Jensen-Shannon Divergence and Non-linear Quantum Dynamics
arXiv:1210.3879 · doi:10.1016/j.physleta.2012.05.007
Abstract
Using the statistical inference method, a non-relativistic, spinless, non-linear quantum dynamical equation is derived with the Fisher information metric substituted by the Jensen-Shannon distance information. Among all possible implications, it is shown that the non-linear Schrödinger equation preserves the symplectic structure of the complex Hilbert space, hence a Hamiltonian dynamics. The canonically projected dynamics is obtained on the corresponding projective Hilbert space of pure state density operators.
19 pages