"On the Remarkable Spectrum of a non Hermitian Random Matrix Model"
Relatore: Prof. Antony Zee- Institute for Theoretical Physics, University of California, Santa Barbara (USA)
19 Ottobre 2004 ore 15.30
|A non-Hermitean random matrix model proposed a few years
ago has a remarkably intricate spectrum. Various attempts
have been made to understand the spectrum, but even
its dimension is not known.
Using the Dyson-Schmidt equation, we show that the spectrum
consists of a non-denumerable set of lines in the complex
plane. Each line is the support of the spectrum of a
periodic Hamiltonian, obtained by the infinite repetition
of any finite sequence of the disorder variables.
Our approach is based on the ``theory of words.''
We make a complete study of all 4-letter words. The spectrum
is complicated because our matrix contains everything that
will ever be written in the history of the universe,
including this particular paper.