Goldstone boson counting in linear sigma models with chemical potential

We analyze the effects of finite chemical potential on spontaneous breaking of internal symmetries within the class of relativistic field theories described by the linear sigma model. Special attention is paid to the emergence of ``abnormal'' Goldstone bosons with quadratic dispersion relation. We show that their presence is tightly connected to nonzero density of the Noether charges, and formulate a general counting rule. The general results are demonstrated on an SU(3)xU(1) invariant model with an SU(3)-sextet scalar field, which describes one of the color-superconducting phases of QCD.Comment: 10 pages, REVTeX4, 4 eps figures, v2: general discussion in Sec. IV expanded and improved, references added, other minor corrections throughout the tex

Randomized Rounding for the Largest Simplex Problem

The maximum volume $j$-simplex problem asks to compute the $j$-dimensional simplex of maximum volume inside the convex hull of a given set of $n$ points in $\mathbb{Q}^d$. We give a deterministic approximation algorithm for this problem which achieves an approximation ratio of $e^{j/2 + o(j)}$. The problem is known to be $\mathrm{NP}$-hard to approximate within a factor of $c^{j}$ for some constant $c > 1$. Our algorithm also gives a factor $e^{j + o(j)}$ approximation for the problem of finding the principal $j\times j$ submatrix of a rank $d$ positive semidefinite matrix with the largest determinant. We achieve our approximation by rounding solutions to a generalization of the $D$-optimal design problem, or, equivalently, the dual of an appropriate smallest enclosing ellipsoid problem. Our arguments give a short and simple proof of a restricted invertibility principle for determinants

Cliffordons

At higher energies the present complex quantum theory with its unitary group might expand into a real quantum theory with an orthogonal group, broken by an approximate $i$ operator at lower energies. Implementing this possibility requires a real quantum double-valued statistics. A Clifford statistics, representing a swap (12) by a difference $\gamma_1-\gamma_2$ of Clifford units, is uniquely appropriate. Unlike the Maxwell-Boltzmann, Fermi-Dirac, Bose-Einstein, and para- statistics, which are tensorial and single-valued, and unlike anyons, which are confined to two dimensions, Clifford statistics are multivalued and work for any dimensionality. Nayak and Wilczek proposed a Clifford statistics for the fractional quantum Hall effect. We apply them to toy quanta here. A complex-Clifford example has the energy spectrum of a system of spin-1/2 particles in an external magnetic field. This supports the proposal that the double-valued rotations --- spin --- seen at current energies might arise from double-valued permutations --- swap --- to be seen at higher energies. Another toy with real Clifford statistics illustrates how an effective imaginary unit $i$ can arise naturally within a real quantum theory.Comment: 15 pages, no figures; original title ("Clifford statistics") changed; to appear in J. Math. Phys., 42, 2001. Key words: Clifford statistics, cliffordons, double-valued representations of permutation groups, spin, swap, imaginary unit $i$, applications to quantum space-time and the Standard Model. Some of these results were presented at the American Physical Society Centennial Meeting, Atlanta, March 25, 199

The relationship between parental education and children's schooling in a time of economic turmoil: The case of East Zimbabwe, 2001 to 2011.

Using data collected from 1998 to 2011 in a general population cohort study in eastern Zimbabwe, we describe education trends and the relationship between parental education and children's schooling during the Zimbabwean economic collapse of the 2000s. During this period, the previously-rising trend in education stalled, with girls suffering disproportionately; however, female enrolment increased as the economy began to recover. Throughout the period, children with more educated parents continued to have better outcomes such that, at the population level, an underlying increase in the proportion of children with more educated parents may have helped to maintain the upwards education trend

A structural perspective of the role of IP6 in immature and mature retroviral assembly

The small cellular molecule inositol hexakisphosphate (IP6) has been known for ~20 years to promote the in vitro assembly of HIV-1 into immature virus-like particles. However, the molecular details underlying this effect have been determined only recently, with the identification of the IP6 binding site in the immature Gag lattice. IP6 also promotes formation of the mature capsid protein (CA) lattice via a second IP6 binding site, and enhances core stability, creating a favorable environment for reverse transcription. IP6 also enhances assembly of other retroviruses, from both the Lentivirus and the Alpharetrovirus genera. These findings suggest that IP6 may have a conserved function throughout the family Retroviridae. Here, we discuss the different steps in the viral life cycle that are influenced by IP6, and describe in detail how IP6 interacts with the immature and mature lattices of different retroviruses

Synchronization of chaotic networks with time-delayed couplings: An analytic study

Networks of nonlinear units with time-delayed couplings can synchronize to a common chaotic trajectory. Although the delay time may be very large, the units can synchronize completely without time shift. For networks of coupled Bernoulli maps, analytic results are derived for the stability of the chaotic synchronization manifold. For a single delay time, chaos synchronization is related to the spectral gap of the coupling matrix. For networks with multiple delay times, analytic results are obtained from the theory of polynomials. Finally, the analytic results are compared with networks of iterated tent maps and Lang-Kobayashi equations which imitate the behaviour of networks of semiconductor lasers

A non-symmetric Yang-Baxter Algebra for the Quantum Nonlinear Schr\"odinger Model

We study certain non-symmetric wavefunctions associated to the quantum nonlinear Schr\"odinger model, introduced by Komori and Hikami using Gutkin's propagation operator, which involves representations of the degenerate affine Hecke algebra. We highlight how these functions can be generated using a vertex-type operator formalism similar to the recursion defining the symmetric (Bethe) wavefunction in the quantum inverse scattering method. Furthermore, some of the commutation relations encoded in the Yang-Baxter equation for the relevant monodromy matrix are generalized to the non-symmetric case.Comment: 31 pages; added some references; minor corrections throughou

Zassenhaus conjecture for central extensions of S5

We confirm a conjecture of Zassenhaus about rational conjugacy of torsion units in integral group rings for a covering group of the symmetric group S5 and for the general linear group GLð2; 5Þ. The first result, together with others from the literature, settles the conjugacy question for units of prime-power order in the integral group ring of a finite Frobenius group