On the momentum distribution in Bose fluids

We comment on some properties of the momentum distribution in an interacting Bose fluid and its relation to the average kinetic energy per particle within the hypernetted chain approach.     

A relation between the radius of the hadronic fluid and the particle rapitidity density on high energy heavy ion reaction

In high energy heavy-ion collisions, the radius R of the hadron-emitting source was measured by hadron interferometry analysis, and the simple relation was observed between R and the produced particle density dN/dy. Solving a simplified fluid equation with cylindrical symmetry, we show that the observed relation is well explained by the fluid model, if reasonable A-dependence of the initial temperature is assumed. Usefulness of the simplified fluid model for other data analyses is also discussed.     

On the relation between k-body interaction and k-particle density

A generalization of the Hohenberg-Kohn theorem is given. It is shown, that the k-particle density determines the k-body potential up to equivalence. The k-body potential is separated in irreducible κ-body parts. The derivation includes the case of degenerate ground states.     

On the relationship between the density functional formalism and the potential distribution theory for nonuniform fluids

It is shown that the variational principle for the grand potential of a nonuniform fluid as a functional of the singlet density yields the potential distribution theory for the equilibrium density. We derive the explicit form that the functional takes for a system of hard rods, and propose an approximate one for hard spheres. Attractive interactions are also considered in mean-field approximation. In all cases the pair direct correlation function of the nonuniform system is obtained and the density gradient expansion of the free energy is investigated.     

On the critical behaviour of Bose systems at constant density

The scaling behaviour of Bose systems at constant density is studied using the ?-expansion method. The chemical potential and equation of state are obtained in terms of t = (T ? T_c)/T_c to first order in ?.     

Modified hypernetted-chain equation for the ground state of Bose fluids

Summary The modified hypernetted-chain equation is used to study the ground state of Bose fluids in the Jastrow approximation. We test the equation for different forms of the pair interaction and of the Jastrow pseudopotential and in all cases the energy of⁴He is given with an error not larger than 0.1 K at all densities. The effect of a triplet term in the wavefunction is also studied.

---

Riassunto L'equazione integrale HNC modificata è applicata allo studio dello stato fondamentale di un fluido di Bose nell'approssimazione di Jastrow per diverse espressioni della interazione binaria e forme diverse della correlazione di Jastrow. In tutti i casi l'energia per⁴He è calcolata con un errore non superiore a 0.1 K a tutte le densità. Si considera inoltre l'effetto di una correlazione a tre corpi nella funzione d'onda.

---

Резюме модифицированное уравнение цепочки используется для исследования основного состояния Ъозе-жидкости в приближении Ястрова. Мы проверяем уравнение для различных форм парного взаимодействия и псевдопотенциала Ястрова. Во всех случаях приводится энергия⁴He с погрешностью не более, чем 0.1 K для всех плотностей. Также исследуется влияине триплетного члена на волновую функцию.

     

也谈概率密度和概率流密度算符

针对<大学物理>2008年第8期上关于粒子概率密度算符和概率流密度算符的讨论一文进行了补充,对一般空间(如动量空间)中的概率和概率流进行了较系统的阐述,并纠正了该文中的有关错误论断.     

A modified soft-core fluid model for the direct correlation function of the square-shoulder and square-well fluids

We propose a simple analytical expression of the direct correlation function for the square-shoulder and square-well fluids. Our approximation is based on an ansatz for the direct correlation function of a modified soft-core fluid, whose parameters are adjusted by fitting the data obtained from Monte Carlo computer simulations. Moreover, it is complemented with a Wertheim-like parametrization to reproduce correctly the direct correlation inside the hard-core. We demonstrate that this approach is in quantitative agreement with the numerical solution of the Ornstein–Zernike equation within the Percus–Yevick approximation. We also show that our results are accurate in a large regime of densities for different interaction ranges and potential strengths. Therefore, this opens up the possibility of introducing the square-shoulder or the square-well potentials as new reference systems in advanced theoretical approximations.     

