitative analysis of interaction effects in generalized Aubry-André-Harper models

We present a quantitative analysis of two-particle interaction effects in generalized, one-dimensional Aubry-Andr\'e-Harper models with the Fermi energy placed in one of the band gaps. We investigate systems with periodic as well as open boundary conditions; for the latter focusing on the number of edge states and the boundary charge. Both these observables are important for the classification of noninteracting topological systems. In our first class of models the unit cell structure stems from periodically modulated single-particle parameters. In the second it results from the spatial modulation of the two-particle interaction. For both types of models, we find that the single-particle band gaps are renormalized by the interaction in accordance with expectations employing general field theoretical arguments. While interaction induced effective edge states can be found in the local single-particle spectral function close to a boundary, the characteristics of the boundary charge are not modified by the interaction. This indicates that our results for the Rice-Mele and Su-Schriefer-Heeger model [Phys. Rev. B 102, 085122 (2020)] are generic and can be found in lattice models with more complex unit cells as well.

Stochastic modelling of abrasive waterjet footprints using finite element analysis

The proposal of erosion models to predict the jet footprint during abrasive waterjet machining is a key element for the development of this technology, but it is very challenging because of the inherent fluctuations of the process. This issue becomes critical when the size of the cutting systems is reduced, since the relative size of these deviations increases. The present paper considers for the first time a modelling framework capable of predicting the average shape of AWJM footprints and, of great novelty, the variability along the trench, combining finite element analysis and Monte Carlo methods, and verifying the model using different feed speeds and tilt angles. For that purpose, the relevance of each random parameter, such as shape (sharpness), size and relative orientation of the abrasive particles, has been investigated through parametric studies on these variables. Multiple particle simulations with randomly generated input were performed to determine the effect of operating parameters in the overall variability of the jet footprint. The process was simulated using Abaqus 6.14 as multiple garnet particles hitting a target of Ti–6Al–4V at very high velocity, eroding the target by plastic deformation and material removal. The model shows successfully the influence of single particle parameters, such as the shape, on the surface variability. The results for the footprint variability show that stochastic methods are suitable to model these fluctuations, and it is also shown that this approach yields accurate estimates of the average profile after multiple jet passes with error less than 5%.

Comparative study of rotational bands in theA≈60mass region: Modification of Nilsson parameters

The large number of high-spin bands that have been observed in A=56-62 nuclei are analyzed systematically within the cranked Nilsson-Strutinsky approach. Optimized Nilsson single-particle parameters are derived from investigations of energy differences between experimental and calculated rotational bands. Specifically, the relative energies of bands in neighboring nuclei whose configurations differ by having a high-j orbital either filled or empty are analyzed. The level schemes calculated with the new Nilsson parameters are compared with those using standard Nilsson parameters. Some configuration assignments are revised.

Discrete element simulations of granular pile formation

Purpose – The purpose of this paper is to examine several calibration techniques that have been developed to determine the discrete element method (DEM) parameters for slow and rapid unconfined flow of granular conical pile formation. This paper also aims to discuss some of the methods currently employed to scale particle properties to reduce computational resources and time to solve large DEM models.Design/methodology/approach – DEM models have been calibrated against simple bench‐scale experimental results to examine the validity of selected parameters for the contact, material and mechanical models to simulate the dynamic and static behaviour of cohesionless polyethylene pellets. Methods to determine quantifiable single particle parameters such as static friction and the coefficient of restitution have been highlighted. Numerical and experimental granular pile formation has been investigated using different slumping and pouring techniques to examine the dependency of the type of flow mechanism on the D...

Strongly Interacting Bosons in a Disordered Optical Lattice

We experimentally probe the properties of the disordered Bose-Hubbard model using an atomic Bose-Einstein condensate trapped in a 3D disordered optical lattice. Controllable disorder is introduced using a fine-grained optical speckle field with features comparable in size to the lattice spacing along every lattice direction. A precision measurement of the disordering potential is used to compute the single-particle parameters of the system. To constrain theories of the disordered Bose Hubbard model, we have measured the change in condensate fraction as a function of disorder strength for several different ratios of tunneling to interaction energy. We observe disorder-induced, reversible suppression of condensate fraction for superfluid and coexisting superfluid-Mott-insulator phases.

