From Modified Newtonian Dynamics to Superfluid Vacuum Theory.

Herein is a review of the essentials of Modified Newtonian Dynamics (MOND) versus dark matter models based on Superfluids for modeling galactic rotation curves. We review the successes and issues of both approaches. We then mention a recent alternative based on the Superfluid Vacuum Theory (SVT) with a nonlinear logarithmic Schrödinger equation (LogSE) which reconciles both approaches, retains the essential success of MOND and the Superfluid nature but does not necessitate the hypothesis of processes including dark matter. We conclude with the implications of this SVT alternative on quantum theory itself.

Direct optimization of nodal hypersurfaces in approximate wave functions.

The fixed-node variant of the diffusion quantum Monte Carlo method (FN-DMC) is capable of obtaining the exact eigenvalues (albeit numerically with statistical error) of a many-electron Hamilton operator, provided that the nodal hypersurface of the exact wave function is given. The use of nodes of a trial wave function leads to the node location error. The authors have developed local criteria to assess the accuracy of the nodes based on the distances of the nodal hypersurfaces of PsiT, TPsiT, and HPsiT which coincide for the exact wave function. These criteria are used to develop direct optimization methods for the nodal hypersurface. The optimization of the nodes is demonstrated for simple wave functions of the Be atom and the C2 molecule and verified with FN-DMC calculations.