الفهرس 
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Abstract
This thesis suggested theoretical model to use rotating interacting ultracold boson gas, in a state of Bose-Einstein condensation (BEC), as a quantum simulator for superfluid Helium 4He. Special attention was paid to the role of BEC in understanding the physical properties of superfluidity. The finite size and interaction effects on the superfluid 4He below λ-transition are identified. In general, effects of superfluidity including the existence of λ-transition in the heat capacity Cv as a function of temperature and the reduction of the moment of inertia are discussed. A step further, the superfluid fraction is calculated. Detailed qualitatively comparison between the calculated parameters with its corresponding experimental data for 4He are given. The above mentioned parameters are calculated using the semiclassical approxima- tion. Within this approximation we empolyed two therotical approches which are the density of stat approach, sum over energy quantum state converted directly to integration over energy or integration over phase space. The outcome results provide a solid theoretical foundation for future BEC experiments in such field, such as superfluidity nature of condensate boson in optical lattice.