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- The conjecture that the orbit-counting generating function for totally symmetric plane partitions can be written as an explicit product formula, has been stated independently by George Andrews and David Robbins around 1983. We present a proof of this long-standing conjecture.
- We introduce a Hopf algebroid associated to a proper Lie group action on a smooth manifold. We prove that the cyclic cohomology of this Hopf algebroid is equal to the de Rham cohomology of invariant differential forms. When the action is cocompact, we develop a generalized Hodge theory for the de Rham cohomology of invariant differential forms. We prove that every cyclic cohomology class of the Hopf algebroid is represented by a generalized harmonic form. This implies that the space of cyclic cohomology of the Hopf algebroid is finite dimensional. As an application of the techniques developed in this paper, we discuss properties of the Euler characteristic for a proper cocompact action.
- We give a short proof of Levinson's result that more than 1/3 of the zeros of the zeta function are on the critical line.
- Feb 24 2010 astro-ph.SR astro-ph.HE arXiv:1002.4402v1LS 5039 is a relatively close microquasar consisting of a late O-type star and a compact object (very possibly a black hole) on a highly eccentric orbit with a period of 3.9 days. The high X-ray, gamma-ray and radio luminosity indicate light-matter interaction, which arise from the stellar wind of the primary star accreting toward the black hole. Former examinations suggest that LS 5039 could be a prototype of wind-fed high mass X-ray binaries (WXBs) with diskless main sequence O primaries. Now there is a great chance to better understand the configuration and the physical processes in the exotic system. In July 2009 LS 5039 was followed by the Canadian MOST space telescope to get ultraprecise photometric data in a month-long semi-continuous time series. Parallel to this, we have taken simultaneous high-resolution optical spectra using the 2.3m ANU telescope of the Siding Spring Observatory, supplemented with further data obtained in early August 2009 with the same instrument. Here we present the first results from the new echelle spectra, which represent the best optical spectroscopy ever obtained for this intriguing system. We determined fundamental orbital and physical parameters of LS 5039 and examined the configuration and the circumstellar environment of the system via radial velocity measurements and detailed line-profile analysis of H-Balmer, He I and He II lines.
- Feb 24 2010 astro-ph.GA arXiv:1002.4401v1We undertake a systematic analysis of the early (< 0.5 Myr) evolution of clustering and the stellar initial mass function in turbulent fragmentation simulations. These large scale simulations for the first time offer the opportunity for a statistical analysis of IMF variations and correlations between stellar properties and cluster richness. The typical evolutionary scenario involves star formation in small-n clusters which then progressively merge; the first stars to form are seeds of massive stars and achieve a headstart in mass acquisition. These massive seeds end up in the cores of clusters and a large fraction of new stars of lower mass is formed in the outer parts of the clusters. The resulting clusters are therefore mass segregated at an age of 0.5 Myr, although the signature of mass segregation is weakened during mergers. We find that the resulting IMF has a smaller exponent (alpha=1.8-2.2) than the Salpeter value (alpha=2.35). The IMFs in subclusters are truncated at masses only somewhat larger than the most massive stars (which depends on the richness of the cluster) and an universal upper mass limit of 150 Msun is ruled out. We also find that the simulations show signs of the IGIMF effect proposed by Weidner & Kroupa, where the frequency of massive stars is suppressed in the integrated IMF compared to the IMF in individual clusters. We identify clusters through the use of a minimum spanning tree algorithm which allows easy comparison between observational survey data and the predictions of turbulent fragmentation models. In particular we present quantitative predictions regarding properties such as cluster morphology, degree of mass segregation, upper slope of the IMF and the relation between cluster richness and maximum stellar mass. [abridged]
- We characterize the monomial complete intersections in three variables satisfying the Weak Lefschetz Property (WLP), as a function of the characteristic of the base field. Our result presents a surprising, and still combinatorially obscure, connection with the enumeration of plane partitions. It turns out that the rational primes p dividing the number, M(a,b,c), of plane partitions contained inside an arbitrary box of given sides a,b,c are precisely those for which a suitable monomial complete intersection (explicitly constructed as a bijective function of a,b,c) fails to have the WLP in characteristic p. We wonder how powerful can be this connection between combinatorial commutative algebra and partition theory. We present a first result in this direction, by deducing, using our algebraic techniques for the WLP, some explicit information on the rational primes dividing M(a,b,c).