Correlated band structure of NiO, CoO, and MnO by variational cluster approximation

The variational cluster approximation proposed by Potthoff is applied to the calculation of the single-particle spectral function of the transition-metal oxides MnO, CoO, and NiO. Trial self-energies and the numerical value of the Luttinger-Ward functional are obtained by exact diagonalization of a ${\text{TMO}}_{6}$ cluster. The single-particle parameters of this cluster serve as variational parameters to construct a stationary point of the grand potential of the lattice system. The stationary point is found by a crossover procedure, which allows to go continuously from an array of disconnected clusters to the lattice system. The self-energy is found to contain irrelevant degrees of freedom, which have marginal impact on the grand potential and need to be excluded to obtain meaningful results. The obtained spectral functions are in good agreement with experimental data.

Benchmark on neutron capture extracted from(d,p)reactions

Direct neutron capture reactions play an important role in nuclear astrophysics and applied physics. Since for most unstable short-lived nuclei it is not possible to measure the $(n,\ensuremath{\gamma})$ cross sections, $(d,p)$ reactions have been used as an alternative indirect tool. We analyze simultaneously ${}^{48}\mathrm{Ca}(d,p){}^{49}\mathrm{Ca}$ reactions at deuteron energies of $2,13,19,$ and 56 MeV and the thermal $(n,\ensuremath{\gamma})$ reaction at 25 meV. We include results for the ground state and the first excited state of $^{49}\mathrm{Ca}$. From the low-energy $(d,p)$ reaction, the neutron asymptotic normalization coefficient (ANC) is determined. Using this ANC, we extract the spectroscopic factor (SF) from the higher energy $(d,p)$ data and the $(n,\ensuremath{\gamma})$ data. The SF obtained through the 56-MeV $(d,p)$ data are less accurate but consistent with those from the thermal capture. We show that to have a similar dependence on the single-particle parameters as in the $(n,\ensuremath{\gamma})$, the $(d,p)$ reaction should be measured at 30 MeV.

Clustering and other exotic phenomena in nuclei

Nuclei feature a rich variety of many-body phenomena. Especially the clustering of nucleons, which leads to molecule like structures, and halos formed by weakly bound nucleons are regarded as exotic phenomena that standard many-body methods like the shell model have difficulties to describe. On the other hand cluster models that build in such structures explicitly use very simplistic effective interactions and have often difficulties if shell model like configurations become important. In the Fermionic Molecular Dynamics approach we aim at a consistent description of well bound nuclei with shell structure as well as of nuclei featuring halos or clustering. We achieve this by exploiting the versatility of Gaussian wave packets. These are able to describe harmonic oscillator single-particle states and cluster states on the same footing. If we allow the width parameter to be a free variational parameter also halos can be described well in this basis. The many-body basis is given by Slater determinants of these wave packets. Different levels of sophistication can be achieved. In the simplest approach we perform a mean-field calculation by variation of the energy expectation value with respect to the single-particle parameters. The mean-field state might break the symmetries of the Hamiltonian which can be restored by explicit projection on parity, angular and linear momentum. In a more sophisticated approach we can perform the variation after projection. An approximate variation after projection can be done in the sense of the generator coordinate method where the intrinsic state is varied under constraints on generator coordinates like the radius or quadrupole deformation. Finally we can perform a multiconfiguration mixing calculation by diagonalizing the Hamiltonian in a set of projected many-body basis states. The same effective interaction is used for all nuclei. It is based on the VUCOM interaction derived from the realistic Argonne V18 interaction by explicitly including short-range central and tensor correlations within the Unitary Correlation Operator Method.

From cluster to solid: Variational cluster approximation applied toNiO

The variational cluster approximation is applied to the calculation of the single-particle spectral function of $\mathrm{NiO}$. Trial self-energies and the numerical value of the Luttinger-Ward functional are obtained by exact diagonalization of ${\mathrm{NiO}}_{6}$ clusters, and the single-particle parameters of the clusters serve as variational parameters to obtain a stationary point of the grand potential of the lattice system. Good agreement with experiment is obtained.

Are spectroscopic factors from transfer reactions consistent with asymptotic normalization coefficients?

