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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., Comment: 36 pages,submitted to Quantum Reports

In this paper we derive a new hybrid model for drift di usion equations. This model provides a description of the quantum phenomena in the parts of the device where they are relevant, and degenerates to a semiclassical model where quantum e ects are negligible, so that the system can be considered classically. The study of quantum correction to the equation of state of an electron gas in a semiconductor with the assumption of localized quantum e ects leads to a further condition on the classical-quantum interface. Moreover, we prove the existence of weak solutions for our hybrid model. Finally, we present numerical results for di erent devices, by means of Colsys software.