q-series and L-functions related to half-derivatives of the Andrews--Gordon identity

Studied is a generalization of Zagier's q-series identity. We introduce a generating function of L-functions at non-positive integers, which is regarded as a half-differential of the Andrews--Gordon q-series. When q is a root of unity, the generating function coincides with the quantum invariant for the torus knot.Comment: 21 pages, related papers can be found from http://gogh.phys.s.u-tokyo.ac.jp/~hikami

Resonant nonlinear spectroscopy in strong fields

A method is presented to describe multiple resonant nonlinear spectra in the presence of strong laser fields. The Liouville equation for the d. operator of the mol. system is transformed to a time-independent linear equation system. This can be easily solved rigorously by numerical methods or, after partitioning into a strong-field part and a perturbation, the soln. can be obtained anal. by a novel perturbative approach. The results account for power broadening. Rabi splitting of signals, and power-induced extra resonances, the latter being related to the pure dephasing-induced resonances in the weak-field limit. The method can be applied to a large no. of multiple resonant nonlinear spectroscopies, esp. CARS, CSRS, coherent Rayleigh scattering and sum- or difference-frequency generation

Long-Term Data Reveal a Population Decline of the Tropical Lizard Anolis apletophallus, and a Negative Affect of El Nino Years on Population Growth Rate

Climate change threatens biodiversity worldwide, however predicting how particular species will respond is difficult because climate varies spatially, complex factors regulate population abundance, and species vary in their susceptibility to climate change. Studies need to incorporate these factors with long-term data in order to link climate change to population abundance. We used 40 years of lizard abundance data and local climate data from Barro Colorado Island to ask how climate, total lizard abundance and cohort-specific abundance have changed over time, and how total and cohort-specific abundance relate to climate variables including those predicted to make the species vulnerable to climate change (i.e. temperatures exceeding preferred body temperature). We documented a decrease in lizard abundance over the last 40 years, and changes in the local climate. Population growth rate was related to the previous years’ southern oscillation index; increasing following cooler-wetter, la niña years, decreasing following warmer-drier, el nino years. Within-year recruitment was negatively related to rainfall and minimum temperature. This study simultaneously identified climatic factors driving long-term population fluctuations and climate variables influencing short-term annual recruitment, both of which may be contributing to the population decline and influence the population’s future persistence

On the harmonic measure of stable processes

Using three hypergeometric identities, we evaluate the harmonic measure of a finite interval and of its complementary for a strictly stable real L{\'e}vy process. This gives a simple and unified proof of several results in the literature, old and recent. We also provide a full description of the corresponding Green functions. As a by-product, we compute the hitting probabilities of points and describe the non-negative harmonic functions for the stable process killed outside a finite interval

The Uq(sl^(2/1))1U_q(\hat{sl}(2/1))_1-module V(Λ2)V(\Lambda_2) and a Corner Transfer Matrix at q=0

The north-west corner transfer matrix of an inhomogeneous integrable vertex model constructed from the vector representation of $U_q\bigl(sl(2/1)\bigr)$ and its dual is investigated. In the limit $q\to0$, the spectrum can be obtained. Based on an analysis of the half-infinite tensor products related to all CTM-eigenvalues $\geq -4$, it is argued that the eigenvectors of the corner transfer matrix are in one-to-one correspondance with the weight states of the $U_q\bigl((\hat{sl}(2/1)\bigr)_1-$module $V(\Lambda_2)$ at level one. This is supported by a comparison of the comlete set of eigenvectors with a nondegenerate triple of eigenvalues of the CTM-Hamiltonian and the generators of the Cartan-subalgebra of $U_q\bigl(sl(2|1)\bigr)$ to the weight states of $V(\Lambda_2)$ with multiplicity one.Comment: 28 pages, revtex accepted for publication in Nuclear Physics

Thermodynamic Bethe Ansatz for the subleading magnetic perturbation of the tricritical Ising model

We give further support to Smirnov's conjecture on the exact kink S-matrix for the massive Quantum Field Theory describing the integrable perturbation of the c=0.7 minimal Conformal Field theory (known to describe the tri-critical Ising model) by the operator $\phi_{2,1}$. This operator has conformal dimensions $(7/16,7/16)$ and is identified with the subleading magnetic operator of the tri-critical Ising model. In this paper we apply the Thermodynamic Bethe Ansatz (TBA) approach to the kink scattering theory by explicitly utilising its relationship with the solvable lattice hard hexagon model. Analytically examining the ultraviolet scaling limit we recover the expected central charge c=0.7 of the tri-critical Ising model. We also compare numerical values for the ground state energy of the finite size system obtained from the TBA equations with the results obtained by the Truncated Conformal Space Approach and Conformal Perturbation Theory.Comment: 22 pages, minor changes, references added. LaTeX file and postscript figur

