Arbitrary Interparticle Interaction Research Articles

On the ground state energy of the inhomogeneous Bose gas

Within the self-consistent Hartree–Fock approximation, an explicit in this approximation expression for the ground state energy of inhomogeneous Bose gas is derived as a functional of the inhomogeneous density of the Bose–Einstein condensate. The results obtained are based on existence of the off-diagonal long-range order in the single-particle density matrix for systems with a Bose–Einstein condensate. This makes it possible to avoid the use of anomalous averages. The explicit form of the kinetic energy, which differs from one in the Gross–Pitaevski approach, is found. The obtained form of kinetic energy is valid beyond the Hartree–Fock approximation and can be applied for arbitrary strong interparticle interaction.

Approaching the s-wave model ground state energy of He-like atomic ions: results from a model Hamiltonian

Amovilli, Howard and March model Hamiltonian is here extended to an arbitrary interparticle interaction strength. The model remains analytically solvable and the ground state wavefunction with a given, variationally determined, choice of parameters provides an approximate two-electron correlated s-wave function. Results are given for the series of nuclear charges between $$Z=1$$ and 10. More than 60 % of s-wave correlation energy is recovered.

The two-dimensional three-body problem in the large magnetic field limit is integrable

The problem of N particles interacting through pairwise central forces is notoriously intractable for N≥3. Some remarkable specific cases have been solved in one dimension. Here we show that the guiding center approximation—valid for charges moving in two dimensions in the limit of large constant magnetic fields—simplifies the three-body problem for an arbitrary interparticle interaction invariant under rotations and translations, making it solvable by quadratures. A spinorial representation for the system is introduced, which allows a visualization of its phase space as the corresponding Bloch sphere. Finally, a discussion of the quantization of the problem is presented.

Theory of electromagnetically induced transparency in strongly correlated quantum gases

We develop a general theory to study the electromagnetically induced transparency (EIT) in ultracold quantum gases, applicable for both Bose and Fermi gases with arbitrary inter-particle interaction strength. We show that, in the weak probe field limit, the EIT spectrum is solely determined by the single particle Green's function of the ground state atoms, and reflects interesting quantum many-body effects when atoms are virtually coupled to the low-lying Rydberg states. As an example, we apply our theory to 1D Luttinger liquid, Bose-Mott insulator state, and the superfluid state of two-component Fermi gases, and show how the many-body features can be observed non-destructively in the unconventional EIT spectrum.

Correlated kinetic energy density functional of ground states of harmonically confined two-electron atoms for arbitrary interparticle interaction

Utilizing the earlier work of Holas et al (2003 Phys. Lett. A 310 451) and the more recent contribution of Akbari et al (2009 Phys. Rev. A 80 032509), we construct an integral equation for the relative motion (RM) contribution tRM(r) to the correlated kinetic energy density for modelling two-electron atoms with harmonic confinement but arbitrary interparticle interaction. It is stressed that tRM = tRM[f(G)], where f(G) is the atomic scattering factor: the Fourier transform of the density ρ(r). As a simple illustrative example of this functional relation for the correlated kinetic energy density, the harmonic Moshinsky case is investigated, the scattering factor then having a Gaussian form.

Multiplication of high-energy electrons in irradiated materials studied using the Boltzmann kinetic equation

Processes involved in the formation of electron collision cascades created by nonrelativistic high-energy electrons, which can develop in materials exposed to electron and gamma radiation fluxes, have been considered. The problem is solved using the Boltzmann kinetic equation for high-energy electrons moving in a medium. A model scattering indicatrix is constructed for this equation with an arbitrary potential of interaction between colliding particles. Using this scattering indicatrix, the distribution of the particle energies is obtained. Based on this energy distribution (with an arbitrary interparticle interaction potential), a cascade function is found that describes the multiplication of knock-out electrons (electron cascade) generated when a high-energy electron with a certain energy is scattered on the electron subsystem of the irradiated material. The cascade function has been calculated for the Coulomb potential of the interaction between a high-energy electron and atomic-shell electrons.

Dynamical generalization of a solvable family of two-electron model atoms with general interparticle repulsion

Holas, Howard and March (2003 Phys. Lett. A 310 451) have obtained analytic solutions for ground-state properties of a whole family of two-electron spin-compensated harmonically confined model atoms whose different members are characterized by a specific interparticle potential energy u(r12). Here, we make a start on the dynamic generalization of the harmonic external potential, the motivation being the serious criticism levelled recently against the foundations of time-dependent density-functional theory (e.g., Schirmer and Dreuw 2007 Phys. Rev. A 75 022513). In this context, we derive a simplified expression for the time-dependent electron density for arbitrary interparticle interaction, which is fully determined by a one-dimensional non-interacting Hamiltonian. Moreover, a closed solution for the momentum space density in the Moshinsky model is obtained.

Exact correlated kinetic energy related to the electron density for two-electron model atoms with harmonic confinement

Abstract For arbitrary interparticle interaction u ( r 12 ) , the model two-electron atom in the title is shown to be such that the ground-state electron density ρ ( r ) is determined uniquely by the correlated kinetic energy density t R ( r ) of the relative motion. Explicit results for t R ( r ) are presented for the Hookean atom with force constant k = 1 / 4 , and also for u ( r 12 ) = λ r 12 2 . Possible relevance of the Hookean atom treatment to the ground state of the helium atom itself is briefly discussed.

