Scaling of the reduced energy spectrum of random matrix ensemble
School of Science, Hangzhou Dianzi University, 310027, Hangzhou, China
Accepted: 31 December 2020
Published online: 13 January 2021
We study the reduced energy spectrum , which is constructed by picking one level from every n levels of the original spectrum , in a Gaussian ensemble of random matrix with Dyson index . It is shown the joint probability distribution of bears the same form as with a rescaled parameter . Notably, the nth-order level spacing and gap ratio in become the lowest order ones in , which explains their distributions found separately by recent studies in a consistent way. Our results also establish the higher-order spacing distributions in random matrix ensembles beyond GOE, GUE and GSE and reveal a hierarchy of structures hidden in the energy spectrum.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2021