ON-DIMENSIONAL MANY-PARTICLE SYSTEM WITH TWO-BODY INTERACTION.

M. N. Adamov, L. N. Labzovskiǐ

Earl L. Andersen, U. Uhlhorn

The methods discussed have been developed with the nuclear many-body problem, formulated as a classical quantum mechanical many-body problem with only twoparticle interaction and without any assumption of the origin of nuclear forces in mind. Two approaches characterized by different wave functions are discussed, and the general equations for the determination of best twoparticle orbitals'' are derived. The problem of the two interacting particles are examined in a common potential. This common potential is chosen as an oscillator. (W.D.M.)

Yang Xian

Kazumoto Iguchi

We conceptually study the existence of four distinct quantum phases: the Luttinger liquid, the Wigner crystal, the Coulomb plasma and the molecular crystal in one-dimensional many-body systems with long-range interaction. We show that the anomaly of the ground state wavefunction indicates a quantum Kosterlitz–Thouless transition at zero temperature, which separates into two regimes of the Luttinger liquid and the Wigner crystal. We also postulate a scaling theory which discriminate the four phases using the Kosterlitz–Thouless scaling theory.

I. I. Ivanchik

Vincent Caudrelier, Nicolas Crampé

The one-dimensional problem of N particles with contact interaction in the presence of a tunable transmitting and reflecting impurity is investigated along the lines of the coordinate Bethe ansatz. As a result, the system is shown to be exactly solvable by determining the eigenfunctions and the energy spectrum. The latter is given by the solutions of the Bethe ansatz equations which we establish for different boundary conditions in the presence of the impurity. These impurity Bethe equations contain as special cases well-known Bethe equations for systems on the half-line. We briefly study them on their own through the toy-examples of one and two particles. It turns out that the impurity can be tuned to lift degeneracies in the energies and can create bound states when it is sufficiently attractive. The example of an impurity sitting at the center of a box and breaking parity invariance shows that such an impurity can be used to confine a stationary state asymmetrically. This could have interesting applications in condensed matter physics.