DOI: 10.5281/zenodo.2638903
title: Data for On The Finite-Size Lyapunov Exponent For The Schrodinger Operator With Skew-Shift Potential

description: A ZIP file of computer code and output used in the numerical calculations for <em>On The Finite-Size Lyapunov Exponent For The Schrodinger Operator With Skew-Shift Potential </em>by Paul Michael Kielstra and Marius Lemm.  The ZIP decompresses to about 26GB, containing multiple files:

201x201 bad set grid.txt: A list of 201x201=40401 evenly spaced points on [0, 1]x[0, 1], each written in the form (x, y) and followed by 30000 values of E which are probably bad for that point.  This gives a total of 40401x30001=1212070401 lines.

Upper bounds.txt: individual upper bounds for equation (9) calculated at various points.  The bound in this equation in the published paper is the worst of these.

E=0/N/2001x2001 grid.tsv: A tab-separated values file of 2001x2001=4004001 evenly spaced points on [0, 1]x[0, 1], with headers:<br>
    X: The x-coordinate of the point represented by the line in question.<br>
    Y: The y-coordinate.<br>
    Exact_x, Exact_y: The x- and y-coordinates to the maximum precision the computer used.  In case, for instance, the x-coordinate is defined to be 0.5 but is actually 0.5000000000000001 in memory.<br>
    Matrix: The matrix generated at this point, modulo a certain normalization (see below).<br>
    Result: The log of the norm of the matrix.  This has been corrected for the normalization -- it is calculated as if the matrix had never been normalized.<br>
    Normalizationcount: The actual matrix generated is too large to store in memory, so the matrix we store and output is (Matrix)x(Normalizer^Normalizationcount).  We used a normalizer of 0.01.<br>
This file was calculated with the values E=0, N=30000, lambda=1/2.  The header line means that this file contains 4004001+1=4004002 lines in total.

E=0/N/2001x2001 random grid.tsv: As with the 2001x2001 grid.tsv file, but missing the exact_x and exact_y coordinates.  Instead, the x and y values are both exact and randomly chosen.  The lines in the file are in no particular order.  This file contains the data for the Monte Carlo approximation used in the paper.

E=0/2N/2001x2001 grid.tsv: As with its counterpart in the folder labeled N, but calculated with N=60000 instead.

E=-2.495: As with its counterpart E=0, but everything is calculated with E=-2.495123260049612 (which we round to -2.49512326 in the paper).  This folder also contains no random or Monte Carlo calculations.

Code/Multiplier.m: MATLAB code to generate the skew matrix at a given point.

Code/Iterator.m: MATLAB code to iterate over a series of points and call Multiplier at each.

Code/Striper.m: MATLAB code to split up the input space into a series of stripes and call Iterator on exactly one of them.  We performed our calculations in parallel, each job consisting of calling Striper on a different stripe number.

Code/Badfinder.m: MATLAB code to take a point and output a series of E-values for which that point is in the bad set.

Code/BadSetIterator.m: As with Iterator.m, but calls Badfinder.

Code/BadSetStriper.m: As with Striper.m, but calls BadSetIterator.  (The function in this file is also called Striper.)