Uncertainty inequalities on groups and homogeneous spaces via isoperimetric inequalities

We prove a family of $L^p$ uncertainty inequalities on fairly general groups and homogeneous spaces, both in the smooth and in the discrete setting. The crucial point is the proof of the $L^1$ endpoint, which is derived from a general weak isoperimetric inequality.Comment: 17 page

Statistical regimes of random laser fluctuations

Statistical fluctuations of the light emitted from amplifying random media are studied theoretically and numerically. The characteristic scales of the diffusive motion of light lead to Gaussian or power-law (Levy) distributed fluctuations depending on external control parameters. In the Levy regime, the output pulse is highly irregular leading to huge deviations from a mean--field description. Monte Carlo simulations of a simplified model which includes the population of the medium, demonstrate the two statistical regimes and provide a comparison with dynamical rate equations. Different statistics of the fluctuations helps to explain recent experimental observations reported in the literature.Comment: Revised version, resubmitted to Physical Review

Dynamical non-axisymmetric instabilities in rotating relativistic stars

We present new results on dynamical instabilities in rapidly rotating neutron-stars. In particular, using numerical simulations in full General Relativity, we analyse the effects that the stellar compactness has on the threshold for the onset of the dynamical bar-mode instability, as well as on the appearance of other dynamical instabilities. By using an extrapolation technique developed and tested in our previous study [1], we explicitly determine the threshold for a wide range of compactnesses using four sequences of models of constant baryonic mass comprising a total of 59 stellar models. Our calculation of the threshold is in good agreement with the Newtonian prediction and improves the previous post-Newtonian estimates. In addition, we find that for stars with sufficiently large mass and compactness, the m=3 deformation is the fastest growing one. For all of the models considered, the non-axisymmetric instability is suppressed on a dynamical timescale with an m=1 deformation dominating the final stages of the instability. These results, together with those presented in [1], suggest that an m=1 deformation represents a general and late-time feature of non-axisymmetric dynamical instabilities both in full General Relativity and in Newtonian gravity.Comment: To appear on CQG, NFNR special issue. 16 pages, 5 color figures, movies from http://www.fis.unipr.it/numrel/BarMode/ResearchBarMode.htm

Can deep sub-wavelength cavities induce Amperean superconductivity in a 2D material?

Amperean superconductivity is an exotic phenomenon stemming from attractive effective electron-electron interactions (EEEIs) mediated by a transverse gauge field. Originally introduced in the context of quantum spin liquids and high-Tc superconductors, Amperean superconductivity has been recently proposed to occur at temperatures on the order of 1-20 K in two-dimensional, parabolic-band, electron gases embedded inside deep sub-wavelength optical cavities. In this work, we first generalize the microscopic theory of cavity-induced Amperean superconductivity to the case of graphene and then argue that this superconducting state cannot be achieved in the deep sub-wavelength regime. In the latter regime, indeed, a cavity induces only EEEIs between density fluctuations rather than the current-current interactions which are responsible for Amperean pairing.Comment: 25 pages. Replaced with a greatly modified version, with the addition of an entirely new Section. This new Section presents a Green's function approach to EEEIs that highlights the profound difference between planar optical cavities and sub-wavelength cavitie

Combined SAXS/EM Based Models of the S. elongatus Post-Translational Circadian Oscillator and its Interactions with the Output His-Kinase SasA

The circadian clock in the cyanobacterium Synechococcus elongatus is composed of a post-translational oscillator (PTO) that can be reconstituted in vitro from three different proteins in the presence of ATP and a transcription-translation feedback loop (TTFL). The homo-hexameric KaiC kinase, phosphatase and ATPase alternates between hypo- and hyper-phosphorylated states over the 24-h cycle, with KaiA enhancing phosphorylation, and KaiB antagonizing KaiA and promoting KaiC subunit exchange. SasA is a His kinase that relays output signals from the PTO formed by the three Kai proteins to the TTFL. Although the crystal structures for all three Kai proteins are known, atomic resolution structures of Kai and Kai/SasA protein complexes have remained elusive. Here, we present models of the KaiAC and KaiBC complexes derived from solution small angle X-ray scattering (SAXS), which are consistent with previous EM based models. We also present a combined SAXS/EM model of the KaiC/SasA complex, which has two N-terminal SasA sensory domains occupying positions on the C-terminal KaiC ring reminiscent of the orientations adopted by KaiB dimers. Using EM we demonstrate that KaiB and SasA compete for similar binding sites on KaiC. We also propose an EM based model of the ternary KaiABC complex that is consistent with the sequestering of KaiA by KaiB on KaiC during the PTO dephosphorylation phase. This work provides the first 3D-catalogue of protein-protein interactions in the KaiABC PTO and the output pathway mediated by SasA

