## Efficient calculation of path integrals with applications to ultra-cold quantum gases

Path integrals provide the general mathematical framework for all quantum theories and statistical systems, but we know surprisingly little about their analytical properties. During the past five years we have obtained new analytical insight about these properties and build it into more efficient algorithms. Our principal focus in the next period will be to apply the method to a wide array of relevant models in condensed matter physics and quantum field theory.

To this end, we will study ultracold Bose systems in the presence of weak and strong disorder. It is known that the introduction of a stochastically disordered component of the trapping potential can lead to three different phases: the expected gas and superfluid phase, and a novel Bose-glass phase. The latter two appear due to a macroscopic occupation of the ground state, which leads either to a global Bose-Einstein condensate or to a set of local ones in the minima of the disorder potential. We will compare analytical (perturbative and non-perturbative) and numerical (Gross-Pitaveskii) approaches in the weak-disorder regime in order to gain new insights and address the problem of strong disorder where the emergence of a quantum phase transition from a superfluid to a Bose-glass phase is expected.

Codes developed and used in these investigations: SPEEDUP.

Codes developed and used in these investigations: SPEEDUP.