It is extremely important to devise a reliable method to extract spectroscopic factors from transfer cross sections. We analyze the standard DWBA procedure and combine it with the asymptotic normalization coefficient, extracted from an independent data set. We find that the single particle parameters used in the past generate inconsistent asymptotic normalization coefficients. In order to obtain a consistent spectroscopic factor, nonstandard parameters for the single particle overlap functions can be used but, as a consequence, often reduced spectroscopic strengths emerge. Different choices of optical potentials and higher order effects in the reaction model are also studied. Our test cases consist of $^{14}\mathrm{C}$($d,p$)$^{15}\mathrm{C}$(g.s.) at ${E}_{d}^{\mathrm{lab}}=14$ MeV, $^{16}\mathrm{O}$($d,p$)$^{17}\mathrm{O}$(g.s.) at ${E}_{d}^{\mathrm{lab}}=15$ MeV and $^{40}\mathrm{Ca}$($d,p$)$^{41}\mathrm{Ca}$(g.s.) at ${E}_{d}^{\mathrm{lab}}=11$ MeV. We underline the importance of performing experiments specifically designed to extract asymptotic normalization coefficients for these systems.

Sensitivity of 8B breakup cross section to projectile structure in CDCC calculations

Given the astrophysical interest of 7Be(p, γ)8B, there have been several experiments applying the Coulomb dissociation method for extracting the capture rate. Measurements at Michigan State are dominated by E1 contributions but have a small E2 component. On the other hand, a lower energy measurement at Notre Dame has a much stronger E2 contribution. The expectation was that the two measurements would tie down the E2 and thus allow for an accurate extraction of the E1 relevant for the capture process. The aim of this paper is to show that the E2 factor in breakup reactions does not translate into a scaling of the E2 contribution in the corresponding capture reaction. We show that changes to the 8B single particle parameters, which are directly related to the E2 component in the capture reaction, do not affect the corresponding breakup reactions, using the present reaction theory.

Nuclear shell structure and rotational bands inNb86

The high spin structures in $^{86}\mathrm{Nb}$ are analyzed using the cranked Nilsson-Strutinsky model. Energy versus spin curves as well as deformations and electric transition quadrupole moments are considered. It is concluded that different single-particle parameters compared with the standard values lead to better agreement with recent experimental results.

Hard-sphere colloidal silica dispersions. The structure factor determined with SANS

Small-angle neutron-scattering experiments were performed on the D11 instrument at Grenoble. The colloidal dispersions in cyclohexane studied contained silica particles sterically stabilized by odadecyl chains terminally g-rafted to the surface. From dilute dispersions the mean particle radius and the radius distribution were obtained. With these single-particle parameters the scattering behavior can be modeled with a hard-sphere interaction potential at all volume fractions up to 4 = 0.4-0.5. Polydispersity effects on the representation of the structure factor were explicitly taken into account. These results confrm and amplify previous results on the modeling of a silica dispersion as a hard-sphere supramolecular fluid.

An interface dilation model for the prediction of wall friction in a particulate bed

In this paper, the normal and shear stress levels detected by a transducer at the wall of a silo have been compared with predictions derived from the study of single particle wall friction. A simple model is developed which is based on the summation of the estimated individual particle-wall stress contributions over the transducer surface. This analysis is capable of not only predicting the magnitude of the coefficient of wall friction sensed by the transducer but also its variation with position and state of flow. The model includes many single-particle parameters, notable of which are the mean particle size, modulus of elasticity and surface roughness and, in addition, certain fundamental and accessible friction parameters. Furthermore, it contains a less accessible but realistic description of bed dilatancy.

Electron correlations in polyacetylene.

The influence of electronic correlations on structural and electronic properties of polyacetylene is studied by adding a Hubbard term (on-site Coulomb coupling U) to the Su-Schrieffer-Heeger Hamiltonian. We use the Gutzwiller wave function as an ansatz for the electronic ground state. For weak electron-phonon coupling (\ensuremath{\lambda}\ensuremath{\ll}1) and U/(4${t}_{0}$)\ensuremath{\ll}1 (where 4${t}_{0}$ is the \ensuremath{\pi} bandwidth) we obtain analytical results for the ground-state energy, the amplitude of bond alternation, the effective force constant for the bond-stretching mode, and a mean-field gap parameter \ensuremath{\Delta}. For intermediate couplings the energy is minimalized numerically. Our results are applicable for U/(4${t}_{0}$)\ensuremath{\lesssim}1 where they agree surprisingly well with the Monte Carlo calculations of Hirsch. We find strong indications that everywhere in this region the ground state is dimerized if \ensuremath{\lambda}>0. For larger U we expect a smooth crossover to the spin-Peierls phase. For \ensuremath{\lambda}<0.37 the Hubbard term initially enhances bond alternation and the dimerization amplitude exhibits a maximum at a finite value of U. For larger values of \ensuremath{\lambda} the maximum occurs at U=0 and electronic correlations decrease bond alternation. Using single-particle parameters as deduced from properties of small organic molecules we compare our results with empirical data on polyacetylene. Our analysis consistently reproduces the measured properties if U is chosen between 7 and 9 eV.

