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

The ratio of two consecutive level spacings has emerged as a very usefulmetric in investigating universal features exhibited by complex spectra. Itdoes not require the knowledge of density of states and is therefore quiteconvenient to compute in analyzing the spectrum of a general system. TheWigner-surmise-like results for the ratio distribution are known for theinvariant classes of Gaussian random matrices. However, for the crossoverensembles, which are useful in modeling systems with partially brokensymmetries, corresponding results have remained unavailable so far. In thiswork, we derive exact results for the distribution and average of the ratio oftwo consecutive level spacings in the Gaussian orthogonal to unitary crossoverensemble using a $3\times 3$ random matrix model. This crossover is useful inmodeling time-reversal symmetry breaking in quantum chaotic systems. Althoughbased on a $3\times 3$ matrix model, our results can also be applied in thestudy of large spectra, provided the symmetry-breaking parameter facilitatingthe crossover is suitably scaled. We substantiate this claim by consideringGaussian and Laguerre crossover ensembles comprising large matrices. Moreover,we apply our result to investigate the violation of time-reversal invariance inthe quantum kicked rotor system.

Distribution of the ratio of two consecutive level spacings in orthogonal to unitary crossover ensembles