  The work derives the quantum evolution in a fluctuating vacuum by introducing
the related (dark) mass density noise into the Madelung quantum hydrodynamic
model. The paper shows that the classical dynamics can spontaneously emerge on
the cosmological scale allowing the realization of the classical
system-environment super system. The work shows that the dark matter-induced
noise is not spatially white and owns a well defined correlation function with
the intrinsic vacuum physical length given by the De Broglie one. The resulting
model, in the case of microscopic systems, whose dimension is much smaller than
the De Broglie length, leads to the Langevin-Schrodinger equation whose
friction coefficient is not constant. The derivation puts in evidence the range
of application of the Langevin-Schrodinger equation and the approximations
inherent to its foundation. The work shows that the classical physics can be
achieved in a description whose length scale is much bigger both than the De
Broglie length and the quantum potential range of interaction. The model shows
that the quantum-to-classical transition is not possible in linear systems, and
defines the long-distance characteristics as well as the range of interaction
of the non-local quantum potential in order to have a coarse-grained
large-scale classical phase. The theory also shows that the process of
measurement (by a large-scale classical observer) satisfies the minimum
uncertainty conditions if interactions and information do not travel faster
than the light speed, reconciling the quantum entanglement with the
relativistic macroscopic locality.
