Statistical mechanics of bosons with attractive interaction

K. K. Singh

J C Martinez, E. Polatdemir

As an effort to present a new working example for an advanced class in statistical mechanics, we employ Lawson's path integral formalism to calculate the microcanonical density operator and apply it to a one-dimensional particle interacting with an attractive delta potential. As an offshoot we derive the ground-state energy for a system of bosons in one dimension interacting via the delta potential.

Ivan Morera, Bruno Juliá-Díaz, Manuel Valiente

We consider interacting one-dimensional bosons in the universal low-energy regime. The interactions consist of a combination of attractive and repulsive parts that can stabilize quantum gases, droplets and liquids. In particular, we study the role of effective three-body repulsion, in systems with weak attractive pairwise interactions. Its low-energy description is often argued to be equivalent to a model including only two-body interactions with non-zero range. Here, we show that, at zero temperature, the equations of state in both theories agree quantitatively at low densities for overall repulsion, in the gas phase, as can be inferred from the $S$-matrix formulation of statistical mechanics. However, this agreement is absent in the attractive regime, where universality only occurs in the long-distance properties of quantum droplets. We develop analytical tools to investigate the properties of the theory, and obtain astounding agreement with exact numerical calculations using the density-matrix renormalization group.

J. Oitmaa

J. Oitmaa

Sergio A Albeverio, L. Dąbrowski, Shao-Ming Fei

The integrability of one-dimensional quantum mechanical many-body problems with general contact interactions is extensively studied. It is shown that besides the pure (repulsive or attractive) δ-function interaction there is another singular point interactions which gives rise to a new one-parameter family of integrable quantum mechanical many-body systems. The bound states and scattering matrices are calculated for both bosonic and fermionic statistics.