  In this Ph.D. thesis quantum Monte Carlo methods are applied to investigate
the properties of a number of ultracold quantum systems. In Chapter 1 we
discuss the analytical approaches and approximations used in the subsequent
Chapters; also we describe the general concepts of the two-particle scattering
problem as a tool to construct Jastrow terms in trial wave functions. Chapter 2
explains in details the Quantum Monte Carlo methods employed in our
calculations from the theoretical and practical points of view. In Chapter 3 we
explain the Ewald summation technique, applied to a power-law 1/|r|k
interaction potential, and a generic approach to obtain the Ewald terms. The
obtained expressions of this analytic work are implemented into simulations of
different physically relevant systems (Rydberg atoms and Yukawa particles).
Chapter 5 is devoted to the modelling of a system, governed by the model
potential between Rydberg atoms $1/r^6$. The phase diagram of the system is
obtained for a relevant range of densities and temperatures, combining quantum
simulations at low temperature and classical treatment at higher temperature. A
special attention is paid to the classical description of this system, composed
of Rydberg atoms, and its comparison to the quantum system. In Chapter 4 we
present the simulation of a system with the Yukawa interaction potential. The
following Chapter 6 presents the results of the Quantum Monte Carlo simulations
of molecular para-hydrogen at zero and finite temperatures, performed in our
Group. Conclusions are drawn in Chapter 7.
