Eigen model as a quantum spin chain: exact dynamics
David Saakian, Chin-Kun Hu
TL;DR
This paper maps the Eigen model of biological evolution onto a quantum spin chain, enabling exact calculations of relaxation times and dynamics using quantum physics methods.
Contribution
It introduces a novel mapping of the Eigen model to a non-Hermitian quantum spin chain, allowing for exact analysis of the model's dynamics.
Findings
Derived exact relaxation periods for the Eigen model.
Analyzed dynamics with a simple fitness function case.
Provided insights into the approach to static energy landscapes.
Abstract
We map Eigen model of biological evolution [Naturwissenschaften {\bf 58}, 465 (1971)] into a one-dimensional quantum spin model with non-Hermitean Hamiltonian. Based on such a connection, we derive exact relaxation periods for the Eigen model to approach static energy landscape from various initial conditions. We also study a simple case of dynamic fitness function.
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