Jensen-Shannon divergence and non-linear quantum dynamics

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• 作者：Saeid Molladavoudi^a ; ^{saeid.molladavoudi@gmail.com} ; Hishamuddin Zainuddin^a ; ^b ; Kar Tim Chan^b
• 关键词：Measures of information theory ; Non-linear quantum dynamics ; Geometry of quantum mechanics
• 刊名：Physics Letters A
• 出版年：2012
• 期刊代码：57_03759601
• 类别：ph
• 出版时间：21 May, 2012
• 卷：376
• 期：26-27
• 页码：1955-1961
• 文件大小：218 K

摘要

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 Schr枚dinger 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.