We show that the one dimensional unitary matrix model with potential of the form aU + bU2 + h.c. is integrable. By reduction to the dynamics of the eigenvalues, we establish the integrability of a system of particles in one space dimension in an external potential of the form a cos(x+α) + b cos(2x+ β) and interacting through two-body potentials of the inverse sine square type. This system const...

The thermodynamic properties of the parabolic-well fluid are considered. intermolecular interaction potential this model, which belongs to class so-called van Hove potentials, shares with square-well and triangular well potentials inclusion a hard-core an attractive relatively short range. analytic second virial coefficient for is computed explicitly equation state derived aid second-order pert...

The thermodynamic functions for square-well gases evaluated till the third virial coefficient are investigated at an isobaric process. Some thermodynamic functions are analytically expressed as functions of intensive variables, temperature, and pressure. Some thermodynamic quantities for H2O are calculated numerically and drawn graphically. In critical states, the heat capacity, thermal expansi...

The PT-symmetric square well problem is considered in a SUSY framework when the coupling strength lies below the critical value where PT symmetry becomes spontaneously broken. We find SUSY partner potentials to exist admitting a hierarchy with energy levels depicting an unbroken SUSY situation. Such a hierarchy is a PT-symmetric analogue of the family of sec2-like potentials, to which it reduce...

We examine the classical problem of an infinite square well by considering Hamilton’s equations in one dimension and Hamilton-Jacobi equation for motion in two dimensions. We illustrate, by means of suitable examples, the nature of the periodic motion of a particle trapped inside the well. E-mail address: [email protected] Directeur de recherches FNRS; E-mail address: [email protected]

Recently, a class of PT -invariant quantum mechanical models described by the nonHermitian HamiltonianH = p2 + x2(ix) was studied. It was found that the energy levels for this theory are real for all > 0. Here, the limit as →∞ is examined. It is shown that in this limit, the theory becomes exactly solvable. A generalization of this Hamiltonian, H = p2 + x2M(ix) (M = 1, 2, 3, . . .) is also stud...

We investigate the ability of the reference hypernetted-chain integral equation to describe the phase diagram of square-well fluids with four different ranges of attraction. Comparison of our results with simulation data shows that the theory is able to reproduce with fairly good accuracy a significant part of the coexistence curve, provided an extrapolation procedure is used to circumvent the ...