Nonlinear quantum mechanics as weyl geometry of a classical statistical ensemble

W. R. Wood, G. Papini

D. I. Blokhint︠s︡ev

Carlos Castro

The nonlinear corrections to the Schrödinger equation based on the results of geometric quantum mechanics (GQM) are derived. Such theory derives quantum mechanics from the underlying Weyl space-time geometry associated with the classical ensemble of particle paths given by the solutions of the Hamilton–Jacobi equation.

Alex E. Bernardini, Orfeu Bertolami A

The extension of the phase-space Weyl-Wigner quantum mechanics to the subset of Hamiltonians in the form of H(q,p)=K(p)+V(q) [with K(p) replacing single p^{2} contributions] is revisited. Deviations from classical and stationary profiles are identified in terms of Wigner functions and Wigner currents for Gaussian and gamma/Laplacian distribution ensembles. The procedure is successful in accounting for the exact pattern of quantum fluctuations when compared with the classical phase-space pattern. General results are then specialized to some specific Hamiltonians revealing nonlinear dynamics, and suggest a novel algorithm to treat quantum modifications mapped by Wigner currents. Our analysis shows that the framework encompasses, for instance, the quantized prey-predator-like scenarios subjected to statistical constraints.

N. N. Bogolyubov, A. M. Kurbatov, A. S. Shumovskiǐ

Yoel Tikochinsky, Dror Shalitin