Constraints on the Ultra High Energy Photon flux using inclined showers from the Haverah Park array

We describe a method to analyse inclined air showers produced by ultra high energy cosmic rays using an analytical description of the muon densities. We report the results obtained using data from inclined events (60^{\circ}<\theta<80^{\circ}) recorded by the Haverah Park shower detector for energies above 10^19 eV. Using mass independent knowledge of the UHECR spectrum obtained from vertical air shower measurements and comparing the expected horizontal shower rate to the reported measurements we show that above 10^19 eV less than 48 % of the primary cosmic rays can be photons at the 95 % confidence level and above 4 X 10^19 eV less than 50 % of the cosmic rays can be photonic at the same confidence level. These limits place important constraints on some models of the origin of ultra high-energy cosmic rays.Comment: 45 pages, 25 figure

Integrable Structure of Conformal Field Theory, Quantum KdV Theory and Thermodynamic Bethe Ansatz

We construct the quantum versions of the monodromy matrices of KdV theory. The traces of these quantum monodromy matrices, which will be called as ``${\bf T}$-operators'', act in highest weight Virasoro modules. The ${\bf T}$-operators depend on the spectral parameter $\lambda$ and their expansion around $\lambda = \infty$ generates an infinite set of commuting Hamiltonians of the quantum KdV system. The ${\bf T}$-operators can be viewed as the continuous field theory versions of the commuting transfer-matrices of integrable lattice theory. In particular, we show that for the values $c=1-3{{(2n+1)^2}\over {2n+3}} , n=1,2,3,...$of the Virasoro central charge the eigenvalues of the ${\bf T}$-operators satisfy a closed system of functional equations sufficient for determining the spectrum. For the ground-state eigenvalue these functional equations are equivalent to those of massless Thermodynamic Bethe Ansatz for the minimal conformal field theory ${\cal M}_{2,2n+3}$; in general they provide a way to generalize the technique of Thermodynamic Bethe Ansatz to the excited states. We discuss a generalization of our approach to the cases of massive field theories obtained by perturbing these Conformal Field Theories with the operator $\Phi_{1,3}$. The relation of these ${\bf T}$-operators to the boundary states is also briefly described.Comment: 24 page

Possible origins of macroscopic left-right asymmetry in organisms

I consider the microscopic mechanisms by which a particular left-right (L/R) asymmetry is generated at the organism level from the microscopic handedness of cytoskeletal molecules. In light of a fundamental symmetry principle, the typical pattern-formation mechanisms of diffusion plus regulation cannot implement the "right-hand rule"; at the microscopic level, the cell's cytoskeleton of chiral filaments seems always to be involved, usually in collective states driven by polymerization forces or molecular motors. It seems particularly easy for handedness to emerge in a shear or rotation in the background of an effectively two-dimensional system, such as the cell membrane or a layer of cells, as this requires no pre-existing axis apart from the layer normal. I detail a scenario involving actin/myosin layers in snails and in C. elegans, and also one about the microtubule layer in plant cells. I also survey the other examples that I am aware of, such as the emergence of handedness such as the emergence of handedness in neurons, in eukaryote cell motility, and in non-flagellated bacteria.Comment: 42 pages, 6 figures, resubmitted to J. Stat. Phys. special issue. Major rewrite, rearranged sections/subsections, new Fig 3 + 6, new physics in Sec 2.4 and 3.4.1, added Sec 5 and subsections of Sec

On the Quantum Invariant for the Spherical Seifert Manifold

We study the Witten--Reshetikhin--Turaev SU(2) invariant for the Seifert manifold $S^3/\Gamma$ where $\Gamma$ is a finite subgroup of SU(2). We show that the WRT invariants can be written in terms of the Eichler integral of the modular forms with half-integral weight, and we give an exact asymptotic expansion of the invariants by use of the nearly modular property of the Eichler integral. We further discuss that those modular forms have a direct connection with the polyhedral group by showing that the invariant polynomials of modular forms satisfy the polyhedral equations associated to $\Gamma$.Comment: 36 page