Can fluctuating quantum states acquire the classical behavior on large scale?

Abstract

The quantum hydrodynamic analogy (QHA) equivalent to the Schrodinger equation is generalized to its stochastic version by a systematic technique. On large scale, the quantum stochastic hydrodynamic analogy (QSHA) shows dynamics that under some circumstances may acquire the classical evolution. The QSHA puts in evidence that in presence of spatially distributed noise the quantum pseudo-potential restores the quantum behavior on a distance shorter than the correlation length of fluctuations (named here lc) of the quantum wave function modulus. The quantum mechanics is achieved in the deterministic limit when lc tends to infinity with respect to the scale of the problem. When the physical length of the problem is of order or larger than lc, the quantum potential may have a finite range of efficacy maintaining the non-local behavior on a distance lL (named here "quantum non-locality length") depending both by the noise amplitude and by the inter-particle strength of interaction. In the deterministic limit (quantum mechanics) the model shows that the "quantum non-locality length" lLalso becomes infinite. The QSHA unveils that in linear systems fluctuations are not sufficient to break the quantum non-locality showing that lL is infinite even if lc is finite.