English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Quantum chaotic systems are characterized by energy correlations in theirspectral statistics, usually probed by the distribution of nearest-neighborlevel spacings. Some signatures of chaos, like the spectral form factor (SFF),take all the correlations into account, while others sample only short-range orlong-range correlations. Here, we characterize correlations betweeneigenenergies at all possible spectral distances. Specifically, we study thedistribution of $k$-th neighbor level spacings ($k$nLS) and compute itsassociated $k$-th neighbor spectral form factor ($k$nSFF). This leads to twonew full-range signatures of quantum chaos, the variance of the $k$nLSdistribution and the minimum value of the $k$nSFF, which quantitativelycharacterize correlations between pairs of eigenenergies with any number oflevels $k$ between them. We find exact and approximate expressions for thesesignatures in the three Gaussian ensembles of random matrix theory (GOE, GUEand GSE) and in integrable systems with completely uncorrelated spectra (thePoisson ensemble). We illustrate our findings in a XXZ spin chain withdisorder, which interpolates between chaotic and integrable behavior. Ourrefined measures of chaos allow us to probe deviations from Poissonian andRandom Matrix behavior in realistic systems. This illustrates how the measureswe introduce bring a new light into studying many-body quantum systems, whichlie in-between the fully chaotic or fully integrable models.

Full range spectral correlations and their spectral form factors in chaotic and integrable models