Abstract：Correlated quantum systems in low dimensions confined with different kinds of potentials show fascinating properties, such as fermionization of bosons and Anderson localization for instance. In this talk, I will first present a study of the Tan contact for Lieb-Liniger bosons trapped by harmonic potentials at finite temperature. In the strongly-interacting regime, we find a maximum contact as a function of temperature, which signals the crossover to fermionization. Then, in the second part, I will present our latest results about the localization and fractality of atoms in shallow 1D quasi-periodic potentials. In particular, we determine the critical properties and the Hausdorff fractal dimension of these systems, and discuss extension to Bose-glass physics.
 H. Yao, D. Clément, A. Minguzzi, P. Vignolo, L. Sanchez-Palencia, Phys. Rev. Lett. 121, 220402 (2018).
 H. Yao, H. Khoudli, L. Bresque, L. Sanchez-Palencia.
Phys. Rev. Lett. 123, 070405 (2019).