Jensen–Shannon divergence and non-linear quantum dynamics

• Published in: Physics letters. A Vol. 376; no. 26-27; pp. 1955 - 1961
• Main Authors: Molladavoudi, Saeid, Zainuddin, Hishamuddin, Chan, Kar Tim
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 21.05.2012
• Subjects: Geometry of quantum mechanics; Measures of information theory; Non-linear quantum dynamics; Geometry of quantum mechanics; Measures of information theory; Non-linear quantum dynamics
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2012.05.007

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. ► Using the inference method, a non-linear Schrödinger equation is derived. ► The non-linear Schrödinger equation is Hamiltonian dynamics in the Hilbert space. ► The canonically projective dynamics is obtained on the projective Hilbert space.