We discuss a realisation of the pentaquark structure proposed by Jaffe and Wilczek within a simple quark model with colour-spin contact interactions and coloured harmonic confinement, which accurately describes the ∆ − N splitting. In this model spatially compact diquarks are formed in the pentaquark but no such compact object exists in the nucleon. The colour-spin attraction brings the Jaffe-W...

For ensemble of bosons trapped in a 1D harmonic potential well we have found an analytical formula for the canonical partition function and shown that, for 100 trapped atoms, the discrepancy between the grand canonical and the canonical predictions for the condensate fraction reaches 10% in the vicinity of the Bose-Einstein threshold. This discrepancy decreases only logarithmically as the numbe...

In this note, we characterize the $f$-harmonic maps and bi-$f$-harmonic with potential. We prove that every map potential from complete Riemannian manifold, satisfying some conditions is a More, study case of conformal between equidimensional manifolds.

The exact joint multifractal distribution for the scaling and winding of the electrostatic potential lines near any conformally invariant scaling curve is derived in two dimensions. Its spectrum f(alpha,lambda) gives the Hausdorff dimension of the points where the potential scales with distance r as H approximately r(alpha) while the curve logarithmically spirals with a rotation angle phi=lambd...

We present a "basin-sampling" approach for calculation of the potential energy density of states for classical statistical models. It combines a Wang-Landau-type uniform sampling of local minima and a novel approach for approximating the relative contributions from local minima in terms of the volumes of basins of attraction. We have employed basin-sampling to study phase changes in atomic clus...

The semiclassical treatment of the two-dimensional harmonic oscillator provides an instructive example of the relation between classical motion and the quantum mechanical energy spectrum. We extend previous work on the anisotropic oscillator with incommensurate frequencies and the isotropic oscillator to the case with commensurate frequencies for which the Lissajous curves appear as classical p...

We give a local characterization of the class of functions having positive distributional derivative with respect to z̄ that are almost everywhere equal to one of finitely many analytic functions and satisfy some mild nondegeneracy assumptions. As a consequence, we show that any subharmonic piecewise harmonic function satisfying these conditions locally coincides with the maximum of finitely man...