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.

Abstract. In this paper we derive a new hybrid model for drift diffusion 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 effects 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 effects 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 different devices, by means of Colsys software.

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Making use of the poroelastic theory for hydrated polymeric matrices, the ultrasound (US) propagation in a gel medium filled by spherical cells is studied. The model describes the connection between the poroelastic structure of living tissues and the propagation behavior of the acoustic waves. The equation of fast compressional wave, its phase velocity and its attenuation as a function of the elasticity, porosity and concentration of the cells into the gel external matrix are investigated. The outcomes of the theory agree with the measurements done on Alginic acid gel scaffolds inseminated by porcine liver cells at various concentrations. The model is promising in the quantitative non-invasive estimation of parameters that could assess the change in the tissue structure, composition and architecture.Keywords ultrasound, non-invasive assessment of biological tissue, poroelastic model of living tissues, high frequency poroelastic waves in soft tissues

The paper investigates the quantum fluctuating dynamics by using the stochastic generalization of the Madelung quantum-hydrodynamic approach. By using the discrete approach, the path integral solution is derived in order to investigate how the final stationary configuration is obtained from the initial quantum superposition of states. The model shows that the quantum eigenstates remain stationary configurations with a very small perturbation of their mass density distribution and that any eigenstate, contributing to a quantum superposition of states, can be reached in the final stationary configuration. When the non-local quantum potential acquires a finite range of interaction, the work shows that the macroscopic coarse-grained description of the theory can lead to a really classical system. The minimum uncertainty attainable in the stochastic Madelung model is shown to be compatible with maximum speed of transmission of information and interactions. The theory shows that, in the quantum deterministic limit, the uncertainty relations of quantum mechanics are obtained. The connections with the decoherence theory and the Copenhagen interpretation of quantum mechanics are also discussed.