Two-particle Model Research Articles

One-dimensional ordering of ultra-low-density ion beams in a storage ring.

The two-particle model, first introduced by Hasse, is employed to predict the beam temperature at which a one-dimensional ordered state of ions will be established in a cooler storage ring. The proposed state does not have the ions (in the beam frame) at rest, but simply has them not passing each other; i.e., remaining in the same (ordered) sequence. The model is applicable to an ultra-low-density beam where collective Coulomb interactions are negligible. It is pointed out that the nature of the anomalous beam behavior observed in electron-cooling experiments at GSI (Darmstadt) and MSL (Stockholm) is approximately free from such parameters as the lattice design, ion species, beam density, and energy. On the basis of the model, which is put in Hamiltonian form, scaled, and numerically studied, a universal criterion of one-dimensional beam ordering at low line density is derived. Analytic work is employed to explain the numerical results and derives an approximate criterion.

Detection of spatial correlations in an ultracold gas of fermions.

Spatial correlations are observed in an ultracold gas of fermionic atoms close to a Feshbach resonance. The correlations are detected by inducing spin-changing rf transitions between pairs of atoms. We observe the process in the strongly interacting regime for attractive as well as for repulsive atom-atom interactions and both in the regime of high and low quantum degeneracy. The observations are compared with a two-particle model that provides theoretical predictions for the measured rf transition rates.

Decoherence in a two-particle model

We consider a simple one-dimensional quantum system consisting of a heavy and a light particle interacting via a point interaction. The initial state is chosen to be a product state, with the heavy particle described by a coherent superposition of two spatially separated wave packets with opposite momentum and the light particle localized in the region between the two wave packets. We characterize the asymptotic dynamics of the system in the limit of small mass ratio, with an explicit control of the error. We derive the corresponding reduced density matrix for the heavy particle and explicitly compute the (partial) decoherence effect for the heavy particle induced by the presence of the light one for a particular set up of the parameters.

Two-body correlations in halo nuclei and effective interactions

Light nuclei with two particles (neutron or proton) or two holes outside a core have been studied in a two-particle RPA model with the Gogny and a zero range density dependent effective interactions. It has been shown that the model is able to consistently describe 6He, 14C, 12Be and 11Li. The case of 12Be, described either as a 10Be-core plus two neutrons or as the core of 14Be, has been discussed in more details and a quasi boson expansion of the ground state wave function has been performed. To get consistent results in the two schemes one has suggested the same inversion of 2s and 1 p 1 2 shells in the n+ 12Be average potential as known in the n+ 10Be one. In the same model, a T=0 neutron-proton zero range effective interaction has been proposed to describe the 1 +, T=0 states in 14N and discussed in 10B.

The transient processes in multi-pulse nitrogen-14 NQR

It has been demonstrated that transient processes, observed in a single crystal of NaNO 2 acted upon by pulse sequences MW-2 and MW-4 and their modifications with 180° flip angle of the pulses (Solid State Nucl. Magn. Resonance 10 (1997) 63; Sov. Phys.—JETP 88(5) (1999) 1580), which manifest themselves in the oscillating form of the NQR signals envelope, can be explained in the frames of a two-particle model. It has been proved that the nature of echo signals in the effective field of multi-pulse sequences received by the inversion of the phase of the sequence pulses or by introducing an additional 180° pulse is connected with re-focusing of accumulated digressions of the flip angle from the ideal 180° pulse. Experimental results of observing single and multiple echoes in a number of powdered nitrogenated substances in the effective field of various sequences at room temperature have been presented.

Two-particle quasi-neutral kinetic model of collisionless solar wind

We present a kinetic model of the stationary solar wind based on the equation for two-particle (electron–proton) velocity distribution. The influence of collisions and the magnetic field is neglected. The approximation of the quasi-neutral plasma is applied to close the model, which results in excluding a Coulomb potential of plasma polarization field from consideration. The kinetic equation is solved using the method of characteristics. Solar wind density and speed are evaluated by integrating the two-particle distribution function over its domain of definition formed by related characteristics. The obtained dependences of the density and velocity on heliocentric distance agree with observational data of the in-ecliptic slow solar wind.

