Data for On The Finite-Size Lyapunov Exponent For The Schrodinger Operator With Skew-Shift Potential

<p>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.&nbsp; The ZIP decompresses to about 26GB, containing multiple files:</p> <p>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.&nbsp; This gives a total of 40401x30001=1212070401 lines.</p> <p>Upper bounds.txt: individual upper bounds for equation (9) calculated at various points.&nbsp; The bound in this equation in the published paper is the worst of these.</p> <p>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> &nbsp;&nbsp; &nbsp;X: The x-coordinate of the point represented by the line in question.<br> &nbsp;&nbsp; &nbsp;Y: The y-coordinate.<br> &nbsp;&nbsp; &nbsp;Exact_x, Exact_y: The x- and y-coordinates to the maximum precision the computer used.&nbsp; In case, for instance, the x-coordinate is defined to be 0.5 but is actually 0.5000000000000001 in memory.<br> &nbsp;&nbsp; &nbsp;Matrix: The matrix generated at this point, modulo a certain normalization (see below).<br> &nbsp;&nbsp; &nbsp;Result: The log of the norm of the matrix.&nbsp; This has been corrected for the normalization -- it is calculated as if the matrix had never been normalized.<br> &nbsp;&nbsp; &nbsp;Normalizationcount: The actual matrix generated is too large to store in memory, so the matrix we store and output is (Matrix)x(Normalizer^Normalizationcount).&nbsp; We used a normalizer of 0.01.<br> This file was calculated with the values E=0, N=30000, lambda=1/2.&nbsp; The header line means that this file contains 4004001+1=4004002 lines in total.</p> <p>E=0/N/2001x2001 random grid.tsv: As with the 2001x2001 grid.tsv file, but missing the exact_x and exact_y coordinates.&nbsp; Instead, the x and y values are both exact and randomly chosen.&nbsp; The lines in the file are in no particular order.&nbsp; This file contains the data for the Monte Carlo approximation used in the paper.</p> <p>E=0/2N/2001x2001 grid.tsv: As with its counterpart in the folder labeled N, but calculated with N=60000 instead.</p> <p>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).&nbsp; This folder also contains no random or Monte Carlo calculations.</p> <p>Code/Multiplier.m: MATLAB code to generate the skew matrix at a given point.</p> <p>Code/Iterator.m: MATLAB code to iterate over a series of points and call Multiplier at each.</p> <p>Code/Striper.m: MATLAB code to split up the input space into a series of stripes and call Iterator on exactly one of them.&nbsp; We performed our calculations in parallel, each job consisting of calling Striper on a different stripe number.</p> <p>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.</p> <p>Code/BadSetIterator.m: As with Iterator.m, but calls Badfinder.</p> <p>Code/BadSetStriper.m: As with Striper.m, but calls BadSetIterator.&nbsp; (The function in this file is also called Striper.)</p>