Equation of State for One-Dimensional Attractive \delta-Bose Gas in Weak Coupling Regime

Luigi Amico A, V. E. Korepin

Tsubasa Ichikawa, Izumi Tsutsui, Nobuhiro Yonezawa

Approximated formulas for real quasimomentum and the associated energy spectrum are presented for one-dimensional Bose gas with weak attractive contact interactions. On the basis of the energy spectrum, we obtain the equation of state in the high-temperature region, which is found to be the van der Waals equation without volume correction.

Xi‐Wen Guan, Zhong-Qi Ma

The Fredholm equations for one-dimensional two-component fermions with repulsive and with attractive $\ensuremath{\delta}$-function interactions are solved by an asymptotic expansion for strong repulsion, weak repulsion, weak attraction, and strong attraction. Consequently, we obtain the first few terms of the expansion of the ground-state energy for the Fermi gas with polarization for these regimes. We also prove that the two sets of Fredhom equations for weakly repulsive and attractive interactions are identical as long as the integration boundaries match each other between the two types. Thus the asymptotic expansions of the energies of repulsive and attractive fermions are identical to all orders in this region. The identity of the asymptotic expansions may not mean that the energy connects analytically.

Li-Chung Ha, Chen-Lung Hung, Xibo Zhang +4 more

Viktor Borisovich Bobrov, Pieter P. J. M. Schram, S. A. Trigger

Toshiaki Iida, Miki Wadati

The Gaudin integral equation for the ground state of a one-dimensional delta-function attractive spin-1/2 fermions is solved in the form of power series. The first few terms of the asymptotic expansions for both strong and weak coupling cases are calculated analytically. The physical quantities such as the ground state energy are expressed in terms of a single dimensionless parameter gamma =c/D, where c is the coupling constant and D is the number density. The results agree with those obtained from the perturbation calculations, which include the one in the classical electrostatics originally by Kirchhoff. In the strong coupling limit, the connection to the solutions of the Lieb-Liniger integral equation for the ground state of a one-dimensional delta-function repulsive bose gas is shown explicitly.