# 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