Quantum chaos for nonstandard symmetry classes in the Feingold-Peres model of coupled tops

We consider two coupled quantum tops with angular momentum vectors $\mathbf{L}$ and $\mathbf{M}$. The coupling Hamiltonian defines the Feinberg-Peres model which is a known paradigm of quantum chaos. We show that this model has a nonstandard symmetry with respect to the Altland-Zirnbauer tenfold symmetry classification of quantum systems which extends the well-known threefold way of Wigner and Dyson (referred to as `standard' symmetry classes here). We identify that the nonstandard symmetry classes BD$I_0$ (chiral orthogonal class with no zero modes), BD$I_1$ (chiral orthogonal class with one zero mode) and C$I$ (antichiral orthogonal class) as well as the standard symmetry class A$I$ (orthogonal class). We numerically analyze the specific spectral quantum signatures of chaos related to the nonstandard symmetries. In the microscopic density of states and in the distribution of the lowest positive energy eigenvalue we show that the Feinberg-Peres model follows the predictions of the Gaussian ensembles of random-matrix theory in the appropriate symmetry class if the corresponding classical dynamics is chaotic. In a crossover to mixed and near-integrable classical dynamics we show that these signatures disappear or strongly change.Comment: 15 page

Adjusted odds ratios (OR) for living in an urban environment and obesity using stratification by country/countries, per capita GNI, year of fieldwork, sex, age of study population and criteria for obesity.

<p>Twenty eight studies contributed to 37 independent age and sex adjusted estimates (<a href="http://www.plosone.org/article/info:doi/10.1371/journal.pone.0113547#pone-0113547-g001" target="_blank">Figure 1</a>); Reference group is living in a rural environment; GNI gross national income; WC waist circumference;</p><p>* p-value for heterogeneity chi-square;</p><p>** Likelihood ratio test for heterogeneity between subgroup by meta-regression, providing F-ratio and p-values.</p><p>Adjusted odds ratios (OR) for living in an urban environment and obesity using stratification by country/countries, per capita GNI, year of fieldwork, sex, age of study population and criteria for obesity.</p

Flow chart of articles included in the review.

<p>Flow chart of articles included in the review.</p

chain drug

drug n....over rough country,see, you had to have drugs. I never used two, though,for all I seed people with two - one on each runner. We always had a chain drug - a chain wrapped around the nose o' the sled,see, to drop.... An' that was a great help sometimes when the dogs 'd want to go where you didn't want 'em to go. You drop that drug an' get 'em buckled down to it, an' they'd understand you wanted them to stop.YesDNE-cit J.D.A. WIDDOWSONAUG 1973Used I and SupUsed IUsed

Association (log odds ratio) between living in an urban environment and obesity by GNI per capita.

<p>Size of circles reflects sample size. Higher log odds ratio (logor) reflect larger effect size for living in an urban environment and obesity; gross national income (GNI) per capita in US dollar corresponding to year and country of fieldwork; Reference group is living in a rural environment.</p