- We demonstrate the Parker Magnetostatic Theorem in terms of a small neighborhood in solution space containing continuous force-free magnetic fields in small deviations from the uniform field. These fields are embedded in a perfectly conducting fluid bounded by a pair of rigid plates where each field is anchored, taking the plates perpendicular to the uniform field. Those force-free fields obtainable from the uniform field by continuous magnetic footpoint displacements at the plates have field topologies that are shown to be a restricted subset of the field topologies similarly created without imposing the force-free equilibirum condition. The theorem then follows from the deduction that a continuous nonequilibrum field with a topology not in that subset must find a force-free state containing tangential discontinuities.
- The zero point kinetic energy of protons in water is large on the scale of chemical interaction energies(29 Kj/mol in bulk room temperature water). Its value depends upon the structure of the hydrogen bond network, and can change as the network is confined or as water interacts with surfaces. These changes have been observed to be large on a chemical scale for water confined in carbon nanotubes and in the pores of xerogel, and may play a fundamental, and neglected, role in biological processes involving confined water. We measure the average momentum distribution of the protons in salmon Na-DNA using Deep Inelastic Neutron Scattering, for a weakly hydrated (6w/bp) and a dehydrated fiber sample. This permits the determination of the change in total kinetic energy of the system per water molecule removed from the DNA and placed in the bulk liquid. This energy is equal, within errors, to the measured enthalpy for the same process, demonstrating that changes in the zero point motion of the protons, arising from changes in structure as water molecules are incorporated in the DNA, are a significant factor in the energetics of the transition from the A to B phase with hydration, in this case, providing the entire binding energy of the water molecules to the DNA. The shape of the momentum distribution in the dehydrated phase is consistent with coherent delocalization of some of the protons in a double well potential, with a separation of the wells of .2 Angstroms.
- Feb 24 2010 astro-ph.EP arXiv:1002.4397v1The apparent source region (or regions) of long-period comets as well as the definition of the dynamically new comet are still open questions.The aim of this investigation is to look for the apparent source of selected long period comets and to refine the definition of dynamically new comets. We show that incorporation of the non-gravitational forces into the orbit determination process significantly changes the situation. We determined precise non-gravitational orbits of all investigated comets and next followed numerically their past and future motion during one orbital period. Applying ingenious Sitarski's method of creating swarms of virtual comets compatible with observations, we were able to derive the uncertainties of original and future orbital elements, as well as the uncertainties of the previous and next perihelion distances. We concluded that the past and future evolution of cometary orbits under the Galactic tide perturbations is the only way to find which comets are really dynamically new. We also have shown that a significant percentage of long-period comets can visit the zone of visibility during at least two or three consecutive perihelion passages.
