Showing papers by "International School for Advanced Studies published in 1996"

Geometry of 2D topological field theories

Abstract: These lecture notes are devoted to the theory of equations of associativity describing geometry of moduli spaces of 2D topological field theories. Introduction. Lecture 1. WDVV equations and Frobenius manifolds. {Appendix A.} Polynomial solutions of WDVV. {Appendix B.} Symmetriies of WDVV. Twisted Frobenius manifolds. {Appendix C.} WDVV and Chazy equation. Affine connections on curves with projective structure. Lecture 2. Topological conformal field theories and their moduli. Lecture 3. Spaces of isomonodromy deformations as Frobenius manifolds. {Appendix D.} Geometry of flat pencils of metrics. {Appendix E.} WDVV and Painlev\'e-VI. {Appendix F.} Branching of solutions of the equations of isomonodromic deformations and braid group. {Appendix G.} Monodromy group of a Frobenius manifold. {Appendix H.} Generalized hypergeometric equation associated to a Frobenius manifold and its monodromy. {Appendix I.} Determination of a superpotential of a Frobenius manifold. Lecture 4. Frobenius structure on the space of orbits of a Coxeter group. {Appendix J.} Extended complex crystallographic groups and twisted Frobenius manifolds. Lecture 5. Differential geometry of Hurwitz spaces. Lecture 6. Frobenius manifolds and integrable hierarchies. Coupling to topological gravity.

The Universal Rotation Curve of Spiral Galaxies: I. the Dark Matter Connection

Abstract: We use a homogeneous sample of about 1100 optical and radio rotation curves (RCs) and relative surface photometry to investigate the main mass structure properties of spirals, over a range of 6 magnitudes and out to � 1.5 and 2 optical radii (for the optical and radio data, respectively). We definitely confirm the strong dependence on luminosity for both the profile and the amplitude of RCs claimed by Persic & Salucci (1991). Spiral RCs show the striking feature that a single global parameter, e.g. luminosity, dictates the rotation velocity at any radius for any object, so unveiling the existence of a Universal RC. At high luminosities, there is a slight discrepancy between the profiles of RCs and those predicted from the luminous matter (LM) distributions: this implies a small, yet detectable, amount of dark matter (DM). At low luminosities, the failure of the LM prediction is much more severe, and the DM is the only relevant mass component. We show that the Universal RC implies a number of scaling properties between dark and luminous galactic structure parameters: (a) the DM/LM mass ratio scales inversely with luminosity; (b) the central halo density scales as L 0.7 ; (c) the halo core radius is comparable to the optical radius, but shrinks for low luminosities; (d) the total halo mass scales as L 0.5 . Such scaling properties can be represented as a curve in the (luminosity)-(DM/LM mass ratio)-(DM core radius)-(DM central density) space, which provides a geometrical description of the tight coupling between the dark and the luminous matter in spiral galaxies.

CP violating decays in leptogenesis scenarios

Abstract: We compute the CP violation in the decays of heavy electroweak singlet neutrinos, arising from both the one--loop vertex corrections and the wave function mixing. We extend the computation to the supersymmetric version of the model and discuss the implications for the generation of a lepton number asymmetry by the out of equilibrium decay of the heavy (s)neutrinos in the early Universe, to be reprocessed later in the observed baryon excess by anomalous electroweak processes.

Analytical estimates of limited sampling biases in different information measures.

Abstract: Measuring the information carried by neuronal activity is made difficult, particularly when recording from mammalian cells, by the limited amount of data usually available, which results in a systematic error. While empirical ad hoc procedures have been used to correct for such error, we have recently proposed a direct procedure consisting of the analytical calculation of the average error, its estimation (up to subleading terms) from the data, and its subtraction from raw information measures to yield unbiased measures. We calculate here the leading correction terms for both the average transmitted information and the conditional information and, since usually one must first regularize the data, we specify the expressions appropriate to different regularizations. Computer simulations indicate a broad range of validity of the analytical results, suggest the effectiveness of regularizing by simple binning and illustrate the advantage of this over the previously used 'bootstrap' procedure.

EAM potential for magnesium from quantum mechanical forces

Abstract: We have developed an empirical EAM potential for magnesium by fitting to ab initio forces (the `force matching' method) and experimental data. The database includes many different structures, including bulk, cluster, liquid and several defect structures. The potential fit to the forces database, which has 2201 forces generated using a local orbital pseudopotential method, is good. This new EAM potential gives good results for various bulk structural properties.

