Thermodynamics of a one-dimensional Bose gas with repulsive contact interactions

Mohamed K. Al-Sugheir, Feras M. Aldweri, G.A. Alna'washi +1 more

R. E. Barfknecht, Angela Foerster, Nikolaj Thomas Zinner

N. M. Bogoliubov

Giulia De Rosi, Pietro Massignan, Maciej Lewenstein +1 more

This work demonstrates that, in the weakly-interacting regime, the thermal behavior of quantum gases is dominated by the Bogoliubov part of the spectrum, while in the strongly-interacting limit, temperature effects may be accurately described in terms of an excluded-volume model.

Marek Napiórkowski, J. Piasecki

We consider two-dimensional imperfect attractive Fermi and repulsive Bose gases consisting of spinless point particles whose total interparticle interaction energy is represented by $a{N}^{2}/2V$ with $a=\ensuremath{-}{a}_{F}\ensuremath{\le}0$ for fermions and $a={a}_{B}\ensuremath{\ge}0$ for bosons. We show that, in spite of the attraction, the thermodynamics of a $d=2$ imperfect Fermi gas remains well defined for $0\ensuremath{\le}{a}_{F}\ensuremath{\le}{a}_{0}={h}^{2}/2\ensuremath{\pi}m$, and is exactly the same as the one of the repulsive imperfect Bose gas with ${a}_{B}={a}_{0}\ensuremath{-}{a}_{F}$. In particular, for ${a}_{F}={a}_{0}$ one observes the thermodynamic equivalence of the attractive imperfect Fermi gas and the ideal Bose gas.

Ovidiu I. Pâţu, Andreas Klümper

We investigate the finite-temperature properties of the one-dimensional two-component Bose gas (2CBG) with repulsive contact interaction in a harmonic trap. Making use of a lattice embedding for the 2CBG and the quantum transfer matrix, we derive a system of two nonlinear integral equations characterizing the thermodynamics of the uniform system for all values of the relevant parameters: temperature, strength of the interaction, chemical potential, and magnetic field. This system allows for an easy numerical implementation in stark contrast with the infinite number of equations obtained by employing the thermodynamic Bethe ansatz. We use this exact solution coupled with the local density approximation to compute the density profiles and local density correlation function of the inhomogeneous gas for a wide range of coupling strengths and temperatures. Our results show that the polarization in the center of the trap influences heavily the local correlator especially in the experimentally accessible Tonks-Girardeau regime.