Statistics of the spectral form factor in the self-dual kicked Ising model

Ana Flack (Author), Bruno Bertini (Author), Tomaž Prosen (Author)

Abstract

We compute the full probability distribution of the spectral form factor in the self-dual kicked Ising model by providing an exact lower bound for each moment and verifying numerically that the latter is saturated. We show that at long enough times the probability distribution agrees exactly with the prediction of random-matrix theory if one identifies the appropriate ensemble of random matrices. We find that this ensemble is not the circular orthogonal one—composed of symmetric random unitary matrices and associated with time-reversal-invariant evolution operators—but is an ensemble of random matrices on a more restricted symmetric space [depending on the parity of the number of sites this space is either S p(N)/U (N) or O(2N)/O(N)×O(N)]. Even if the latter ensembles yield the same averaged spectral form factor as the circular orthogonal ensemble, they show substantially enhanced fluctuations. This behavior is due to a recently identified additional antiunitary symmetry of the self-dual kicked Ising model.

Keywords

statističma fizika;kvantni kaos;statistical physics;quantum chaos;

Data

Language:	English
Year of publishing:	2020
Typology:	1.01 - Original Scientific Article
Organization:	UL FMF - Faculty of Mathematics and Physics
UDC:	536
COBISS:	49281539
ISSN:	2643-1564
Views:	269
Downloads:	149
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary keywords:	statističma fizika;kvantni kaos;
Pages:	str. 043403-1-043403-14
Volume:	ǂVol. ǂ2
Issue:	ǂiss. ǂ4
Chronology:	2020
DOI:	10.1103/PhysRevResearch.2.043403
ID:	12512672