Calculation of Gamow-Teller β-strength functions in the rubidium region in the RPA approximation with Nilsson-model wave functions

We calculate allowed Gamow-Teller and, in a few cases, Fermi β-strength functions in a model that is applicable to studies of nuclei throughout the periodic system. For our first study we have selected a sequence of rubidium isotopes, namely 37 89Rb- 37 99Rb. We develop a model that uses calculated Nilsson-model wave functions, spherical or deformed, as the case may be, as the starting point for determining the wave functions of the mother and daughter nuclei in the β-decay. Pairing is treated in the BCS approximation. To account for the retardation of low-energy GT decay rates we add, as is customarily done, a simple residual interaction specific to GT decay, namely V GT = : β 1− β 1+:, to the hamiltonian. This residual interaction is treated in the RPA approximation. The strength of the interaction is adjusted to get agreement between the calculated and experimental energy of the giant Gamow-Teller resonance for 208Pb and 144Sm. Since the present model is based on calculated wave functions and single-particle levels, studies of nuclei far from stability, where little experimental information is available, are more straightforward relative to calculations where “experimental” levels are used. The model can treat deformed nuclei employing wave functions calculated to desired accuracy, within the framework of the model, for the deformed single-particle well. The calculations show that use of single-particle parameters appropriate to the region studied and taking deformation into account is important. We find good agreement between calculated and experimental spectra over the region studied, provided an appropriate choice of single-particle parameters and deformation is made.

Fluid-dynamical representations of the Dirac equation

A relative kinetic mass operator is defined bym =c −2·(E −eΦ), and it is shown that bt using it in a symmetric form one can correlate the (charge) velocity operatorα in the Dirac theory exactly with the general quantum mechanical momentum —ih∇. Then the net force, defined as the rate of change of the relative momentum with time, is exactly equal to the Lorentz force. The contribution due to the time variation of mass equals the negative of space variation of the scalar potential, the Newtonian force, whereas the time variation of the charge current absorbs the entire vector potential dependence. The analogous Euler equations can be written either in terms of the charge current or in terms of the mass current. For a many particle system one needs the usual net single particle parameters and the consideration of both the direct and exchange contributions of the two particle interaction. These Euler equations yield two different conditions of the stationary state. It is shown that the charge-current condition is necessary but not sufficient, whereas the mass-current condition retains the appropriate scalar potential dependence. These two conditions are compared for the spherically symmetric case. The charge density, charge current and relative mass current are tabulated for atomic spinors. Differences between the quantum and classical forces for the H 2 + molecular ion exhibit the inadequacy of ordinary atomic spinor basis in forming molecular spinors.

An investigation of the scaled modified oscillator potential

In the second volume of their book Nuclear structure, Bohr and Mottelson propose that in the modified oscillator potential the spin-orbit term and the l 2 term should be scaled according to the deformation of the potential. This scaling has been studied in detail, and some of its more general consequences are discussed. The single-particle parameters κ and μ have been fitted for nuclei in the rare earth region, for lead and for actinides. The scaled potential has been used for a detailed investigation of the nuclei in the actinide region, including calculations of potential energy surfaces, fission barriers and ground-state masses. Both symmetric and reflection asymmetric deformations have been considered and the results thus obtained with the scaled potential have been compared to those obtained with the modified oscillator potential and the folded-Yukawa potential.

Inelastic Electron Scattering from Even Tin Isotopes and Microscopic Theories of Vibrational States

Two- and four-quasiparticle microscopic theories are applied to fit the most recent data on the reactions ${\mathrm{Sn}}^{116}(e, {e}^{\ensuremath{'}}){\mathrm{Sn}}^{116}({{2}_{1}}^{+}, {{3}_{1}}^{\ensuremath{-}})$. The effective nuclear force is the realistic nucleon-nucleon potential of Tabakin renormalized by the core-polarization corrections. The observed angular distributions and the absolute values of the form factors can be reproduced for quite reasonable values of the single-particle parameters.