Phonon dispersion from stationary Schrödinger boundary problem for domain wall for data storage of nanosized ferroics

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In the article we have specified the analytical quantized solutions for the frequency dispersion of soft phonon modes in nanosize ferroics in framework of Landau-Ginsburg-Devonshire (LGD) theory as well as the numerical calculation results for the thin SrTiO_{3} nanofilm have been presented. The frequency quantized dispersion of soft phonon modes in nanosize ferroics found from stationary Schrödinger boundary problem for domain wall are shown to be related with the Rashba and Dresselhaus quantized energies as well as their wave vectors for electrons in quantized magnetic field.       The quantized polarization as well as elastic displacement of stationary Schrödinger boundary problem for domain wall for data storage based on bulk ferroics are found. We have found the quantized solutions of stationarity non-linear high-polinomial Schrödinger or Euler-Lagrange boundary problem for the order parameter as well as elastic displacement in nanosize ferroics. Quantized solutions of one-dimensional Maxwell equations for thin ferroelectric films have been specified which were bonded with stationary solution of cubic and 5-polinomial Schrödinger equation are found.

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