Quantum Fluid Dynamics from Path Integrals

In this work, we develop analytical solutions to the general problem of computing Quantum Trajectories, within the framework of quantum fluid dynamics (QFD). The state-of-the-art technique in the field is to simultaneously solve the non-linear, coupled partial differential equations (PDEs) numerically. We, however, set off from Feynman Path Integrals, and analytically compute the propagator for a general system. This, then, is used to compute the Quantum Potential, which can generate Quantum Trajectories. For cases, where a closed-form solution is not possible, the problem is shown to be reducible to a single real-valued numerical integration (linear time complexity). The work formally bridges the Path Integral approach with Quantum Fluid Dynamics. As a model application to illustrate the method, we solve for the Quantum Potential of Quartic Anharmonic Oscillator and delve into seeking insight into one of the long-standing debates with regard to Quantum Tunneling.