On the remarkable spectrum of a non-Hermitian random matrix model

Authors: Holz D.E.¹; Orland H.¹; Zee A.¹

Source: Journal of Physics A: Mathematical and General, Volume 36, Number 12, 2003 , pp. 3385-3400(16)

Publisher: Institute of Physics Publishing

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Abstract:

A non-Hermitian 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 four-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.

Language: English

Document Type: Miscellaneous

Affiliations: 1: Institute for Theoretical Physics, University of California, Santa Barbara, CA 93106, USA

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