Quantum theta functions and Gabor frames for modulation spaces

Representations of the celebrated Heisenberg commutation relations in quantum mechanics and their exponentiated versions form the starting point for a number of basic constructions, both in mathematics and mathematical physics (geometric quantization, quantum tori, classical and quantum theta functions) and signal analysis (Gabor analysis). In this paper we try to bridge the two communities, represented by the two co--authors: that of noncommutative geometry and that of signal analysis. After providing a brief comparative dictionary of the two languages, we will show e.g. that the Janssen representation of Gabor frames with generalized Gaussians as Gabor atoms yields in a natural way quantum theta functions, and that the Rieffel scalar product and associativity relations underlie both the functional equations for quantum thetas and the Fundamental Identity of Gabor analysis.Comment: 38 pages, typos corrected, MSC class change

Imprints of the Quantum World in Classical Mechanics

The imprints left by quantum mechanics in classical (Hamiltonian) mechanics are much more numerous than is usually believed. We show Using no physical hypotheses) that the Schroedinger equation for a nonrelativistic system of spinless particles is a classical equation which is equivalent to Hamilton's equations.Comment: Paper submitted to Foundations of Physic

A New Recursion Relation for the 6j-Symbol

The 6j-symbol is a fundamental object from the re-coupling theory of SU(2) representations. In the limit of large angular momenta, its asymptotics is known to be described by the geometry of a tetrahedron with quantized lengths. This article presents a new recursion formula for the square of the 6j-symbol. In the asymptotic regime, the new recursion is shown to characterize the closure of the relevant tetrahedron. Since the 6j-symbol is the basic building block of the Ponzano-Regge model for pure three-dimensional quantum gravity, we also discuss how to generalize the method to derive more general recursion relations on the full amplitudes.Comment: 10 pages, v2: title and introduction changed, paper re-structured; Annales Henri Poincare (2011

Audiovisual and digital ethnography at Leiden

Global Challenges (FSW

Generalized Quantum Theory of Recollapsing Homogeneous Cosmologies

A sum-over-histories generalized quantum theory is developed for homogeneous minisuperspace type A Bianchi cosmological models, focussing on the particular example of the classically recollapsing Bianchi IX universe. The decoherence functional for such universes is exhibited. We show how the probabilities of decoherent sets of alternative, coarse-grained histories of these model universes can be calculated. We consider in particular the probabilities for classical evolution defined by a suitable coarse-graining. For a restricted class of initial conditions and coarse grainings we exhibit the approximate decoherence of alternative histories in which the universe behaves classically and those in which it does not. For these situations we show that the probability is near unity for the universe to recontract classically if it expands classically. We also determine the relative probabilities of quasi-classical trajectories for initial states of WKB form, recovering for such states a precise form of the familiar heuristic "J d\Sigma" rule of quantum cosmology, as well as a generalization of this rule to generic initial states.Comment: 41 pages, 4 eps figures, revtex 4. Modest revisions throughout. Physics unchanged. To appear in Phys. Rev.

Lifetime distributions in the methods of non-equilibrium statistical operator and superstatistics

A family of non-equilibrium statistical operators is introduced which differ by the system age distribution over which the quasi-equilibrium (relevant) distribution is averaged. To describe the nonequilibrium states of a system we introduce a new thermodynamic parameter - the lifetime of a system. Superstatistics, introduced in works of Beck and Cohen [Physica A \textbf{322}, (2003), 267] as fluctuating quantities of intensive thermodynamical parameters, are obtained from the statistical distribution of lifetime (random time to the system degeneracy) considered as a thermodynamical parameter. It is suggested to set the mixing distribution of the fluctuating parameter in the superstatistics theory in the form of the piecewise continuous functions. The distribution of lifetime in such systems has different form on the different stages of evolution of the system. The account of the past stages of the evolution of a system can have a substantial impact on the non-equilibrium behaviour of the system in a present time moment.Comment: 18 page

Mutation update for the SATB2 gene

SATB2-associated syndrome (SAS) is an autosomal dominant neurodevelopmental disorder caused by alterations in the SATB2 gene. Here we present a review of published pathogenic variants in the SATB2 gene to date and report 38 novel alterations found in 57 additional previously unreported individuals. Overall, we present a compilation of 120 unique variants identified in 155 unrelated families ranging from single nucleotide coding variants to genomic rearrangements distributed throughout the entire coding region of SATB2. Single nucleotide variants predicted to result in the occurrence of a premature stop codon were the most commonly seen (51/120=42.5%) followed by missense variants (31/120=25.8%). We review the rather limited functional characterization of pathogenic variants and discuss current understanding of the consequences of the different molecular alterations. We present an expansive phenotypic review along with novel genotype-phenotype correlations. Lastly, we discuss current knowledge on animal models and present future prospects. This review should help provide better guidance for the care of individuals diagnosed with SAS

Volume I. Introduction to DUNE

The preponderance of matter over antimatter in the early universe, the dynamics of the supernovae that produced the heavy elements necessary for life, and whether protons eventually decay—these mysteries at the forefront of particle physics and astrophysics are key to understanding the early evolution of our universe, its current state, and its eventual fate. The Deep Underground Neutrino Experiment (DUNE) is an international world-class experiment dedicated to addressing these questions as it searches for leptonic charge-parity symmetry violation, stands ready to capture supernova neutrino bursts, and seeks to observe nucleon decay as a signature of a grand unified theory underlying the standard model. The DUNE far detector technical design report (TDR) describes the DUNE physics program and the technical designs of the single- and dual-phase DUNE liquid argon TPC far detector modules. This TDR is intended to justify the technical choices for the far detector that flow down from the high-level physics goals through requirements at all levels of the Project. Volume I contains an executive summary that introduces the DUNE science program, the far detector and the strategy for its modular designs, and the organization and management of the Project. The remainder of Volume I provides more detail on the science program that drives the choice of detector technologies and on the technologies themselves. It also introduces the designs for the DUNE near detector and the DUNE computing model, for which DUNE is planning design reports. Volume II of this TDR describes DUNE\u27s physics program in detail. Volume III describes the technical coordination required for the far detector design, construction, installation, and integration, and its organizational structure. Volume IV describes the single-phase far detector technology. A planned Volume V will describe the dual-phase technology