|
ИСТИНА |
Войти в систему Регистрация |
ИСТИНА ИНХС РАН |
||
Rare-event statistics and modular invarianceстатья
Статья опубликована в высокорейтинговом журнале
Статья опубликована в журнале из списка Web of Science и/или Scopus- Авторы: Nechaev S.K., Polovnikov K.E.
- Журнал: Physics Uspekhi
- Том: 60
- Год издания: 2017
- Издательство: Russian Academy of Sciences
- Местоположение издательства: Russian Federation
- DOI: 10.3367/UFNe.2017.01.038106
- Аннотация: We provide simple geometric arguments, based on the Euclid orchard construction, that explain the equivalence of various distributions, resulting from the rare-event statistics. In particular, we discuss the number-theoretic properties of the spectral density of exponentially weighted ensemble of linear polymer chains. It can be shown that the eigenvalue statistics of corresponding adjacency matrices in the sparse regime demonstrates peculiar hierarchical structure and are described by the popcorn (Thomae) function, discontinuous in the dense set of rational numbers. Moreover, at the edges the spectral density exhibits the Lifshitz tails, reminiscent of the 1D Anderson localization. Finally, we suggest a continuous approximation of the popcorn function, based on the Dedekind-function, and demonstrate that the hierarchical ultrametric structure of the popcorn-like distributions is ultimately connected with hidden SL(2;Z) modular symmetry.
- Добавил в систему: Половников Кирилл Евгеньевич