Dynamical left-right symmetry breaking.

Abstract: We study a left–right symmetric model which contains only elementary gauge boson and fermion fields and no scalars. The phenomenologically required symmetry breaking emerges dynamically leading to a composite Higgs sector with a renormalizable effective Lagrangian. We discuss the pattern of symmetry breaking and phenomenological consequences of this scenario. It is shown that a viable top quark mass can be achieved for the ratio of the VEVs of the bi–doublet tan β ≡ κ/κ ′ ≃ 1.3–4. For a theoretically plausible choice of the parameters the right–handed scale can be as low as ∼ 20 T eV ; in this case one expects several intermediate and low–scale scalars in addition to the Standard Model Higgs boson. These may lead to observable lepton flavour violation effects including � → eγ decay with the rate close to its present experimental upper bound.

Spontaneous rhythmic bursts induced by pharmacological block of inhibition in lumbar motoneurons of the neonatal rat spinal cord

Abstract: 1. The effects of blocking gamma-aminobutyric acid- and glycine-mediated synaptic transmission by bicuculline and strychnine on the neonatal rat isolated spinal cord were investigated by intracellu...

Localization of Rhythmogenic Networks Responsible for Spontaneous Bursts Induced by Strychnine and Bicuculline in the Rat Isolated Spinal Cord

Abstract: Spontaneous rhythmic bursting induced by coapplication of strychnine (1 microM) and bicuculline (20 microM) was observed with electrophysiological recording from pairs of lumbar ventral roots (usually L5) in an isolated preparation of the neonatal rat spinal cord. Bursting was insensitive to exogenously applied GABA or glycine, confirming that it was attributable to block of glycine and GABAA receptor-mediated inhibition. NMDA accelerated bursting in a dose-dependent manner. Complete coronal spinal transection at L3 or L6 level did not block bursting recorded from L5 or L2 roots, respectively. Gradual cutting of the cord along the midline through a sagittal plane preserved bursting activity in both disconnected sides but led to loss of synchronicity. Once the spinal cord was fully separated into left and right halves, regular bursting persisted on each side with no phase-coupling between the two preparations. Section along a frontal plane to remove dorsal horns and much of the central canal area did not affect burst frequency or left-to-right synchronicity, whereas it reduced burst duration. A quadrant preparation containing mainly a single ventral horn displayed enhanced burst frequency while bursts became very short events. Bath application of 5-hydroxytryptamine (30 microM) or NMDA (5 microM) increased burst frequency and decreased burst duration in all types of preparation except the isolated quadrants, in which brief bursts were accelerated but not shortened by these chemical agents. These results suggest that bursting induced by strychnine and bicuculline apparently relied on distinct mechanisms for burst triggering and intraburst structure. The first required a relatively smaller neuronal network that was confined to a ventral quadrant. Intraburst structure was dependent on a larger circuitry comprising either both ventral horns or one side of the spinal cord including more than two segments.

New high-pressure phase of ice.

Abstract: Based on ab initio constant pressure molecular dynamics simulation, we predict a new phase transition in ice from ice X to a new phase (ice XI) at $\ensuremath{\sim}3\mathrm{Mbar}$ and room temperature. Ice XI preserves the symmetric hydrogen bond and is a wide gap insulator up to and beyond 7 Mbar. This new phase is stable up to 2000 K at 4 Mbar, where the system shows large protonic diffusion.

A New Technique for the Detection of Periodic Signals in ``Colored'' Power Spectra

Abstract: The light curves from a variety of celestial objects display aperiodic variations, often giving rise to red–noise components in their power spectra. Searching for a narrow power spectrum peak resulting from a periodic modulation over the frequency range in which these “coloured” noise components are dominant has proven a very complex task. Commonly used methods rely upon spectral smoothing or incoherent summation of sample spectra in order to decrease the variance of the power estimates. The consequent reduction in frequency resolution causes also a reduction of sensitivity to periodic signals. We develop here a technique aimed at detecting periodicities in the presence of “coloured” power spectrum components, while mantaining the highest Fourier frequency resolution. First we introduce a simple approximation to the statistical properties of the “coloured” power spectra from celestial objects, based on a few examples and the theory of linear processes. We then estimate the continuum components in the power spectrum through an ad hoc smoothing technique. This involves averaging the spectral estimates adjacent to each frequency over a suitably chosen interval, in order to follow steep red–noise features and produce estimates that are locally unaffected by the possible presence of a sharp peak. By dividing the sample spectrum by the smoothed one, a white–noise like spectrum is obtained, Affiliated to the International Center for Relativistic Astrophysics Now at the Astronomical Observatory of Rome, Via dell’Osservatorio 2, I–00040, Monteporzio Catone (Roma), Italy

