Phase Transitions in the One-Dimensional Pair-Hopping Model: a Renormalization Group Study

The phase diagram of a one-dimensional tight-binding model with a pair-hopping term (amplitude V) has been the subject of some controvery. Using two-loop renormalization group equations and the density matrix renormalization group with lengths L<=60, we argue that no spin-gap transition occurs at half-filling for positive V, contrary to recent claims. However, we point out that away from half-filling, a *phase-separation* transition occurs at finite V. This transition and the spin-gap transition occuring at half-filling and *negative* V are analyzed numerically.Comment: 7 pages RevTeX, 6 uuencoded figures which can be (and by default are) directly included. Received by Phys. Rev. B 20 April 199

Responses to colour and host odour cues in three cereal pest species, in the context of ecology and control

Many insects show a greater attraction to multimodal cues, e.g. odour and colour combined, than to either cue alone. Despite the potential to apply the knowledge to improve control strategies, studies of multiple stimuli have not been undertaken for stored product pest insects. We tested orientation towards a food odour (crushed white maize) in combination with a colour cue (coloured paper with different surface spectral reflectance properties) in three storage pest beetle species, using motion tracking to monitor their behaviour. While the maize weevil, Sitophilus zeamais (Motsch.), showed attraction to both odour and colour stimuli, particularly to both cues in combination, this was not observed in the bostrichid pests Rhyzopertha dominica (F.) (lesser grain borer) or Prostephanus truncatus (Horn) (larger grain borer). The yellow stimulus was particularly attractive to S. zeamais, and control experiments showed that this was neither a result of the insects moving towards darker-coloured areas of the arena, nor their being repelled by optical brighteners in white paper. Visual stimuli may play a role in location of host material by S. zeamais, and can be used to inform trap design for the control or monitoring of maize weevils. The lack of visual responses by the two grain borers is likely to relate to their different host-seeking behaviours and ecological background, which should be taken into account when devising control methods

Correspondence in Quasiperiodic and Chaotic Maps: Quantization via the von Neumann Equation

A generalized approach to the quantization of a large class of maps on a torus, i.e. quantization via the von Neumann Equation, is described and a number of issues related to the quantization of model systems are discussed. The approach yields well behaved mixed quantum states for tori for which the corresponding Schrodinger equation has no solutions, as well as an extended spectrum for tori where the Schrodinger equation can be solved. Quantum-classical correspondence is demonstrated for the class of mappings considered, with the Wigner-Weyl density $\rho(p,q,t)$ going to the correct classical limit. An application to the cat map yields, in a direct manner, nonchaotic quantum dynamics, plus the exact chaotic classical propagator in the correspondence limit.Comment: 36 pages, RevTex preprint forma

Electromagnetic form factors of light vector mesons

The electromagnetic form factors G_E(q^2), G_M(q^2), and G_Q(q^2), charge radii, magnetic and quadrupole moments, and decay widths of the light vector mesons rho^+, K^{*+} and K^{*0} are calculated in a Lorentz-covariant, Dyson-Schwinger equation based model using algebraic quark propagators that incorporate confinement, asymptotic freedom, and dynamical chiral symmetry breaking, and vector meson Bethe-Salpeter amplitudes closely related to the pseudoscalar amplitudes obtained from phenomenological studies of pi and K mesons. Calculated static properties of vector mesons include the charge radii and magnetic moments: r_{rho+} = 0.61 fm, r_{K*+} = 0.54 fm, and r^2_{K*0} = -0.048 fm^2; mu_{rho+} = 2.69, mu_{K*+} = 2.37, and mu_{K*0} = -0.40. The calculated static limits of the rho-meson form factors are similar to those obtained from light-front quantum mechanical calculations, but begin to differ above q^2 = 1 GeV^2 due to the dynamical evolution of the quark propagators in our approach.Comment: 8 pages of RevTeX, 5 eps figure

q-Newton binomial: from Euler to Gauss

A counter-intuitive result of Gauss (formulae (1.6), (1.7) below) is made less mysterious by virtue of being generalized through the introduction of an additional parameter

