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This Dissertation presents results of a thorough study of ultracold bosonic and fermionic gases in three-dimensional and quasi-one-dimensional systems. Although the analyses are carried out within various theoretical frameworks (Gross-Pitaevskii, Bethe ansatz, local density approximation, etc.) the main tool of the study is the Quantum Monte Carlo method in different modifications (variational Monte Carlo, diffusion Monte Carlo, fixed-node Monte Carlo methods). We benchmark our Monte Carlo calculations by recovering known analytical results (perturbative theories in dilute limits, exactly solvable models, etc.) and extend calculations to regimes, where the results are so far unknown. In particular we calculate the equation of state and correlation functions for gases in various geometries and with various interatomic interactions.
We present two Diffusion Monte Carlo (DMC) algorithms for systems of ultracold quantum gases featuring synthetic spin-orbit interactions. The first one is a discrete spin generalization of the T- moves spin-orbit DMC, which provides an upper bound to
The ground state properties of spin-polarized deuterium (D$downarrow$) at zero temperature are obtained by means of the diffusion Monte Carlo calculations within the fixed-node approximation. Three D$downarrow$ species have been investigated (D$downa
The ground-state properties of two-component repulsive Fermi gases in two dimensions are investigated by means of fixed-node diffusion Monte Carlo simulations. The energy per particle is determined as a function of the intercomponent interaction stre
This is a review of recent developments in Monte Carlo methods in the field of ultra cold gases. For bosonic atoms in an optical lattice we discuss path integral Monte Carlo simulations with worm updates and show the excellent agreement with cold ato
We study a resonant Bose-Fermi mixture at zero temperature by using the fixed-node diffusion Monte Carlo method. We explore the system from weak to strong boson-fermion interaction, for different concentrations of the bosons relative to the fermion c