- Feb 24 2010 astro-ph.SR astro-ph.GA arXiv:1002.4391v1Context: Chromospheric activity produces both photometric and spectroscopic variations that can be mistaken as planets. Large spots crossing the stellar disc can produce planet-like periodic variations in the light curve of a star. These spots clearly affect the spectral line profiles and their perturbations alter the line centroids creating a radial velocity jitter that might contaminate" the variations induced by a planet. Precise chromospheric activity measurements are needed to estimate the activity-induced noise that should be expected for a given star. Aims: We obtain precise chromospheric activity measurements and projected rotational velocities for nearby (d < 25 pc) cool (spectral types F to K) stars, to estimate their expected activity-related jitter. As a complementary objective, we attempt to obtain relationships between fluxes in different activity indicator lines, that permit a transformation of traditional activity indicators, i.e, CaII H & K lines, to others that hold noteworthy advantages. Methods: We used high resolution (~50000) echelle optical spectra. To determine the chromospheric emission of the stars in the sample, we used the spectral subtraction technique. Rotational velocities were determined using the cross-correlation technique. To infer activity-related radial velocity (RV) jitter, we used empirical relationships between this jitter and the R'_HK index. Results: We measured chromospheric activity, as given by different indicators throughout the optical spectra, and projected rotational velocities for 371 nearby cool stars. We have built empirical relationships among the most important chromospheric emission lines. Finally, we used the measured chromospheric activity to estimate the expected RV jitter for the active stars in the sample.
- Feb 24 2010 cond-mat.str-el arXiv:1002.4396v1Recent developments of high-order CCM have been to extend existing formalism and codes to $s \ge \frac 12$ for both the ground and excited states, and independently to "generalised" expectation values for a wide range of one- and two-body spin operators. An advantage of the CCM is that the Goldstone linked-cluster theorem is obeyed at all levels of approximation and so it provides results in the infinite lattice limit $N \to \infty$ from the outset. However, recent results have also shown that the CCM can provide exact (symmetry-breaking) results for the spin-half linear-chain $J_1$--$J_2$ at the Majumdar-Ghosh point $J_2/J_1=0.5$ by identifying special solutions of the CCM equations for the usual Néel model state. Interestingly, the CCM provides exact (non-symmetry-breaking) results for systems in which small magnetic clusters become de-coupled from each other when the bonds connecting them tend to zero. These exact results involve the identification of "special solutions" of the CCM equations for the Néel state. An example of this is given by a spin-half system with nearest-neighbour bonds for an underlying lattice corresponding to the magnetic material CaV$_4$O$_9$ (CAVO) in which one of the two different types of bonds on the lattice tend to zero. Larger finite-sized systems may be considered by appropriate choice of the unit cell and the bonds on it. We show here that exact diagonalisation results for ground-state energy and excitation energy gap for the spin-half and spin-one linear Heisenberg model on chains of length up to N=12 sites for s=1/2 and N=6 sites for s=1 with periodic boundary conditions are reproduced exactly using high-order CCM via this "brute-force" approach; i.e., one in which none of the translational or point-group symmetries of the finite lattice are used.
- Feb 24 2010 hep-ph arXiv:1002.4395v1We have considered a supersymmetric scenario in which the minimal supersymmetric standard model is augmented with a right-chiral neutrino superfield for each generation. Such a scenario can have a lightest supersymmetric particle (LSP) dominated by the right-chiral sneutrino state and the lighter stau as the next-to-lightest supersymmetric particle (NLSP). This can easily be motivated by assuming a high scale framework of supersymmetry breaking like minimal supergravity (mSUGRA). Due to the extremely small neutrino Yukawa coupling, the decay of the NLSP to the LSP is suppressed and consequently the NLSP, here the lighter stau mass eigenstate, becomes stable at the length scale of the detector. The collider signal in this case consists of charged tracks of massive stable particles in the muon chamber. Following up on our earlier studies on neutralino and chargino reconstruction in such a scenario, we have shown the kinematical information obtained from these charged tracks allows us to reconstruct the left-chiral tau-sneutrino as well over a significant region of the mSUGRA parameter space. Two methods for reconstruction are suggested and their relative merits are discussed.
- Feb 24 2010 math.NA arXiv:1002.4394v1One main issue, when numerically integrating autonomous Hamiltonian systems, is the long-term conservation of some of its invariants, among which the Hamiltonian function itself. Recently, a new class of methods, named Hamiltonian Boundary Value Methods (HBVMs) has been introduced and analysed, which are able to exactly preserve polynomial Hamiltonians of arbitrarily high degree. We here study a further property of such methods, namely that of having, when cast as a Runge-Kutta method, a matrix of the Butcher tableau with the same spectrum (apart from the zero eigenvalues) as that of the corresponding Gauss-Legendre method, independently of the considered abscissae. Consequently, HBVMs are always perfectly A-stable methods. This, in turn, allows to elucidate the existing connections with classical Runge-Kutta collocation methods.
