This paper gives a generalization of the AJL algorithm for quantum computation of the Jones polynomial to continuous ranges of values on the unit circle for the Jones parameter. We show that the Kauffman-Lomonaco 3-strand algorithm for the Jones polynomial is a special case of this generalization of the AJL algorithm.

A simultaneous improvement of the diffusion and dielectric properties of the simple point charge (SPC) model for liquid water appears to be very difficult with conventional reparametrization of the commonly used Lennard-Jones and Coulomb interaction functions and without including a self-energy correction in the effective pair-potential as is done in the SPC/E model. Here, a different approach ...

A model of random walk on knot diagrams is used to study the Alexander polynomial and the colored Jones polynomial of knots. In this context, the inverse of the Alexander polynomial of a knot plays the role of an Ihara-Selberg zeta function of a directed weighted graph, counting with weights cycles of random walk on a 1-string link whose closure is the knot in question. The colored Jones polyno...

It is shown that the two-by-two Jones-matrix formalism for polarization optics is a six-parameter two-by-two representation of the Lorentz group. The attenuation and phase-shift filters are represented respectively by the threeparameter rotation subgroup and the three-parameter Lorentz group for two spatial and one time dimensions. It is noted that the Lorentz group has another three-parameter ...

It is known, that the Leonard–Jones (L–J) potential describes the interaction of atoms of simple non-polar gases [1]. However, at large distances between atoms the interaction forces fall faster, than it is described by the L–J potential [1]. The corresponding corrections (including light atoms) are suggested in papers [2]–[6]. These authors had a suspicion, that, for light atoms, either L–J fo...

The quantum theorem of corresponding states is applied to N=13 and N=26 cold quantum fluid clusters to establish where para-hydrogen clusters lie in relation to more and less quantum delocalized systems. Path integral Monte Carlo calculations of the energies, densities, radial and pair distributions, and superfluid fractions are reported at T=0.5 K for a Lennard-Jones (LJ) (12,6) potential usin...

The glass transition is usually regarded as a kinetic phenomenon but it can be treated in a purely thermodynamic way when physical constraints, rather than lack of time, are applied to prevent a liquid from sampling its many glasses. Simulations of Lennard Jones fluids show that they can be made glassy at any density or temperature and that the glass transition is accompanied by a decrease in t...

On the basis of the icosahedral and decahedral lattices, the lowest energies of the Lennard-Jones (LJ) clusters containing 562-1000 atoms with the two motifs are obtained by using a greedy search method (GSM). Energy comparison between the decahedra and icosahedra shows that icosahedral structures are predominant. However, most of the icosahedral structures with the central vacancy are more sta...