Riemannian theory of Hamiltonian chaos and Lyapunov exponents

Abstract: This paper deals with the problem of analytically computing the largest Lyapunov exponent for many degrees of freedom Hamiltonian systems. This aim is succesfully reached within a theoretical framework that makes use of a geometrization of newtonian dynamics in the language of Riemannian geometry. A new point of view about the origin of chaos in these systems is obtained independently of homoclinic intersections. Chaos is here related to curvature fluctuations of the manifolds whose geodesics are natural motions and is described by means of Jacobi equation for geodesic spread. Under general conditions ane effective stability equation is derived; an analytic formula for the growth-rate of its solutions is worked out and applied to the Fermi-Pasta-Ulam beta model and to a chain of coupled rotators. An excellent agreement is found the theoretical prediction and the values of the Lyapunov exponent obtained by numerical simulations for both models.

Stochastic growth equations and reparametrization invariance

Abstract: This article reviews the role of reparametrization invariance (the invariance of the properties of a system with respect to the choice of the co-ordinate system used to describe it) in deriving stochastic equations that describe the growth of surfaces. By imposing reparametrization invariance on a system, the authors identify the physical origin of many of the terms in its growth equations. Both continuum-growth equations for interfaces and equations for the coarse-grained evolution of discrete-lattice models are derived with this method. A detailed analysis of the discrete-lattice case and its small-gradient expansion provides a physical basis for terms found in commonly studied growth equations. The reparametrization-invariant formulation of growth processes also has the advantage of allowing one to model shadowing effects that are lost in the no-overhang approximation and to conserve underlying symmetries of the system that are lost in a small-gradient expansion. Finally, a knowledge of the full equation of motion, beyond the lowest-order gradient expansion, may be relevant in problems where the usual perturbative renormalization methods fail. [S0034-6861(96)00104-3]

Universality Classes of Optimal Channel Networks

Abstract: Energy minimization of both homogeneous and heterogeneous river networks shows that, over a range of parameter values, there are only three distinct universality classes. The exponents for all three classes of behavior are calculated.

Differential expression of outer hair cell potassium currents in the isolated cochlea of the guinea-pig.

Abstract: 1 Whole-cell currents were recorded from outer hair cells (OHCs) in undissociated tissues from the organ of Corti The experiments allowed ionic currents to be measured in cells with precise localization on the three most apical cochlear turns 2 Two major potassium currents were expressed in the cells One current, named IK, was half-activated at -24 mV and was most prominent in the most apical turn, turn 4 A second, named IKn, was half-activated at -92 mV and was the major contributor to the current-voltage (I-V) curve of cells from the more basal turns, turns 3 and 2, of the cochlea 3 IK was specifically blocked by 100 microM 4-aminopyridine (4-AP) In contrast, IKn was reduced by 5 mM external barium Superfusion with zero calcium produced no effect on currents in the range from -60 to 0 mV, but reduced currents by a maximum of 15% outside this range 4 The cell input conductance increased systematically from 34 nS in turn 4 to 40 nS in turn 2 measured at a holding potential of -70 mV 5 The mean leak conductance, measured from the slope of the I-V curve at -110 mV, decreased systematically from 52 nS in turn 2, to 29 nS in turn 3 and 22 nS in turn 4 6 These data show that hair cell properties can be determined in undissociated cells and are likely to provide a good estimate of the properties of the cells in the intact cochlea Differences with the properties of isolated OHCs are discussed

