| Summary: | The primary goal of this thesis is to find the distribution function of number of particles imbalance for ultra cold bosons trapped in a double well potential elongated in one direction for different strength of interaction between particles. This distribution function has been found to be Gaussian distribution function in two different limits. The first limit is weak interaction limit, where we only consider one energy level per well that is called "two mode approximation" regime. The second limit is when the interaction energy is in the same order as gap between energy levels where in this case, we consider finite number of levels per well. The standard deviation of number of particles distribution also has been found in both limits to be proportional to the square root of the total number of particles. In addition, some numerical work is done to find these distribution functions and the results are in agreement with analytical results.
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