Superfluid and superconducting transitions in low-dimensional systems

Superfluid and superconducting phase transitions of interacting bosons are observed in diverse physical systems such as helium, superconducting materials, ultra-cold atomic gases, etc. For all these systems one-, two-, and three-dimensional (1D, 2D, and 3D) realizations are experimentally accessible. However, the current experimental focus is shifting to the low dimensional systems (e.g., films and wires) due to facilitated measurement techniques and a constant demand of technological applications. From a theoretical standpoint large fluctuations in 1D and 2D systems make them a challenging problem, especially when disorder is present. Here we study peculiarities associated with disorder in low-dimensional cases. Specifically, we are interested in the class of the systems where superfluid or superconducting transitions can be mapped to the finite temperature 2D superfluid-normal Kosterlitz-Thouless (KT) transition: (a) 2D bosonic system with a strong diagonal disorder, (b) 1D system of lattice bosons with off-diagonal disorder in the limit of large integer filling factor at zero temperature, and (c) 3D layered superconductors with no tunnelling between layers in zero external magnetic field