A computationally efficient particle-puff model for concentration variance from steady releases

This paper presents a computationally efficient particle-puff model that can be used to calculate both average concentration and concentration variance in turbulent flows. The model is self-contained in the sense that it does not need externally supplied parameterizations of puff spread, but rather calculates the spread with an internally-built module for relative dispersion of particles—all existing particle-puff models rely on parameterizations of puff spread derived from theoretical considerations and observational data for dispersion of a point source in isotropic turbulence. Preliminary evaluations show that the model performs as well as a computationally demanding two-particle trajectory model in predicting the mean concentration and concentration variance in two different flows: isotropic turbulence and a wind tunnel boundary layer. Because of its numerical efficiency, the present particle-puff model can be built into conventional, regulatory air quality models as a module to calculate the mean concentration and concentration variance in the near field. The reason for the numerical efficiency of present particle-puff model is that it needs to track only thousands of particle-pairs in order to calculate the puff spread, while (the original) two-particle Lagrangian stochastic (LS) models need millions of particle-pairs to achieve statistically stable predictions.

Short-lived two-soliton bound states in weakly perturbed nonlinear Schrodinger equation.

Resonant soliton collisions in the weakly discrete nonlinear Schrodinger equation are studied numerically. The fractal nature of the soliton scattering, described in our previous works, is investigated in detail. We demonstrate that the fractal scattering pattern is related to the existence of the short-lived two-soliton bound states. The bound state can be regarded as a two-soliton quasiparticle of a new type, different from the breather. We establish that the probability P of a bound state with the lifetime L follows the law P approximately L(-3). In the frame of a simple two-particle model, we derive the nonlinear map, which generates the fractal pattern similar to that observed in the numerical study of soliton collisions. (c) 2002 American Institute of Physics.

Critical and tricritical hard objects on bicolourable random lattices: exact solutions

We address the general problem of hard objects on random lattices, and emphasize the crucial role played by the colourability of the lattices to ensure the existence of a crystallization transition. We first solve explicitly the naive (colourless) random-lattice version of the hard-square model and find that the only matter critical point is the non-unitary Lee–Yang edge singularity. We then show how to restore the crystallization transition of the hard-square model by considering the same model on bicoloured random lattices. Solving this model exactly, we show moreover that the crystallization transition point lies in the universality class of the Ising model coupled to 2D quantum gravity. We finally extend our analysis to a new two-particle exclusion model, whose regular lattice version involves hard squares of two different sizes. The exact solution of this model on bicolourable random lattices displays a phase diagram with two (continuous and discontinuous) crystallization transition lines meeting at a higher order critical point, in the universality class of the tricritical Ising model coupled to 2D quantum gravity.

The Asymptotic Dynamics of two-dimensional (anti-)de Sitter Gravity

We show that the asymptotic dynamics of two-dimensional de Sitter or anti-de Sitter Jackiw-Teitelboim (JT) gravity is described by a generalized two-particle Calogero-Sutherland model. This correspondence is established by formulating the JT model of (A)dS gravity in two dimensions as a topological gauge theory, which reduces to a nonlinear 0+1-dimensional sigma model on the boundary of (A)dS space. The appearance of cyclic coordinates allows then a further reduction to the Calogero-Sutherland quantum mechanical model.

Ground state of the 4α + Λ nucleus within the 4α+Λ cluster model

The s-wave bound state of the 4α+Λ system is investigated. The relevant solution to the Schrodinger equation is expanded in the basis formed by the eigenfunctions of Hamiltonian for the 4α subsystem. Differential equations for Yakubovsky components are employed to calculate basis functions. Phenomenological potentials for αα and αΛ interactions are used. In the 4α system, additional three-particle potentials for the interaction between α clusters are introduced in such a way as to reproduce the experimental data on the binding energies, the root-mean-square radii, and the charge form factors for the 12C and the 16O nucleus. The binding energy, the root-mean-square radius, and the hyperon distribution in the ground state of the Λ 17 O nucleus are calculated. The results of the calculations are in good agreement with those obtained on the basis of the 16O+Λ two-particle model with the phenomenological Woods-Saxon potential.

Bc mesons in a relativistic three-dimensional two-particle quasipotential model

Abstract We apply three-dimensional relativistic equation for the system of two-particles with unequal masses to the B c mesons family. The method of ℏ-expansion is applied for deriving the masses of B c mesons on the basis of three-dimensional relativistic two-particle equation. Numerical calculations for the Cornell potential are presented.

