A Path Integral approach to Quantum Fluid Dynamics.

In this work we develop a new alternative approach towards solutions of Quantum Trajectories, within the framework of quantum fluid dynamics (QFD), using the Path Integral method. The state-of-the-art technique in the field is to solve the non-linear, coupled partial differential equations (PDEs) simultaneously. We, however opt for a fundamentally different route, by first developing a formal closed form expression for the Path Integral propagator as a functional of the classical path. The method is exact and is applicable in many dimensions as well as multi-particle cases. This, then, is used to compute the Quantum Potential, which, in turn, can generate Quantum Trajectories. For cases, where closed form solution is not possible, the problem is boiled down to solving the classical path (linear time complexity) as a boundary value problem. The work formally bridges the Path Integral approach with Quantum Fluid Dynamics. As a model application to illustrate the method, we work out a toy model viz. the double-well potential, where the boundary value problem for the classical path has been computed perturbatively. We, then, delve in seeking insight into one of the long standing debates with regard to Quantum Tunneling.