Simulation of the growth of nanoparticle aggregates reproducing their natural structure in disperse systems

A three-dimensional continuum model of the generation of aggregates of spherical particles is developed that allows us to reproduce natural conditions of structure formation in real disperse systems with an arbitrary viscosity of a dispersion medium. The exchange between translational and rotational degrees of freedom for aggregates, subaggregates, and single particles at an arbitrary interparticle interaction potential, as well as at the preset functions of the distribution over particle sizes and thicknesses of the adsorption layer, is taken into account in the model. The interaction potential of the particles includes electrostatic (among them, screened), elastic, and van der Waals interactions and allows for the effect of external electric, magnetic, and gravitational fields. Structural and statistical characteristics of aggregates formed at different stages of particle coagulation are studied, and the quasi-ordering of single subaggregates in the elastic adsorption layer of particles is revealed. The model can be applied to the study of optical absorption by large aggregates of nanoparticles with natural structure and the kinetics of sol aggregation as functions of the properties of the adsorption layer of particles and the action of external physical factors.

Interacting inhomogeneous electron liquids with harmonic confinement: s-wave model

In an earlier work by Holas et al. [A. Holas, I.A. Howard, N.H. March. Phys. Lett. A, 310, 451 (2003)], the ground-state electron density ρ( r ) for model two-electron spin-compensated atoms was obtained in terms of the relative motion wave function for the case of harmonic confinement and arbitrary interparticle interaction u(r 12). Following recent interest in the s-wave approximation to ρ( r ) for Coulombic potential energy at separation r 12 between the electrons, we here consider both harmonic interaction u(r 12) proportional to and also the inverse square law . The interplay between correlation and confinement clearly emerges in such spin-compensated models of interacting inhomogeneous electron liquids.

Numerical calculation of the energy barrier distribution in disordered many-particle systems: the path integral method

We present a numerical method for the evaluation of the distribution of energy barriers between metastable states in many-particle systems with arbitrary interparticle interaction. The method is based on the search for the optimal path between the two given metastable states using the minimization of the corresponding action occurring in the Onsager–Machlup functional for the transition probability between these two states. Test results for a non-interacting system of magnetic particles and for a dipolar magnetic glass are reported.

Calculation of the energy barriers in strongly interacting many-particle systems

A numerical method which allows the evaluation of the energy barrier height between any two metastable states in a many-particle system with continuous degrees of freedom and arbitrary interparticle interaction is presented. The method uses the minimization of the Onsager–Machlup action corresponding to the given path between the two states. The path which minimizes this action is supposed to be the optimal path between the states under consideration and the height of the energy barrier separating these states is determined as the energy barrier along this optimal path. Test results for a simple two-dimensional potential (where the optimal path can easily be visualized) and for a dipolar glass are presented.

Quantum Lattice-Gas Models for the Many-Body Schrödinger Equation

A general class of discrete unitary models are described whose behavior in the continuum limit corresponds to a many-body Schrödinger equation. On a quantum computer, these models could be used to simulate quantum many-body systems with an exponential speedup over analogous simulations on classical computers. On a classical computer, these models give an explicitly unitary and local prescription for discretizing the Schrödinger equation. It is shown that models of this type can be constructed for an arbitrary number of particles moving in an arbitrary number of dimensions with an arbitrary interparticle interaction.

The exact statistical thermodynamics of classical fluids

A scheme which may be considered ‘‘efficient’’ has been evolved for the ‘‘exact’’ determination of the free energy of classical fluids with arbitrary interparticle many-body interaction potentials. The judgment as to the extent of closeness of this scheme to an ‘‘ultimate’’ approach (which up until now has been sought by researchers for the investigation of equilibrium properties of fluids) is one presently expected to be subjective. The versatility of the ‘‘recipe,’’ however, is one that may be considered quite remarkable; and its ‘‘natural flavor’’ seems to suggest the approach is one that is forced upon us rather than the approach being a tool that has been artifically fashioned and forced by us into the problem. Application of the scheme to a few simple realistic fluid models has proved quite successful. However, more elaborate applications are expected in the future to provide an ultimate test of the suitability of the scheme.

Nonlocal exchange energy of many-fermion systems of arbitrary dimensionality and interparticle interaction.

Nonlocal exchange energy of many-fermion systems of arbitrary dimensionality and interparticle interaction.

Exchange contribution to the surface energy of an arbitrary fermion system within the infinite barrier model

The surface energy of a many electron system within the infinite barrier model has produced a considerable amount of interest. These studies have provided solutions for the exchange and correlation (within the RPA) surface energies with which approximate treatments of more realistic surfaces have been compared. In this note we present the first generalization, within this model, of the exchange contribution to the surface energy for a general Fermion system of arbitrary interparticle interaction. Such results should be useful for testing approximate methods for a much wider range of Fermion systems.

Self-consistent Hartree-Fock calculation of exchange effects in a weakly inhomogeneous electron gas

An exact calculation is given for the function B x ( n) which enters the Hohenberg-Kohn-Sham expansion, in powers of ▿n( r) , of the echange energy of an inhomogeneous eletron gas. The calculation is made for arbitrary inter-particle interaction. It is shown that the gradient expansion does not exist, in the case of Coulomb interaction, unless correlations are taken into account.