Hard-core Repulsive Potential Research Articles

Wavefunction exchange and entanglement in one-dimensional collisions

We show that when two quantum-mechanical particles of the same mass, interacting through a hard-core repulsive potential, collide in one dimension, they exchange their wavefunctions, making them look as if they had passed through each other. We give a simple explanation of this phenomenon, and compare to its classical analog, which can be demonstrated using the “Newton's cradle” toy. We also consider briefly what happens when the masses are unequal, showing how entanglement arises in this case.

Multiscale Filler Structure in Simplified Industrial Nanocomposite Silica/SBR Systems Studied by SAXS and TEM

Simplified silica (Zeosil 1165 MP) and SBR (140k carrying silanol end-groups) nanocomposites have been formulated by mixing of a reduced number of ingredients with respect to industrial applications. The thermo-mechanical history of the samples during the mixing process was monitored and adjusted to identical final temperatures. The filler structure on large scales up to micrometers was studied by transmission electron microscopy (TEM) and very small-angle X-ray scattering (SAXS). A complete quantitative model extending from the primary silica nanoparticle (of radius \approx 10 nm), to nanoparticles aggregates, up to micrometer-sized branches with typical lateral dimension of 150 nm is proposed. Image analysis of the TEM-pictures yields the fraction of zones of pure polymer, which extend between the branches of a large-scale filler network. This network is compatible with a fractal of average dimension 2.4 as measured by scattering. On smaller length scales, inside the branches, small silica aggregates are present. Their average radius has been deduced from a Kratky analysis, and it ranges between 35 and 40 nm for all silica fractions investigated here (\phi_si = 8-21% vol.). A central piece of our analysis is the description of the interaggregate interaction by a simulated structure factor for polydisperse spheres representing aggregates. A polydispersity of 30% in aggregate size is assumed, and interactions between these aggregates are described with a hard core repulsive potential. The same distribution in size is used to evaluate the polydisperse form factor. Comparison with the experimental intensity leads to the determination of the average aggregate compacity (assumed identical for all aggregates in the distribution, between 31% and 38% depending on \phi_si), and thus aggregation number (ca. 45, with a large spread). Because of the effect of aggregate compacity and of pure polymer zones, the volume fraction of aggregates is higher in the branches than \phi_si. The repulsion between aggregates has a strong effect on the apparent isothermal compressibility: it leads to a characteristic low-q depression, which cannot be interpreted as aggregate mass decrease in our data. In addition, the reinforcement effect of these silica structures in the SBR-matrix is characterized with oscillatory shear and described with a model based on the same aggregate compacity. Finally, our results show that it is possible to analyze the complex structure of interacting aggregates in nanocomposites of industrial origin in a self-consistent and quantitative manner.

Positron binding to atoms and apolar molecules: A convergence of theory and experiment

The problem of the bound states of a positron with atoms and apolar molecules is studied with a regularized polarization potential $V={V}_{{r}_{c}}\ensuremath{-}\frac{\ensuremath{\alpha}{r}^{\ensuremath{-}4}}{2}$, where ${V}_{{r}_{c}}$ is a repulsive hard-core potential. A continuous relation between the core radius and the target polarizability is identified for alkanes, leading to the observed linear relation between their experimental binding energies and polarizabilities. New values for the binding energies for I and Pt atoms are suggested. Some predictions for related molecules are made, suggesting positron binding to GeH${}_{4}$ and, possibly, to C${}_{2}$F${}_{6}$.

Ground state of interacting quantum magnetic dipoles: Transition from a ferromagnetic Fermi liquid to an antiferromagnetic solid

We show that the ground state of a system of magnetic dipoles, with no electric charge, is a ferromagnetic quantum Fermi liquid at high densities, driven by the dipolar exchange energy. As in the system of classical point dipoles, the direct dipole energy is zero in this case. With decreasing density, there is a transition to an antiferromagnetic lattice state. An addition of short range hard core repulsive potential will arrest the infinite density collapse of the ferromagnetic state, and possible melting of the low density antiferromagnetic lattice state.

N identical particles under quantum confinement: a many-body dimensional perturbation theory approach

Systems that involve N identical interacting particles under quantum confinement appear throughout many areas of physics, including chemical, condensed matter, and atomic physics. In this paper, we present the methods of dimensional perturbation theory, a powerful set of tools that uses symmetry to yield simple results for studying such many-body systems. We present a detailed discussion of the dimensional continuation of the N-particle Schrödinger equation, the spatial dimension D→∞ equilibrium ( D 0) structure, and the normal-mode ( D −1) structure. We use the FG matrix method to derive general, analytical expressions for the many-body normal-mode vibrational frequencies, and we give specific analytical results for three confined N-body quantum systems: the N-electron atom, N-electron quantum dot, and N-atom inhomogeneous Bose–Einstein condensate with a repulsive hard-core potential.

Strongly interacting Luttinger liquid and superconductivity in an exactly solvable model

A new family of exactly solvable one dimensional models with a hard-core repulsive potential is solved by the Bethe Ansatz for an arbitrary hard-core radius. The exact ground state phase diagrams in a plane 'electron density - on-site interaction' have been studied for several values of a hard-core radius. It is shown that superconducting phase and strongly interacting Luttinger liquid state are coexisted at a high electron density and unusually high value of repulsive on-site Coulomb interaction.

