We present a theoretical study based upon quantum Monte Carlo methods of the Bose polaron in onedimensional systems with contact interactions. In this instance of the problem of a single impurity immersed in a quantum bath, the medium is a Lieb-Liniger gas of bosons ranging from the weakly interacting to the Tonks-Girardeau regime, whereas the impurity is coupled to the bath via a different contact potential, producing both repulsive and attractive interactions. Both the case of a mobile impurity, having the same mass as the particles in the medium, and the case of a static impurity with infinite mass are considered. We make use of numerical techniques that allow us to calculate the ground-state energy of the impurity, its effective mass, and the contact parameter between the impurity and the bath. These quantities are investigated as a function of the strength of interactions between the impurity and the bath and within the bath. In particular, we find that the effective mass rapidly increases to very large values when the impurity gets strongly coupled to an otherwise weakly repulsive bath. This heavy impurity hardly moves within the medium, thereby realizing the "self-localization" regime of the Landau-Pekar polaron. Furthermore, we compare our results with predictions of perturbation theory valid for weak interactions and with exact solutions available when the bosons in the medium behave as impenetrable particles.

By using exact quantum Monte-Carlo methods we calculate the ground-state properties of the liquid phase in one-dimensional Bose mixtures with contact interactions. We find that the liquid state can be formed if the ratio of coupling strengths between inter-species attractive and intraspecies repulsive interactions exceeds a critical value. As a function of this ratio we determine the density where the energy per particle has a minimum and the one where the compressibility diverges, thereby identifying the equilibrium density and the spinodal point in the phase diagram of the homogeneous liquid. Furthermore, in the stable liquid state, we calculate the chemical potential, the speed of sound, as well as structural and coherence properties such as the pair correlation function, the static structure factor and the one-body density matrix, thus providing a detailed description of the bulk region in self-bound droplets.Ultracold atoms provide a rich toolbox to realize different states of matter where many-body correlations can be investigated in a very clean experimental setup. In early years, the most common gas phase, both in the normal and superfluid regime, and artificial crystals created by external lattice potentials were routinely produced [1]. More recently, interaction effects have been exploited to obtain spontaneous breaking of translational symmetry in ordered arrangements of particles subject to long-range forces [2] and in most exotic supersolid systems, featuring both the rigidity of standard solids and the dissipationless motion of vacancies typical of superfluids [3,4]. Furthermore, self-bound liquid droplets were generated as a result of quantum fluctuations in samples interacting via anisotropic dipolar forces [5-9] as well as via contact interparticle potentials [10][11][12].In three and two dimensions such droplets would collapse according to mean-field theory and are stabilized, for large enough numbers of particles, by repulsive correlations beyond the mean-field description. Dipolar droplets were characterized theoretically by means of a generalized nonlocal, nonlinear Schrödinger equation [13] and also by exact quantum Monte-Carlo (QMC) methods, employing a model two-body potential with hardcore repulsion [14]. Droplets in a two-component Bose gas with short-range interactions have been first predicted and studied using a generalized Gross-Pitaevskii (GGP) equation in Ref. [15]. QMC simulations of these latter systems have also been carried out, even though only for limited numbers of particles [16].In one spatial dimension (1D), quantum droplets of Bose mixtures with contact interactions have been predicted to occur as a result of a different mechanism. Here, beyond mean-field fluctuations are attractive and one needs a net mean-field repulsion in order to stabilize the droplet, which therefore are expected to form in the region where, according to mean-field theory, the homo-geneous gas mixture is still stable [17]. The approach based on the GGP equation is valid in the weak-coupling limit an...

Abstract.Loop Quantum Cosmology strongly modifies the high-energy dynamics of Friedman-Robertson-Walker models and removes the big-bang singularity. We investigate how LQC corrections affect the stability properties of the Einstein static universe. In General Relativity, the Einstein static model with positive cosmological constant Λ is unstable to homogeneous perturbations. Using dynamical systems methods, we show that LQC modifications can lead to an Einstein static model which is neutrally stable for a large enough positive value of Λ.

We consider static cosmological solutions along with their stability properties in the framework of a recently proposed theory of massive gravity. We show that the modification introduced in the cosmological equations leads to several new solutions, only sourced by a perfect fluid, generalizing the Einstein static universe found in general relativity. Using dynamical system techniques and numerical analysis, we show that the found solutions can be either neutrally stable or unstable against spatially homogeneous and isotropic perturbations