General source design for prescribed nonequilibrium evolution

Determine whether, for a specified Hamiltonian and desired ratio-field profile f_desired(x,t), there exists a mathematically admissible pair consisting of a Schrödinger source field J(x,t) and Hamiltonian operator H such that the source-modified de Broglie-Bohm ratio field satisfies f(x,t;H,J)=f_desired(x,t) for almost all configuration-space points and times.

Background

The source-modified transport equation permits the source field to act as a local source or sink for the ratio f=P/|ψ_J|². The paper solves a special trajectory-level design problem by constructing sources that enforce exponential relaxation toward f=1. It does not establish a general existence theory for arbitrary prescribed profiles, Hamiltonians, and source fields.