On the relation between the wave aberration function and the phase transfer function for an incoherent imaging system with circular pupil

The consideration is carried out in its general formulation: the wave aberration function is represented in terms of classical aberrations (the Zernike polynomials), the phase transfer function (argument of the complex optical transfer function) is defined by a chain of transformations originating from the generalized pupil function. Quasi-analytical quadrature formulas are derived that link the optical transfer function and the phase transfer function with the aberration terms. It is shown that the phase transfer function contains information on the odd-order aberrations, which can be retrieved from coefficients to the Taylor expansion of the derived quadrature relation. Received 16 June 2001     

On the three-particle structure function of bose fluids

We derive an approximate expression for the three-particle structure function of a Bose fluid in its ground state. Specialization of our result regains the convolution approximation as well as the Berdahl-Family-Gould approximation. A discussion of the quality of these approximants is presented.Research supported by the Republican Council for Scientific Work of Bosnia and Herzegovina, Yugoslavia     

A linear relation between the compressibility and density of blood

By considering the blood as a mixture of ultrafiltrate and protein concentrate, the additive nature of compressibility and density from the components is utilized to deduce a linear relation between the compressibility and density for blood. This deduction also indicates that the intercept and slope of the linear relation are independent of the hematocrit, plasma protein concentration, and hemoglobin concentration of red blood cells. To verify experimentally this linear relation, saline and plasma dilutions on porcine or canine blood flowing in an extracorporeal circuit were carried out. The hematocrit of the experiments ranges from 0% to 55% and the plasma protein concentration ranges from 10 to 90 g/l. A resonance device in the circuit measured the density rhob of blood at 37 degrees C and an ultrasound system measured the sound velocity cb. The range of density is from 1,010 to 1,060 g/l and that of sound velocity is from 1,530 to 1,580 m/s. The linear relation that best fits the data of compressibility [computed as (rhob cb(2))-1] and density has a correlation coefficient of 0.9978. The linear relation is found to fit well the dependence of compressibility on density derived from the sound velocity data of human, horse, and porcine blood in the literature.     

On the relation between mechanisms for single-transverse-spin asymmetries

Recent studies have shown that two widely-used mechanisms for single-transverse-spin asymmetries based on either twist-three contributions or on transverse-momentum-dependent (Sivers) parton distributions become identical in a kinematical regime of overlap. This was demonstrated for the so-called soft-gluon-pole and hard-pole contributions to the asymmetry associated with a particular quark–gluon correlation function in the nucleon. In this Letter, using semi-inclusive deep inelastic scattering as an example, we extend the study to the contributions by soft-fermion poles and by another independent twist-three correlation function. We find that these additional terms organize themselves in such a way as to maintain the mutual consistency of the two mechanisms for single-spin asymmetries.     

The velocity distribution and the density near a particle of an equilibrium one component plasma

The equation governing the conditional relative velocity distribution of an equilibrium one component plasma at distances smaller than the interparticle distance is derived from elementary principles of classical dynamics and probability, the latter defined from the temporal point of view. It becomes obvious that in accordance with todays accepted views the maxwellian velocity distribution satisfies the above equation. Using this result it is also shown that the conditional number density has the form n(r) = n₀exp(-e²/rk_BT).     

On the particle density of mass zero bosons and energy density of mass zero fermions

It is shown that even nonlocal generalizations of the usual expressions for

1. the particle probability density of mass zero, spin zero (one) bosons;
2. the energy density of mass zero spin one half fermions;

can become negative, indicating that the method of obtaining positive definite expressions for massive particles^2,4 for the above quantities does not work here.     

On the relation between momentum and velocity for elementary systems

We investigate how the quantum mechanical position operator can be defined for elementary systems so that the connection, postulated by the special theory of relatively, between velocity (the time derivative of the position) and momentum remains valid.