Repulsive Delta Potential Research Articles

Transfer Matrix Spectrum for O(N) High Temperature Lattice Classical Ferromagnetic Spin Systems and Staggering Transformations

We obtain the low-lying energy-momentum spectrum for the imaginary-time lattice quantum field model associated with d-dimensional lattice ferromagnetic classical N-component vector spin systems at high temperature (0 < β << 1). Each system is characterized by a single site a priori spin probability distribution. The energy-momentum spectrum exhibits isolated dispersion curves which are identified as single particles and multi-particle bands. Our two-particle bound state analysis is restricted to a ladder approximation of the Bethe–Salpeter equation, and the existence of bound states depend on whether or not Gaussian domination for the four-point function is verified. It is known that two-particle bound states appear below the two-particle band if Gaussian domination does not hold. Here, we show that two two-particle bound states appear above the two-particle band if Gaussian domination is verified. We also show how the complete two-particle spectral pattern for these models can be understood by making a correspondence between the Bethe–Salpeter equation and a two-particle lattice Schrödinger Hamiltonian operator with attractive or repulsive spin-dependent delta potentials at the origin. A staggering transformation is used to relate the attractive and repulsive potential cases, as well as their associated Hamiltonians spectrum and eigenfunctions.

Algebraic Bethe ansatz for the nonlinear Schrodinger model. II. Mixed fermion and boson fields

For pt.I see ibid., vol.21, p.2391, (1988). The Bethe ansatz equations for a mixture of species of fermions and bosons in one dimension, interacting with a repulsive delta potential, are obtained. It is shown that the matrix periodic boundary conditions of the system can be obtained from those of a fermion or boson system. Finally, the extension of these results to the nonlinear Schrodinger model with a supermatrix is made.

Long-range order Hartree-Fock states with different magnetic properties

The Hartree-Fock (HF) energies of a new set of HF orbitals with long-range order are calculated for two different models which involve a system of many fermions interacting via repulsive delta potentials as a preliminary step facing such problems as the electron gas system, 3He systems, etc., where, however, the calculation of the relevant matrix elements is considerably more difficult. The models considered illustrate paramagnetic and antiferromagnetic behaviour. The authors find a whole new set of HF orbitals which are more stable than the (trivial) plane wave orbitals as well as the classic Overhauser ones.