Critical behaviour of ultra-cold bosonic gases in a confining potential.
by
Jacopo Nespolo(P)
→
Europe/Rome
248 (Building C, first floor)
248
Building C, first floor
Description
Experiments with ultra-cold atoms use a confining potential to keep the sample trapped in place. However, the presence of the trap is most often neglected in the modelling and analyses, in favour of treatments based on homogeneous descriptions, such as the local density approximation. The trap qualitatively modifies the critical behaviour of these systems near a phase transition: most notably, it bounds the correlation length to remain finite. The trap-size scaling can provide a sound treatment of the effects of the confining potential, much in the same way as finite-size scaling can account for corrections to the critical behaviour of finite systems. In this seminar, I shall review some general aspects of finite-size and trap-size scaling. I shall then concentrate on its applications to the Bose-Hubbard model, which realistically describe a bosonic gas in an optical lattice. Finally, I shall show that an effective control parameter is needed for a correct trap-size scaling treatment of some particular points of the phase boundary of this model.
