




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 onevalued
offpeak 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
twovalued offpeak 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 lowenergy 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 = {37313749}, volume = {31} }
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© by Stephan Mertens
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updated on Thursday, April 29th 2010, 14:52:17 CET;