Non-Equilibrium Dynamics of Bose Fluids with Time-Dependent Hypernetted-Chain Euler-Lagrange Theory

The aim of this master thesis is to theoretically describe a system of ultracold bosons with an arbitrary time-dependent interaction potential. A time-dependent generalization of the hyper- netted chain Euler-Lagrange formalism has been used to study the dynamics of the Jastrow-type wave function. This method is a variational approach which uses the Meyer-Cluster expansion to relate the radial distribution function to the two-body correlation function. The triplet and elementary diagrams have been neglected. Assuming a homogeneous system we neglect the single particle contributions. The three particle distribution function is approximated by the Kirkwood superposition or the convolution approximation, respectively, resulting in two approximations for the equations of motion. The equations of motion can be simplified by assuming rotational invariance of the interac- tion potential. This simplification allows to reduce the numerical complexity of the problem from three to effectively one dimension and hence allows a simpler numerical treatment. The derived equations of motion (obtained with the Kirkwood superposition approximation) have been solved numerically with the Euler integrator, since the actually planed method (variatio- nal integrators) did not gave satisfying results. This has been verified in the study of the single quantum particle problem in the Madelung formulation. In this work a second numerical method has been investigated. The rotational symmetry of the potential allows to write the result of the Kirkwood superposition approximation as a single, non-linear Schrödinger-like equation. This resulting equation is solved by the operator splitting method. Results for several different quenches of the interaction potential have been obtained with the operator splitting method. It is possible to obtain the dynamic behaviour of the radial distribution function and the pair-phase function with the operator splitting method. The limits of the operator splitting method are analysed within this work, as for ...