Quantum Fluid Dynamics (QFD ) or Bohmian Representation of Schrödinger Equation with Navier – Stokes Type Dissipation Attila Askar Koc University, Sariyer, Istanbul 34450, Turkey

The Quantum Fluid Dynamics (QFD) representation has its foundations in the works of Madelung, De Broglie and Bohm. It is an interpretation of quantum mechanics with the goal to find classically identifiable dynamical variables at the sub-particle level. The approach is partly motivated by Einstein’s questioning of the completeness of the quantum theory. Einstein expected the complete theory to have nonlinearity and admit solutions with “particle” nature, similar to solitons in contemporary terminology.
The QFD approach leads to two conservation laws, for ”mass” and ”momentum”, similar to those in fluid-dynamics for a compressible fluid as a set of nonlinear partial differential equations. The QFD formalism is utilized advantageously for solving the time dependent Schrödinger equation for scattering problems.
This paper extends the QFD formalism to include dissipation in the form of Navier – Stokes term in classical fluid dynamics. The introduction of dissipation in the Navier – Stokes sense transform the differential equations from hyperbolic to parabolic type, with nonlinear and dispersive terms. These offer a natural framework for fundamentally new phenomena, in particular possibility of dissipation in quantum mechanics, solitons, vortices and chaos.