The observational appearance of slim accretion disks

Abstract: We reexamine the hypothesis that the optical/UV/soft X-ray continuum of active galactic nuclei (AGNs) is thermal emission from an accretion disk. Previous studies have shown that fitting the spectra with the standard optically thick and geometrically thin accretion disk models often led to luminosities that contradict the basic assumptions adopted in the standard model. There is no known reason why the accretion rates in AGNs should not be larger than the thin disk limit. In fact, more general, slim accretion disk models are self-consistent even for moderately super-Eddington luminosities. We calculate here spectra from a set of thin and slim, optically thick accretion disks, assuming for simplicity a modified blackbody local emission with no relativistic corrections. We discuss the differences between the thin and slim disk models, stressing the implications of these differences for the interpretation of the observed properties of AGNs. We find that the spectra can be fitted not only by models with a high mass and a low accretion rate (as in the case of thin disk fitting) but also by models with a low mass and a high accretion rate. In the first case, fitting the observed spectra in various redshift categories gives black hole masses of ∼ 109 M⊙ for a wide range of redshifts and for accretion rates ranging from 0.4 (low redshift) to 8 M⊙ yr-1 (high redshift). In the second case, the accretion rate is ∼102 M⊙ yr-1 for all AGNs, and the mass ranges from 3 × 106 (low redshift) to 108 M⊙ (high redshift). Unlike the disks with a low accretion rate, the spectra of the high accretion rate disks extend into the soft X-ray region. A comparison with observations shows that such disks could produce the soft X-ray excesses claimed for some AGNs. We show also that the sequence of our models with fixed mass and different accretion rates can explain the time evolution of the observed spectra in Fairall 9.

Invasion percolation and Eden growth: Geometry and universality.

Abstract: The mapping of optimal paths in the strong disorder limit to the strands of invasion percolation clusters is shown to lead to a new universal property of these clusters. We suggest that the corresponding strands arising in the annealed Eden growth process are in the same universality class as directed polymers in weak quenched disorder with an upper critical dimension #6. (S0031-9007(96)00188-3) PACS numbers: 64.60.Ak We address several issues in this Letter. What are the geometries of the optimal polymer in a strongly disordered medium in higher dimensions? What is the upper critical dimensionality for this problem? Is the geometry of the polymer in a strongly disordered medium universal? Our study is carried out in the context of a growing invasion percolation cluster. In this procedure, the bonds of the lattice are assigned strengths in a quenched random manner, and a cluster grows by invading the weakest interfacial bond. We will show that both bond and site variants of percolation lead to the same universality class. We then go on to study an analogous model with annealed instead of quenched disorder. In this case all interfacial bonds have an equal probability of being invaded. We present arguments and numerical evidence that even though the randomness is annealed, the effects of quenched disorder are self-generated within the model leading to geometries that are self-affine and characterized by the roughness exponent aDP . Thus, within the same process, the interface of the Eden cluster is characterized by a dynamical exponent zKPZ, whereas the static wandering exponent of the strands of the cluster is given by 1yzKPZ (a strand is defined as the unique path that excludes dead ends from an arbitrary site to a central seed site). Our results have a wide range of applicability— the strong disorder limit is relevant up to a correlation length in a variety of situations (7) including transport in amorphous semiconductors at low temperatures, electrical conduction and fluid flow in porous rocks, and the magnetic properties of doped semiconductors. Further, there are novel forms of percolation that are equivalent to the problem of the optimal polymer in a strongly disordered environment (6). Our prediction of the self- generated quenched randomness ought to be observable in Eden growth and other random invasion processes. We begin with an alternative way to view the geometry of the polymer in a strongly disordered environment. We

Universality properties of N=2 and N=1 Heterotic threshold corrections

Abstract: In the framework of heterotic compactifications, we consider the one-loop corrections to the gauge couplings, which were shown to be free of any infra-red ambiguity. For a class of N=2 models, namely those that are obtained by toroidal compactification to four dimensions of generic six-dimensional N=1 ground states, we give an explicit formula for the gauge-group independent thresholds, and show that these are equal within this class, as a consequence of an anomaly-cancellation constraint in six dimensions. We further use these results to compute the (N=2)-sector contributions to the thresholds of N=1 orbifolds. We then consider the full contribution of N=1 sectors to the gauge couplings which generically are expected to modify the unification picture. We compute such corrections in several models. We finally comment on the effect of such contributions to the issue of string unification.

