Quantum spin model fitting the Yule distribution of oligonucleotides in DNA

A quantum spin chain is identified by the labels of a vector state of a Kashiwara crystal basis. The intensity of the one-spin flip is assumed to depend from the variation of the labels. The rank ordered plot of the numerically computed, averaged in time, transition probabilities is nicely fitted by a Yule distribution, which is the observed distribution of the ranked short oligonucleotides frequency in DNA.