The spectrum of massive excitations of 3d 3-state Potts model and universality

We consider the mass spectrum of the 3$d$ 3-state Potts model in the broken phase (a) near the second order Ising critical point in the temperature - magnetic field plane and (b) near the weakly first order transition point at zero magnetic field. In the case (a), we compare the mass spectrum with the prediction from universality of mass ratios in the 3$d$ Ising class; in the case (b), we determine a mass ratio to be compared with the corresponding one in the spectrum of screening masses of the (3+1)$d$ SU(3) pure gauge theory at finite temperature in the deconfined phase near the transition. The agreement in the comparison in the case (a) would represent a non-trivial test of validity of the conjecture of spectrum universality. A positive answer to the comparison in the case (b) would suggest the possibility to extend this conjecture to weakly first order phase transitions.Comment: 20 pages, 12 figures; uses axodraw.st

q-Deformed quaternions and su(2) instantons

We have recently introduced the notion of a q-quaternion bialgebra and shown its strict link with the SO_q(4)-covariant quantum Euclidean space R_q^4. Adopting the available differential geometric tools on the latter and the quaternion language we have formulated and found solutions of the (anti)selfduality equation [instantons and multi-instantons] of a would-be deformed su(2) Yang-Mills theory on this quantum space. The solutions depend on some noncommuting parameters, indicating that the moduli space of a complete theory should be a noncommutative manifold. We summarize these results and add an explicit comparison between the two SO_q(4)-covariant differential calculi on R_q^4 and the two 4-dimensional bicovariant differential calculi on the bi- (resp. Hopf) algebras M_q(2),GL_q(2),SU_q(2), showing that they essentially coincide.Comment: Latex file, 18 page

Finite-size scaling and the deconfinement transition in gauge theories

We introduce a new method for determining the critical indices of the deconfinement transition in gauge theories. The method is based on the finite size scaling behavior of the expectation value of simple lattice operators, such as the plaquette. We test the method for the case of SU(3) pure gauge theory in (2+1) dimensions and obtain a precise determination of the critical index $\nu$, in agreement with the prediction of the Svetitsky-Yaffe conjecture.Comment: 6 pages. Several comments and one reference added, results unchange

Unidirectional Rotation Neurones in the Optomotor System of the Crab, Carcinus

1. Among the optomotor fibres to the eye muscles in Carcinus a class was found which responds to unidirectional fast rotations around various body axes. All had large signals and are therefore of large diameter. 2. In one set of these fibres which fires especially for rotations around the dorsoventral axis, it could be shown that discharges take place especially during accelerations and that, when a rotation in the null direction is suddenly stopped, a short discharge occurs. The fibres for other axes behave in a similar manner. 3. For rotations around the ventro-dorsal axis, but not for other directions, mediumsized fibres are present which, in contrast to the fast fibres, respond to visual stimulation, as well as to body rotations in darkness, thus combining the input properties of the unidirectional fast rotatory and the unidirectional purely optokinetic small fibres. Their sensitivity to visual input is for low rotation velocities, to body rotations is for high rotation velocities

Single photon absorption and dynamic control of a coupled quantum dot-cavity system

We theoretically investigate the dynamic interaction of a quantum dot in a nanocavity with timesymmetric single photon pulses. The simulations, based on a wavefunction approach, reveal that almost perfect single photon absorption occurs for quantum dot-cavity systems operating on the edge between strong and weak coupling regime. The computed maximum absorptions probability is close to unity for pulses with a typical length comparable to the half of the Rabi period. Furthermore, the dynamic control of the quantum dot energy via electric fields allows the freezing of the light-matter interaction leaving the quantum dot in its excited state. Shaping of single photon wavepackets by the electric field control is limited by the occurrence of chirping of the single photon pulse. This understanding of the interaction of single photon pulses with the quantum dot-cavity system provides the basis for the development of advanced protocols for quantum information processing in the solid state.Comment: 7 pages, 4 figure

Factors Regulating the Discharge Frequency in Optomotor Fibres Of Carcinus Maenas

The influence of the excited state of the animal on various motor neurone discharges and accompanying muscle action potentials was studied in the eyestalk of the crab, Carcinus maenas. In most cases large increases in firing frequency could be obtained during such states. An exception is the tonic eye-withdrawal system in which an inhibitory effect is caused. A pronounced difference in habituation to constant stimuli between spring and summer was found for the position fibres; in spring it was slow and in summer much quicker

The Evolution of Active Galactic Nuclei in Warm Dark Matter Cosmology

Recent measurements of the abundance of AGN with low-luminosities (L_X< 10^44 erg/s in the 2-10 keV energy band) at high redshifts z>4 provide a serious challenge for Cold Dark Matter (CDM) models based on interaction-driven fueling of AGN. Using a semi-analytic model of galaxy formation we investigate how such observations fit in a Warm Dark Matter (WDM) scenario of galaxy formation, and compare the results with those obtained in the standard CDM scenario with different efficiencies for the stellar feedback. Taking on our previous exploration of galaxy formation in WDM cosmology, we assume as a reference case a spectrum which is suppressed - compared to the standard CDM case - below a cut-off scale ~ 0.2$ Mpc corresponding (for thermal relic WDM particles) to a mass m_X=0.75 keV. We run our fiducial semi-analytic model with such a WDM spectrum to derive AGN luminosity functions from z~6 to the present over a wide range of luminosities (10^43< L_X/erg/s < 10^46 in the 2-10 keV X-ray band), to compare with recent observations and with the results in the CDM case. When compared with the standard CDM case, the luminosity distributions we obtain assuming a WDM spectrum are characterized by a similar behaviour at low redshift, and by a flatter slope at faint magnitudes for z>3, which provide an excellent fit to present observations. We discuss how such a result compares with CDM models with maximized feedback efficiency, and how future deep AGN surveys will allow for a better discrimination between feedback and cosmological effects on the evolution of AGN in interaction-driven models for AGN fueling.Comment: Accepted for publication in The Astrophysical Journal; typos and references correcte

q-Quaternions and q-deformed su(2) instantons

We construct (anti)instanton solutions of a would-be q-deformed su(2) Yang-Mills theory on the quantum Euclidean space R_q^4 [the SO_q(4)-covariant noncommutative space] by reinterpreting the function algebra on the latter as a q-quaternion bialgebra. Since the (anti)selfduality equations are covariant under the quantum group of deformed rotations, translations and scale change, by applying the latter we can generate new solutions from the one centered at the origin and with unit size. We also construct multi-instanton solutions. As they depend on noncommuting parameters playing the roles of `sizes' and `coordinates of the centers' of the instantons, this indicates that the moduli space of a complete theory will be a noncommutative manifold. Similarly, gauge transformations should be allowed to depend on additional noncommutative parameters.Comment: Latex file, 39 pages. Final version appeared in JM

Unbraiding the braided tensor product

We show that the braided tensor product algebra $A_1\underline{\otimes}A_2$ of two module algebras $A_1, A_2$ of a quasitriangular Hopf algebra $H$ is equal to the ordinary tensor product algebra of $A_1$ with a subalgebra of $A_1\underline{\otimes}A_2$ isomorphic to $A_2$, provided there exists a realization of $H$ within $A_1$. In other words, under this assumption we construct a transformation of generators which `decouples' $A_1, A_2$ (i.e. makes them commuting). We apply the theorem to the braided tensor product algebras of two or more quantum group covariant quantum spaces, deformed Heisenberg algebras and q-deformed fuzzy spheres.Comment: LaTex file, 29 page