Physics with nonperturbative quantum gravity: Radiation from a quantum black hole

Abstract: We study quantum gravitational effects on black hole radiation, using loop quantum gravity. Bekenstein and Mukhanov have recently considered the modifications caused by quantum gravity on Hawking's thermal black-hole radiation. Using a simple ansatz for the eigenstates of the area, they have obtained the intriguing result that the quantum properties of geometry affect the radiation considerably, yielding a discrete spectrum, definitely non-thermal. Here, we replace the simple ansatz employed by Bekenstein and Mukhanov with the actual eigenstates of the area computed using loop quantum gravity. We derive the emission spectra, using a classic result in number theory by Hardy and Ramanujan. Disappointingly, we do not recover the Bekenstein-Mukhanov discrete spectrum, but — effectively — a continuum spectrum, consistent with Hawking's result. The Bekenstein-Mukhanov argument for the discreteness of the specrum is therefore likely to be an artifact of the ansatz, rather than a robust result (at least in its present kinematical version). The result is an example of concrete (although somewhat disappointing) application of nonperturbative quantum gravity.

Towards a nonequilibrium quantum field theory approach to electroweak baryogenesis.

Abstract: We propose a general method to compute {ital CP} violating observables from extensions of the standard model in the context of electroweak baryogenesis. It is an alternative to the one recently developed by Huet and Nelson and relies on a nonequilibrium quantum field theory approach. The method is valid for all shapes and sizes of the bubble wall expanding in the thermal bath during a first-order electroweak phase transition. The quantum physics of {ital CP} violation and its suppression coming from the incoherent nature of thermal processes are also made explicit. {copyright} {ital 1996 The American Physical Society.}

Thermodynamics of Fractal Networks

Abstract: Optimal channel networks are fractal structures that bear a striking resemblance to real rivers. They are obtained by minimizing an energy functional associated with spanning trees. We show that large network development effectively occurs al zero temperature since the entropy scales subdominantly with system size compared to the energy. Thus these networks develop under generic conditions and freeze into a static scale-free structure. We suggest a link of optimal channel networks with self-organized critical systems and critical phenomena which exhibit spatial and temporal fractality, the former under generic conditions and the latter on fine tuning.

Multiplicity results for periodic solutions of second order ODEs with asymmetric nonlinearities

Abstract: We prove various results on the existence and multiplicity of harmonic and subharmonic solutions to the second order nonautonomous equation x′′+ g(x) = s+w(t, x), as s→ +∞ or s→ −∞, where g is a smooth function defined on a open interval ]a, b[⊂ R. The hypotheses we assume on the nonlinearity g(x) allow us to cover the case b = +∞ (or a = −∞) and g having superlinear growth at infinity, as well as the case b < +∞ (or a > −∞) and g having a singularity in b (respectively in a). Applications are given also to situations like g′(−∞) 6= g′(+∞) (including the so-called “jumping nonlinearities”). Our results are connected to the periodic Ambrosetti Prodi problem and related problems arising from the Lazer McKenna suspension bridges model.

Classical nilpotent orbits as hyperkähler quotients

Abstract: We show that on an arbitrary nilpotent orbit in where is a direct sum of classical simple Lie algebras, there is a G-invariant hyperKahler structure obtainable as a hyperKaher quotient of the flat hyperKahler manifold ℝ4N≅ℍN. Coincidences between various low-dimensional simple Lie groups lead to some nilpotent orbits being described as hyperKahler quotients (in some cases in fact finite quotients) of other nilpotent orbits. For example, from the construction we are able to read off pairs of orbits in different classical Lie algebras such that there is a finite -equivariant surjection between the orbit closures. We include a table listing examples of hyperKahler quotients between small nilpotent orbits. The above-mentioned results have consequences in quaternionic Kahler geometry: it is known that nilpotent orbits in complex semisimple Lie algebras give rise to quaternionic Kahler manifolds. Our approach gives a more direct proof of this in the classical case as these manifolds turn out to be quaternionic Kahler quotients of quaternionic projective spaces. We find that many of these manifolds can also be constructed as quaternionic Kahler quotients of complex Grassmannians .

Phonon Softening and Superconductivity in Tellurium under Pressure.

Abstract: The phonon dispersion and the electron-phonon interaction for the {beta}-Po and the bcc high pressure phases of tellurium are computed with density-functional perturbation theory. Our calculations reproduce and explain the experimentally observed pressure dependence of the superconducting critical temperature ({ital T}{sub {ital c}}) and confirm the connection between the jump in {ital T}{sub {ital c}} and the structural phase transition. The phonon contribution to the free energy is shown to be responsible for the difference in the structural transition pressure observed in low and room temperature experiments. {copyright} {ital 1996 The American Physical Society.}