Pseudospectra of a NonHermitian Anderson Model
Dimension N=1000
This example of a NonHermitian Anderson model is a tridiagonal matrix
with has exp(0.4) on the first superdiagonal,
exp(0.4) on the first subdiagonal, and
random entries uniformly distributed between [1.5,1.5] on
the main diagonal.
This type of model was first suggested by N. Hatano and D. R. Nelson,
"Localization transitions in nonHermitian quantum mechanics",
Phys. Rev. Lett. 77 (1996), 570573.
Pseudospectra of a related random bidiagonal model are analyzed in
[TCE01].
Further details about this example can be found on the page:
Pseudospectra of Random Matrices: The NonHermitian Anderson Model.
Use the following MATLAB code compute a similar image using
EigTool.
To mimic the example above, set N=1000 below.
N = 100;
g = 0.4;
A = exp(g)*diag(ones(N1,1),1) + ...
diag(3*rand(N,1)1.5) + ...
exp(g)*diag(ones(N1,1),1);
opts.npts = 20;
opts.ax = [4 4 1.5 1.5];
opts.levels = [11:1];
eigtool(A, opts)
Download this code: randand.m.
