Jensen–Shannon divergence and non-linear quantum dynamics
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 pres...
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Published in | Physics letters. A Vol. 376; no. 26-27; pp. 1955 - 1961 |
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Main Authors | , , |
Format | Journal Article |
Language | English |
Published |
Elsevier B.V
21.05.2012
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Subjects | |
Online Access | Get full text |
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Summary: | 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. |
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ISSN: | 0375-9601 1873-2429 |
DOI: | 10.1016/j.physleta.2012.05.007 |