The evaluation of a Lagrangian model for turbulent transport and chemistry

A Lagrangian two-particle model for the relative diffusion and mixing of two reactive species is proposed. It describes the relative motion of a pair of fluid particles and includes the possibility for chemical interaction. The model was tested for consistency in simple geometrical configurations and has been compared to experimental data, Eulerian first- and second-order closure models as well as to other Lagrangian models. The transport algorithm was adapted in order to accommodate dispersion in decaying grid turbulence so that a comparison could be made with a series of wind tunnel measurements of the reaction of NO with O3. Three chemical closures are formulated and compared with experimental results. It appears that the formation of the reaction product is sensitive for both the description of the dispersion process and the chemical closure and that an accurate assessment of chemical closures is only possible with an accurate description of the dispersion process.

A heuristic Lagrangian stochastic particle model of relative diffusion: model formulation and preliminary results

A new method is proposed to calculate two-particle statistics of turbulent diffusion in complex flows. The method is a combination of a single-particle Lagrangian stochastic model and a two-particle model applicable to isotropic turbulence. An encouraging preliminary evaluation of the method is presented.

Some issues in sintering science and technology

Various sintering theories based on two-particle model are no longer valid. Apart from this the basic properties and data of materials are also much more accurate in the present date, thus casting doubt in the previous theories. The role of electronic structure of additives in activating sintering processes has been convincingly put forth. In the field of sintering practice still a gap is apparent with the theory. Various techno-economic factors including the nature of starting powders have, of late, given good impetus in tackling this challenge.

A new model of morphological instabilities during epitaxial growth: from step bunching to mounds formation

We show that the theoretical description of the spontaneous evolution of an epitaxially growing surface towards self-organised structures, changes qualitatively when the simultaneous presence of several chemical species is taken into account. In the framework of a two-particle model studied by Monte-Carlo simulations we prove that a growing surface can exhibit step meandering, step bunching and mounding in different growth regimes, assuming only positive Ehrlich–Schwoebel step-edge barrier.

Particle-in-a-box model of one-dimensional excitons in conjugated polymers

A simple two-particle model of excitons in conjugated polymers is proposed as an alternative to usual highly computationally demanding quantum chemical methods. In the two-particle model, the exciton is described as an electron-hole pair interacting via Coulomb forces and confined to the polymer backbone by rigid walls. Furthermore, by integrating out the transverse part, the two-particle equation is reduced to one-dimensional form. It is demonstrated how essentially exact solutions are obtained in the cases of short and long conjugation length, respectively. From a linear combination of these cases an approximate solution for the general case is obtained. As an application of the model the influence of a static electric field on the electron-hole overlap integral and exciton energy is considered.

Exact double-continuum solution of a correlated atomic model

The dynamics of double ionization is of considerable interest as being a striking manifestation of the electron correlation. This is an essentially nonseparable problem for which it is highly desirable to have an analytically soluble model for reference. In this paper, the correlated double-continuum solution of a two-particle atomic model is obtained in closed form. Although particles are one-dimensional and potentials are of -type, this model provides for double photoionization of helium, energy distributions of ejected electrons and total cross sections in qualitative agreement with those of more realistic calculations.

Two-particle model of anaerobic solid state fermentation

A structured mathematical model of anaerobic solid state fermentation (ASSF) has been developed. Since a stable ASSF requires addition of significant quantities of methanogenic seed sludge and mass-transfer limitation becomes important, the model postulates the existence of two different types of particles inside the fermenting solid mass--so-called "seed" particles with low biodegradability and high methanogenic activity and so-called "waste" particles with high biodegradability and low methanogenic activity. Any particle is assumed to be a completely mixed reactor and mass transfer of solutes between the particles is brought about by diffusion. The model includes multiple-reaction stoichiometry, microbial growth kinetics, material balances, liquid-gas interactions and liquid phase equilibrium chemistry. The theoretical model agrees on the qualitative level with existing experimental studies of ASSF. Hypothetical computer simulations are presented to illustrate the influence of biodegradability and mass transfer intensity on the stability of ASSF. On this basis, possible measures are proposed to prevent accumulation of volatile fatty acids inside the "seed" particles beyond their assimilative methanogenic capacity.

Novel mechanism for the onset of morphological instabilities during chemical vapour epitaxial growth

A novel mechanism leading to the onset of step bunching instabilities during chemical vapour epitaxial growth on vicinal substrates is presented. It is based on the coupling between the surface densities of diffusing precursor molecules and of adatoms, in the presence of Ehrlich–Schwoebel barriers at step edges. We propose and investigate a simple two-particle model accounting for this coupling, and we are able to show that step flow growth is unstable against step pairing. This is contrary to what happens in one-particle models for, say, molecular beam epitaxy, where Ehrlich–Schwoebel barriers oppose step pairing during step flow growth.