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Extreme physical information and the nonlinear wave equationFormat | Member Price | Non-Member Price |
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Paper Abstract

The nonlinear wave equation an be derived from a principle of extreme physical information (EPI) K. This is for a scenario where a probe electron moves through a medium in a weak magnetic field. The field is caused by a probabilistic line current source. Assume that the probability current density S of the electron is approximately constant, and directed parallel to the current source. Both the source probability amplitudes (rho) and the electron probability amplitudes (phi) are unknowns (called 'modes') of the problem. The net physical information K here consists of two components: functional K

_{1}[(phi) ] due to modes (phi) and K_{2}[(rho) ] due to modes (rho) , respectively. To form K_{1}[(phi) ], the Fisher information functional I_{1}[(phi) ] for the electron modes is first constructed. This is of a fixed mathematical form. Then, a unitary transformation on (phi) to a physical space is sought that leaves I_{1}invariant, as form J_{1}. This is, of course, the Fourier transformation, where the transform coordinates are momenta and I_{1}is essentially the mean-square electron momentum. Information K_{1}[(phi) ] is then defined as (I_{1}- J_{1}). Information K_{2}is formed similarly. The total information K is formed as the sum of the two components K_{1}[(phi) ] and K_{2}[(rho) ], by the additivity of Fisher information, and is then extremized in both (phi) and (rho) . Extremizing first in (rho) gives a Taylor series in powers of (phi)_{n}*(phi)_{n}, which is cut off at the quadratic term. Back-substituting this into the total Lagrangian gives one that is quadratic in (phi)_{n}*(phi)_{n}. Now varying (phi) * gives the required cubic wave equation in (phi) .
Paper Details

Date Published: 15 September 1995

PDF: 10 pages

Proc. SPIE 2528, Optical and Photonic Applications of Electroactive and Conducting Polymers, (15 September 1995); doi: 10.1117/12.219553

Published in SPIE Proceedings Vol. 2528:

Optical and Photonic Applications of Electroactive and Conducting Polymers

Sze Chang Yang; Prasanna Chandrasekhar, Editor(s)

PDF: 10 pages

Proc. SPIE 2528, Optical and Photonic Applications of Electroactive and Conducting Polymers, (15 September 1995); doi: 10.1117/12.219553

Show Author Affiliations

B. Roy Frieden, Optical Sciences Ctr./Univ. of Arizona (United States)

Published in SPIE Proceedings Vol. 2528:

Optical and Photonic Applications of Electroactive and Conducting Polymers

Sze Chang Yang; Prasanna Chandrasekhar, Editor(s)

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