A method is developed to construct the solutions of one and many variable, linear differential equations of arbitrary order. Using this, the N -particle Sutherland model, with pair-wise inverse sine-square interactions among the particles, is shown to be equivalent to free particles on a circle. Applicability of our method to many other few and many-body problems is also illustrated. PACS: 03.6...

A method is developed to construct the solutions of one and many variable, linear differential equations of arbitrary order. Using this, the N -particle Sutherland model, with pair-wise inverse sine-square interactions among the particles, is shown to be equivalent to free particles on a circle. Applicability of our method to many other few and many-body problems is also illustrated. PACS: 03.6...

We have reinvestigated the structural and thermodynamic properties of the squarewell and the square-shoulder system using two different theoretical frameworks, i.e., the optimized random-phase approximation and the Rogers–Young integral equation. We discuss the limits of applicability of the respective concepts and compare the results with ‘exact’ Monte Carlo simulation results and with data ob...

We formulate combinatorial principles that combine the square principle with various strong forms of the diamond principle, and prove that the strongest amongst them holds in L for every infinite cardinal. As an application, we prove that the following two hold in L: (1) For every infinite regular cardinal λ, there exists a special λ-Aronszajn tree whose projection is almost Souslin; (2) For ev...

We calculate the Wigner distribution function for the Calogero-Sutherland system which consists of harmonic and inverse-square interactions. The Wigner distribution function is separated out into two parts corresponding to the relative and center-of-mass motions. A general expression for the relative Wigner function is obtained in terms of the Laguerre polynomials by introducing a new identity ...

Vapor–liquid interfacial tension of square-well ~SW! fluids is calculated using three different methods viz., molecular dynamics ~MD! with collision-based virial evaluation, Monte Carlo with virial computed by volume perturbation, and Binder’s density-distribution method in conjunction with grand-canonical transition-matrix Monte Carlo ~GC-TMMC!. Three values of the SW attractive well range par...

The analytic and numerical methods introduced previously to study the phase behavior of hard sphere fluids starting from the Yvon-Born-Green (YBG) equation under the Kirkwood superposition approximation (KSA) are adapted to the square-well fluid. We are able to show conclusively that the YBG equation under the KSA closure when applied to the square-well fluid: (i) predicts the existence of an a...

Phase equilibria of a square-well fluid in planar slit pores with varying slit width are investigated by applying the grand-canonical transition-matrix Monte Carlo (GC-TMMC) with the histogram-reweighting method. The wall-fluid interaction strength was varied from repulsive to attractive such that it is greater than the fluid-fluid interaction strength. The nature of the phase coexistence envel...