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 Tools annual

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 Tools monthly

Global: Zendy Plus monthly

Presents the access of premium content as premium feature

Premium Content

Global: Zendy Plus annual

Global: Zendy Free Plan

Spectral statistics such as the level spacing statistics and spectral formfactor (SFF) are widely expected to accurately identify ``ergodicity'',including the presence of underlying macroscopic symmetries, in generic quantumsystems ranging from quantized chaotic maps to interacting many-body systems.By studying various quantizations of maximally chaotic maps that break adiscrete classical symmetry upon quantization, we demonstrate that thisapproach can be misleading and fail to detect macroscopic symmetries. Notably,the same classical map can exhibit signatures of different random matrixsymmetry classes in short-range spectral statistics depending on thequantization. While the long-range spectral statistics encoded in the earlytime ramp of the SFF are more robust and correctly identify macroscopicsymmetries in several common quantizations, we also demonstrate analyticallyand numerically that the presence of Berry-like phases in the quantizationleads to spectral anomalies, which break this correspondence. Finally, weprovide numerical evidence that long-range spectral rigidity remains directlycorrelated with ergodicity in the quantum dynamical sense of visiting acomplete orthonormal basis.

Spectral anomalies and broken symmetries in maximally chaotic quantum maps