Movies for Revivals and Fractalization
in the Linear Schrödinger Equation


Movies connected with the paper

  • Olver, P.J., Sheils, N.E., and Smith, D.A., Revivals and fractalisation in the linear free space Schrödinger equation, preprint, 2018.   pdf

    The Julia code used to make these videos is available on GitLab.


    Pseudoperiodic boundary conditions

    Piecewise constant initial data with energy-conserving boundary conditions

    β_{11}=-1, β_{12}=0, β_{13}=5, β_{14}=0, β_{22}=-1, β_{23}=0, β_{24}=1/5, L=1, c=L/2, w=L/4


    Piecewise constant initial data with energy-non-conserving boundary conditions

    β_{11}=-1, β_{12}=0, β_{13}=2, β_{14}=0, β_{22}=-1, β_{23}=0, β_{24}=1/5, L=1, c=L/2, w=L/4


    narrow piecewise linear initial data with energy-non-conserving boundary conditions

    β_{11}=-1, β_{12}=0, β_{13}=2, β_{14}=0, β_{22}=-1, β_{23}=0, β_{24}=1/5, L=1, c=L/8, w=L/50, r=8


    Narrow piecewise linear initial data which translates with energy-non-conserving boundary conditions

    β_{11}=-1, β_{12}=0, β_{13}=2, β_{14}=0, β_{22}=-1, β_{23}=0, β_{24}=1/5, L=1, w=L/50, r=8


    Generic linear homogeneous boundary conditions

    Piecewise constant initial data with real Robin boundary data (κ_j real)

    β_{11}=-2, β_{12}=1, β_{13}=0, β_{14}=0, β_{22}=0, β_{23}=0, β_{24}=1, L=1, c=L/2, w=L/4, r=0


    piecewise constant initial data with real Robin boundary data (κ_j real or imaginary)

    β_{11}=-.7, β_{12}=1, β_{13}=0, β_{14}=0, β_{22}=0, β_{23}=0, β_{24}=1, L=1, c=L/2, w=L/4, r=0


    Piecewise constant initial data with generic boundary data (κ_j complex, energy growth)

    β_{11}=10, β_{12}=-13, β_{13}=2, β_{14}=-.1, β_{22}=19, β_{23}=1, β_{24}=.1, L=1, c=L/2, w=L/4, r=0


    Piecewise constant initial data with complex Robin boundary data (energy decay)

    β_{11}=-4, β_{12}=i, β_{13}=0, β_{14}=0, β_{22}=0, β_{23}=0, β_{24}=1, L=1, c=L/2, w=L/4, r=0