We study a one-dimensional singular potential plus three types of regular interactions: constant electric field, harmonic oscillator and infinite square well. We use the Lippman-Schwinger Green function technique in order to search for the bound state energies. In the electric field case the unique bound state coincides with that found in an earlier study as the field is switched off. For non-z...

The Shasty-Sutherland model, which consists of a set of spin 1/2 dimers on a 2D square lattice, is simple and soluble but captures a central theme of condensed matter physics by sitting precariously on the quantum edge between isolated, gapped excitations and collective, ordered ground states. We compress the model Shastry-Sutherland material, SrCu(2)(BO(3))(2), in a diamond anvil cell at cryog...

Various Monte Carlo techniques are used to determine the complete phase diagrams of the square-well model for the attractive ranges lambda = 1.15 and lambda = 1.25. The results for the latter case are in agreement with earlier Monte Carlo simulations for the fluid-fluid coexistence curve and yield new results for the liquidus-solidus lines. Our results for lambda = 1.15 are new. We find that th...

The results of calculations of gas emission spectra with both central and extended sources of ion-ization have been compared to the ratio of line intensities observed in the extended narrow line region of NGC1068. The origin of an extended structure of anomalous strength in the OIII]5007 and NeV ]3425 lines found by Evans & Dopita (1986) and Bergeron et al.(1989) could be due to an additional s...

In these lectures, I review some recent results on the Calogero-Sutherland model and the Haldane Shatry-chain. The list of topics I cover are the following: 1) The Calogero-Sutherland Hamiltonien and fractional stastistics. The form factor of the density operator. 2) The Dunkl operators and their relations with monodromy matrices, Yangians and aane-Hecke algebras. 3) The Haldane-Shastry chain i...

We report a simulation study of the gas-liquid critical point for the square-well potential, for values of well width delta as small as 0.005 times the particle diameter sigma. For small delta, the reduced second virial coefficient at the critical point B2*c is found to depend linearly on delta. The observed weak linear dependence is not sufficient to produce any significant observable effect i...

We examine a model system to study the effect of pressure on the surface tension of a vapor-liquid interface. The system is a two-component mixture of spheres interacting with the square-well (A-A) and hard-sphere (B-B) potentials and with unlike (A-B) interactions ranging (for different cases) from hard sphere to strongly attractive square well. The bulk-phase and interfacial properties are me...