The Berry-Tabor Conjecture

Abstract. One of the central observations of quantum chaology is that sta-tistical properties of quantum spectra exhibit surprisingly universal features, which seem to mirror the chaotic or regular dynamical properties of the under-lying classical limit. I will report on recent studies of simple regular systems, where some of the observed phenomena can be established rigorously. The results discussed are intimately related to the distribution of values of qua-dratic forms, and in particular to a quantitative version of the Oppenheim conjecture. Quantum chaos One of the main objectives of quantum chaology is to identify characteristic prop-erties of quantum systems which, in the semiclassical limit, reflect the regular or chaotic features of the underlying classical dynamics. Take for example the geodesic flow on the unit tangent bundle of a compact two-dimensional Riemannian surface M. The corresponding quantum system is described by the stationary Schrödinger equation −∆ϕj = λjϕj, (1) where ∆ is the Laplacian of M, λj represent the quantum energy eigenvalues and ϕj the corresponding eigenfunctions. The spectrum of the negative Laplacian is a discrete ordered subset of the real line, 0 ≤ λ1 < λ2 ≤ λ3 ≤ · · · → ∞. (2) According to Weyl’s law, the number of eigenvalues below λ is asymptotically #{j: λj ≤ λ} ∼ area(M)4pi λ (3) as λ → ∞. Hence the mean spacing between adjacent levels is asymptotically 4pi / area(M). For simplicity, we may assume in what follows that area(M) = 4pi

Gender strategies in antiquity : Judith's performance.

Although the construction of gender as inherently hierarchical, patriarchal and heterosexually biased has been all-pervasive in society, there has been an equally consistent pattern of deconstruction, evident from antiquity to the present day. Perhaps surprisingly one can see this subversive gender play being utilized by biblical authors. This paper focuses on the story of the female heroine, Judith, as an illustration of gender subversion in the ancient world. Judith is allowed to break traditional gender constraints and stride across the gender spectrum. The author of the book of Judith uses the device of unconventionality to subvert the readers' expectations. In permitting Judith to transcend gender roles and boundaries, the power of the deity is emphasized