Distribution of instanton sizes in a simplified instanton gas model

We investigate the distribution of instanton sizes in the framework of a simplified model for ensembles of instantons. This model takes into account the non-diluteness of instantons. The infrared problem for the integration over instanton sizes is dealt with in a self-consistent manner by approximating instanton interactions by a repulsive hard core potential. This leads to a dynamical suppression of large instantons. The characteristic features of the instanton size distribution are studied by means of analytic and Monte Carlo methods. In one dimension exact results can be derived. In any dimension we find a power law behaviour for small sizes, consistent with the semiclassical results. At large instanton sizes the distribution decays exponentially. The results are compared with those from lattice simulations.

Dynamical suppression of large instantons

We investigate the distribution of instanton sizes in the framework of a simplified model for ensembles of instantons. This model takes into account the non-diluteness of instantons. The infrared problem for the integration over instanton sizes is dealt with in a self-consistent manner by approximating instanton interactions by a repulsive hard core potential. This leads to a dynamical suppression of large instantons. The characteristic features of the instanton size distribution are studied by means of analytic and Monte Carlo methods. We find a power law behaviour for small sizes, consistent with the semi-classical results. At large instanton sizes the distribution decays exponentially. The results are compared with those from lattice simulations.

Model boson fluid with disorder in the self-consistent field approximation

We study the ground-state properties of a model neutral boson fluid in the presence of disorder effects. The effective interaction between the bosons is obtained through the self-consistent field method which renormalizes the bare interaction consisting of a hard-core repulsive potential with an attractive tail at zero temperature. We introduce disorder effects within a number-conserving approximation by modifying the density–density response function. Our results for the static structure factor and the collective mode dispersion reflect the effect of disorder in qualitative agreement with other calculational approaches.

Strongly interacting Luttinger-liquid state in the integrable model of spinless fermions

A family of spinless fermion models with a hard core potential is formulated and solved by the Bethe ansatz method in one dimension for an arbitrary core radius. The Hamiltonian has two levels of strong interaction: the repulsive hard core potential and the kinetic energy with hopping integrals, values of which depend on the configuration of the particles. The Fermi velocity and the critical exponents describing the asymptotic behavior of the correlation functions at long distances have been calculated numerically for an arbitrary density of electrons and hard core radius. We discuss the effect of the hard core potential. The hard core potential defines an anomalous behavior of the critical exponent \ensuremath{\Theta} of the momentum distribution function. In the high-electron-density region the long-distance behavior is described by a strongly interacting Luttinger-liquid state with \ensuremath{\Theta}>1 and the residual Fermi surface disappears.

Structure of a model one-dimensional liquid 3He– 4He mixture

We study the ground state properties of a one-dimensional liquid 3He– 4He mixture interacting via a hard-core repulsive potential at zero temperature. We use the self-consistent field approach to calculate the ground state partial structure factors, the effective interactions between the species, and collective modes. Our results are in qualitative agreement with more sophisticated approaches.

Distribution of instanton sizes in a simplified instanton gas model

We investigate the distribution of instanton sizes in the framework of a simplified model for ensembles of instantons. This model takes into account the non-diluteness of instantons. The infrared problem for the integration over instanton sizes is dealt with in a self-consistent manner by approximating instanton interactions by a repulsive hard core potential. This leads to a dynamical suppression of large instantons. The characteristic features of the instanton size distribution are studied by means of analytic and Monte Carlo methods. In one dimension exact results can be derived. In any dimension we find a power law behaviour for small sizes, consistent with the semi-classical results. At large instanton sizes the distribution decays exponentially. The results are compared with those from lattice simulations.

Model boson-fermion mixture within the self-consistent-field approximation

We study the ground state properties of a boson-fermion mixture interacting via a hard-core repulsive potential with an attractive tail at zero temperature. We use the self-consistent field approach to calculate the ground state partial structure factors and the effective interactions between the species. We compare our results with the experimental data on liquid ${}^{3}\mathrm{He}{\ensuremath{-}}^{4}\mathrm{He}$ mixtures to find qualitative agreement. Collective modes and dynamic structure factors for the mixture are also discussed.

TWO COMPONENT ANYON SUPERFLUID WITH COMPLEMENTARY STATISTICS: A MODEL WITH SUPPRESSED PARITY VIOLATION

We analyze an anyon superfluid of the standard kind. The model is composed of equal number density of two types of anyons carrying complementary statistics and interacting via a repulsive hard-core potential. This system shows a suppression of parity violation. The analysis is carried out in the limit of quasi-bosonic statistics, where we show that the interactions induced by the statistics tend to suppress the condensate. We argue that a phase transition occurs as the hard-core interaction becomes sufficiently weak and give an estimate of the critical coupling.