Recent advances in neutrinoless double beta decay search

Even after the discovery of neutrino flavour oscillations, based on data from atmospheric, solar, reactor, and accelerator experiments, many characteristics of the neutrino remain unknown. Only the neutrino square-mass differences and the mixing angle values have been estimated, while the value of each mass eigenstate still hasn't. Its nature (massive Majorana or Dirac particle) is still escaping. Neutrinoless double beta decay ($0\nu$-DBD) experimental discovery could be the ultimate answer to some delicate questions of elementary particle and nuclear physics. The Majorana description of neutrinos allows the $0\nu$-DBD process, and consequently either a mass value could be measured or the existence of physics beyond the standard should be confirmed without any doubt. As expected, the $0\nu$-DBD measurement is a very difficult field of application for experimentalists. In this paper, after a short summary of the latest results in neutrino physics, the experimental status, the R&D projects, and perspectives in $0\nu$-DBD sector are reviewed.Comment: 36 pages, 7 figures, To be publish in Czech Journal of Physic

A mathematical framework for critical transitions: normal forms, variance and applications

Critical transitions occur in a wide variety of applications including mathematical biology, climate change, human physiology and economics. Therefore it is highly desirable to find early-warning signs. We show that it is possible to classify critical transitions by using bifurcation theory and normal forms in the singular limit. Based on this elementary classification, we analyze stochastic fluctuations and calculate scaling laws of the variance of stochastic sample paths near critical transitions for fast subsystem bifurcations up to codimension two. The theory is applied to several models: the Stommel-Cessi box model for the thermohaline circulation from geoscience, an epidemic-spreading model on an adaptive network, an activator-inhibitor switch from systems biology, a predator-prey system from ecology and to the Euler buckling problem from classical mechanics. For the Stommel-Cessi model we compare different detrending techniques to calculate early-warning signs. In the epidemics model we show that link densities could be better variables for prediction than population densities. The activator-inhibitor switch demonstrates effects in three time-scale systems and points out that excitable cells and molecular units have information for subthreshold prediction. In the predator-prey model explosive population growth near a codimension two bifurcation is investigated and we show that early-warnings from normal forms can be misleading in this context. In the biomechanical model we demonstrate that early-warning signs for buckling depend crucially on the control strategy near the instability which illustrates the effect of multiplicative noise.Comment: minor corrections to previous versio

Application of information entropy to nuclei

Shannon's information entropies in position- and momentum- space and their sum $S$ are calculated for various $s$-$p$ and $s$-$d$ shell nuclei using a correlated one-body density matrix depending on the harmonic oscillator size $b_0$ and the short range correlation parameter $y$ which originates from a Jastrow correlation function. It is found that the information entropy sum for a nucleus depends only on the correlation parameter $y$ through the simple relation $S= s_{0A} + s_{1A} y^{-\lambda_{sA}}$, where $s_{0A}$, $s_{1A}$ and $\lambda_{sA}$ depend on the mass number $A$. A similar approximate expression is also valid for the root mean square radius of the nucleus as function of $y$ leading to an approximate expression which connects $S$ with the root mean square radius. Finally, we propose a method to determine the correlation parameter from the above property of $S$ as well as the linear dependence of $S$ on the logarithm of the number of nucleons.Comment: 10 pages, 10 EPS figures, RevTeX, Phys.Rev.C accepted for publicatio

A Step Beyond the Bounce: Bubble Dynamics in Quantum Phase Transitions

We study the dynamical evolution of a phase interface or bubble in the context of a \lambda \phi^4 + g \phi^6 scalar quantum field theory. We use a self-consistent mean-field approximation derived from a 2PI effective action to construct an initial value problem for the expectation value of the quantum field and two-point function. We solve the equations of motion numerically in (1+1)-dimensions and compare the results to the purely classical evolution. We find that the quantum fluctuations dress the classical profile, affecting both the early time expansion of the bubble and the behavior upon collision with a neighboring interface.Comment: 12 pages, multiple figure

First-order cosmological phase transitions in the radiation dominated era

We consider first-order phase transitions of the Universe in the radiation-dominated era. We argue that in general the velocity of interfaces is non-relativistic due to the interaction with the plasma and the release of latent heat. We study the general evolution of such slow phase transitions, which comprise essentially a short reheating stage and a longer phase equilibrium stage. We perform a completely analytical description of both stages. Some rough approximations are needed for the first stage, due to the non-trivial relations between the quantities that determine the variation of temperature with time. The second stage, instead, is considerably simplified by the fact that it develops at a constant temperature, close to the critical one. Indeed, in this case the equations can be solved exactly, including back-reaction on the expansion of the Universe. This treatment also applies to phase transitions mediated by impurities. We also investigate the relations between the different parameters that govern the characteristics of the phase transition and its cosmological consequences, and discuss the dependence of these parameters with the particle content of the theory.Comment: 38 pages, 3 figures; v2: Minor changes, references added; v3: several typos correcte