greenline
rgstripes
Otto-Bild Stephan Mertens - Publications
Home | Research | Publications | Teaching | Smorgasbord
greenline

On the ground states of the Bernasconi model

Stephan Mertens and Christine Bessenrodt


Abstract

The ground states of the Bernasconi model are binary $\pm1$ sequences of length $N$ with low autocorrelations. We introduce the notion of perfect sequences, binary sequences with one-valued off-peak correlations of minimum amount. If they exist, they are ground states. Using results from the mathematical theory of cyclic difference sets, we specify all values of $N$ for which perfect sequences do exist and how to construct them. For other values of $N$, we investigate almost perfect sequences, i.e.\ sequences with two-valued off-peak correlations of minimum amount. Numerical and analytical results support the conjecture that almost perfect sequences do exist for all values of $N$, but that they are not always ground states. We present a construction for low-energy configurations that works if $N$ is the product of two odd primes.


BiBTeX Entry

@article{,
   author    = {Stephan Mertens and Christine Bessenrodt},
   title     = {On the ground states of the {B}ernasconi model},
   year      = {1998},
   journal   = {J.~Phys.~A},
   pages     = {3731-3749},
   volume    = {31}
}

Download:

mertens-bessenrodt.pdf

greenline
rgstripes
top Home | Research | Publications | Teaching | Smorgasbord
greenline

© by Stephan Mertens
URL: http://
updated on Thursday, April 29th 2010, 14:52:17 CET;