Strongly Interacting Particles in One Dimensional Traps

Volosniev, Petrosyan, Valiente, Fedorov, Jensen, Zinner

We examine trapped one-dimensional systems assuming that two-body potentials
have zero range. We show that when the repulsion between particles is very large
the properties of the system can be found analytically. Using this analytical approach
we also demonstrate that strongly interacting gases in one dimension realize the
Heisenberg Hamiltonian with coupling constants highly dependent on the confining potential.
In order to illustrate the perspectives of our findings we show the dependence
of the quantum state transfer on the shape of the trapping potential.