Asymptotics for the number of eigenvalues of three-particle Schr\"{o}dinger operators on lattices

We consider the Hamiltonian of a system of three quantum mechanical particles (two identical fermions and boson)on the three-dimensional lattice $\Z^3$ and interacting by means of zero-range attractive potentials. We describe the location and structure of the essential spectrum of the three-particle discrete Schr\"{o}dinger operator $H_{\gamma}(K),$ $K$ being the total quasi-momentum and $\gamma>0$ the ratio of the mass of fermion and boson. We choose for $\gamma>0$ the interaction $v(\gamma)$ in such a way the system consisting of one fermion and one boson has a zero energy resonance. We prove for any $\gamma> 0$ the existence infinitely many eigenvalues of the operator $H_{\gamma}(0).$ We establish for the number $N(0,\gamma; z;)$ of eigenvalues lying below $z<0$ the following asymptotics $$\lim_{z\to 0-}\frac{N(0,\gamma;z)}{\mid \log \mid z\mid \mid}={U} (\gamma) .$$ Moreover, for all nonzero values of the quasi-momentum $K \in T^3$ we establish the finiteness of the number $N(K,\gamma;\tau_{ess}(K))$ of eigenvalues of $H(K)$ below the bottom of the essential spectrum and we give an asymptotics for the number $N(K,\gamma;0)$ of eigenvalues below zero.Comment: 25 page

Thick tori around AGN: the case for extended tori and consequences for their X-ray and IR emission

Two families of models of dusty tori in AGNs (moderately thick and extended versus very thick and compact) are tested against available observations. The confrontation suggests that the former class better explains the IR broad-band spectra of both broad and narrow line AGNs, the anisotropy of the emission deduced by comparing IR properties of Seyfert 1 and 2 nuclei, the results of IR spectroscopy and those of high spatial resolution observations. There is however clear evidence for a broad distribution of optical depths. We also examine the relationship between IR and X-ray emission. The data support a view in which the matter responsible for the X-ray absorption is mostly dust free, lying inside the dust sublimation radius. The consequences of these results for the hard X-ray background as well as IR counts and background are discussed.Comment: 33 pages, 9 Postscript figures, to appear in ApJ, September 199

Exact and Truncated Dynamics in Nonequilibrium Field Theory

Nonperturbative dynamics of quantum fields out of equilibrium is often described by the time evolution of a hierarchy of correlation functions, using approximation methods such as Hartree, large N, and nPI-effective action techniques. These truncation schemes can be implemented equally well in a classical statistical system, where results can be tested by comparison with the complete nonlinear evolution obtained by numerical methods. For a 1+1 dimensional scalar field we find that the early-time behaviour is reproduced qualitatively by the Hartree dynamics. The inclusion of direct scattering improves this to the quantitative level. We show that the emergence of nonthermal temperature profiles at intermediate times can be understood in terms of the fixed points of the evolution equations in the Hartree approximation. The form of the profile depends explicitly on the initial ensemble. While the truncated evolution equations do not seem to be able to get away from the fixed point, the full nonlinear evolution shows thermalization with a (surprisingly) slow relaxation.Comment: 30 pages with 12 eps figures, minor changes; to appear in Phys.Rev.

Supergravity p-branes revisited: extra parameters, uniqueness, and topological censorship

We perform a complete integration of the Einstein-dilaton-antisymmetric form action describing black p-branes in arbitrary dimensions assuming the transverse space to be homogeneous and possessing spherical, toroidal or hyperbolic topology. The generic solution contains eight parameters satisfying one constraint. Asymptotically flat solutions form a five-parametric subspace, while conditions of regularity of the non-degenerate event horizon further restrict this number to three, which can be related to the mass and the charge densities and the asymptotic value of the dilaton. In the case of a degenerate horizon, this number is reduced by one. Our derivation constitutes a constructive proof of the uniqueness theorem for $p$-branes with the homogeneous transverse space. No asymptotically flat solutions with toroidal or hyperbolic transverse space within the considered class are shown to exist, which result can be viewed as a demonstration of the topological censorship for p-branes. From our considerations it follows, in particular, that some previously discussed p-brane-like solutions with extra parameters do not satisfy the standard conditions of asymptotic flatness and absence of naked singularities. We also explore the same system in presence of a cosmological constant, and derive a complete analytic solution for higher-dimensional charged topological black holes, thus proving their uniqueness.Comment: Revtex4, no figure