Molecular statistical model for ferroelectric - antiferroelectric transition in chiral smectic liqitid crystals

Abstract We discuss ferroelectric-antiferroelectric transition in chiral smectic liquid crystmais with molecular theorp. The pair interaction between model molecules consist's of repulsive hard core potential aid short range attractive force. We take a distinction of the head and tail of the molecule into consideration as an asymmery of the short range attractive part of the pair interaction. Using this model, we show that the head-tail asymmetry contributes to the stability of the ferrielectric phase.

On the spectral problem for anyons

We consider the spectral problem resulting from the Schrodinger equation for a quantum system ofn≧2 indistinguishable, spinless, hard-core particles on a domain in two dimensional Euclidian space. For particles obeying fractional statistics, and interacting via a repulsive hard core potential, we provide a rigorous framework for analysing the spectral problem with its multi-valued wave functions.

Model of a two-dimensional Fermi liquid

In this paper we use a self-consistent scheme proposed by Singwi, Tosi, Land, and Sjolander to study a two-dimensional Fermi liquid whose particles interact via a repulsive hard-core potential with or without an attractive tail. We determine the Landau parameters F 0 s and F 0 a , the static structure factors, and we discuss the effect of adding the attractive tail to the hard-core potential

Computer simulation of depolarized light scattering from diatoms with hard core and square well interactions at low temperatures

We show that the depolarized light scattered from two interacting atoms is qualitatively different for a purely repulsive hard core potential and partially attractive square well potential. This difference is due to the bound states possible with attractive potentials and is used to obtain the spectra from these dimers. The spectra were calculated from the autocorrelation of the scattered electric field found by an effective field model. Values were phase space averaged using Gaussian integration. Molecular dynamics routines evolved the phase space points in time for the autocorrelation. The hard core spectra showed an exponential decay characterized by the mean passage time. The square well spectra consisted of a hard core-type term, plus a harmonic component due to dimer contributions. Subtraction of the hard core spectra from the square well spectra gave the dimer component. The dimer component of the spectra was proportional to the square of the number of dimers and was characterized by the thermal rotational energy for temperatures below the saturation temperature.

Model Fermi liquid interacting via a hard-core repulsive potential and an attractive tail.

In this paper we present an extensive microscopic study of the collective and single-particle properties of a model Fermi liquid whose particles interact via a repulsive hard-core potential and an attractive tail. The model system is intended to simulate liquid $^{3}\mathrm{He}$. The study is based on an approximate theoretical scheme of Singwi, Tosi, Land, and Sj\"olander, which was devised to treat correlations in Coulomb Fermi liquids. The primary aim of this study is to learn how far the model system is capable of reproducing some of the salient features observed in normal liquid $^{3}\mathrm{He}$, and about the role of the repulsive and attractive parts of the bare potential in the determination of the properties of $^{3}\mathrm{He}$. We have calculated the Landau parameters ${F}_{0}^{s}$ and ${F}_{0}^{a}$ and their variation with pressure, the wave-number and pressure dependence of the spin-symmetric and spin-antisymmetric polarization potentials, pressure dependence of the dispersion of the zero sound, the static structure factors, and the quasiparticle mass. It is our belief that this study has provided us with some physical insight into the nature of liquid $^{3}\mathrm{He}$ although much remains to be done for its quantitative understanding.

Note on a Simple Model of the Columnar Phase of Disc-Like Molecular Liquid Crystals

In recent times it is known that some of disc­ like molecules exhibit a rich polymorphism of their mesophases similar to that of the liquid crystalline phases of rod-like molecules; among other meso phases the columnar phase, in which molecules form a columnar or tubular arrangement, is characteristic of the disc-like molecular liquid crystals. To date several kinds of the disc-like molecular liquid crystals exhibiting the columnar phase have been synthesized and their properties and phase transitions have been studied. It is reported that the crystalline phase changes into the columnar phase and the columnar phase is followed by the nematic or the isotropic phase as the temperature increases and in the columnar phase the columns always form a two-dimensional array, hexagonal or rectangular lattice but in each column the molecules are irregularly stacked.!) Since the polymorphism of the meso phases of the liquid crystals is attributable to the peculiar shapes of the molecules, it is of interest to study what type of the interaction potential between a pair of molecules makes the columnar phase possible. The phase transition of disc-like molecules has been theoretically studied by several authors. Katz has discussed the problem in the framework of the Landau theory.) A molecular mean field theory of the phase transition has been developed by extending McMillan's model) of smectic A;4) there the intermolecular potential was assumed to be the same one as was adopted by McMillan for the study about the smectic A-nematic­ isotropic transition of rod-like molecules. An approach by means of the cluster expansion technique has also been done for systems of molecules with a repulsive hard core potential;5) in the third virial approximation, it was shown that the columnar phase can exist. In this paper we study the phase transitions of the disc-like molecular liquid crystals by using a model potential of the Lennard-Jones type, where we adopt the lattice gas model and the Bragg­ Williams approximation treatment to calculate the partition function. Let us assume that nA atoms constitute a molecule which has a rigid structure and each atom belonging to one molecule is under the influence of potential energy of the Lennard-Jones type produced by every atom belonging to a neighbouring molecule and total of these interaction potential energy amounts to the interaction energy between the two molecules under consideration_ 6 ) The interaction potential energy is then given by