- Momentum sum rules for fragmentation functions are considered. In particular, we give a general proof of the Schäfer-Teryaev sum rule for the transverse momentum dependent Collins function. We also argue that corresponding sum rules for related fragmentation functions do not exist. Our model-independent analysis is supplemented by calculations in a simple field-theoretical model.
- This paper presents the integration into the GIPSY of Lucx's context calculus defined in Wan's PhD thesis. We start by defining different types of tag sets, then we explain the concept of context, the types of context and the context calculus operators. Finally, we present how context entities have been abstracted into Java classes and embedded into the GIPSY system.
- We construct spaces of quantum increasing sequences, which give quantum families of maps in the sense of Soltan. We then introduce a notion of quantum spreadability for a sequence of noncommutative random variables, by requiring their joint distribution to be invariant under taking quantum subsequences. Our main result is a free analogue of a theorem of Ryll-Nardzewski: for an infinite sequence of noncommutative random variables, quantum spreadability is equivalent to free independence and identical distribution with respect to a conditional expectation.
- Feb 24 2010 math.GT arXiv:1002.4389v1Ozsvath and Szabo construct a spectral sequence with E_2 term \Lambda^*(H^1(Y;Z))⊗Z[U,U^-1] converging to HF^∞(Y,s) for a torsion Spin^c structure s. They conjecture that the differentials are completely determined by the integral triple cup product form via a proposed formula. In this paper, we prove that HF^∞(Y,s) is in fact determined by the integral cohomology ring when s is torsion. Furthermore, for torsion Spin^c structures, we give a complete calculation of HF^∞with mod 2 coefficients when b_1 is 3 or 4.
- Feb 24 2010 cond-mat.stat-mech arXiv:1002.4254v2In this paper, a unified mathematical expression for the constraints leading to the equilibrium distributions of both extensive and non-extensive systems is presented. Based on this expression, a recommendation is made to replace Tsallis' q-average without obvious physical meaning with the statistical harmonic mean for a generalized system.
- Feb 24 2010 cond-mat.mes-hall arXiv:1002.4199v3Assumption of certain hierarchy of soft ferromagnet energy terms, realized in small enough flat nano-elements, allows to obtain explicit expressions for their magnetization distributions. By minimising the energy terms sequentially, from most to the least important, magnetization distributions are expressed as solutions of Riemann-Hilbert boundary value problem for a function of complex variable. A number of free parameters, corresponding to positions of vortices and anti-vortices, still remain in the expression. These parameters can be found by computing and minimizing the total magnetic energy of the particle with no approximations. Thus, the presented approach is a factory of realistic Ritz functions for analytical micromagnetic calculations. These functions are so versatile, that they may even find applications on their own (e.g. for fitting magnetic microscopy images). Examples are given for multi-vortex magnetization distributions in circular cylinder, and for 2-dimensional domain walls in thin magnetic strips.
- Feb 24 2010 cond-mat.mes-hall cond-mat.str-el arXiv:1002.4359v2We examine the quantum phase diagram of the fractional quantum Hall effect (FQHE) in the lowest two Landau levels in half-filled bilayer structures as a function of tunneling strength and layer separation, i.e., we revisit the lowest Landau level filling factor 1/2 bilayer problem and make new predictions involving bilayers in the half-filled second Landau level (i.e., filling factor 5/2). Using numerical exact diagonalization we investigate the important question of whether this system supports a FQHE described by the non-Abelian Moore-Read Pfaffian state in the strong tunneling regime. In the lowest Landau level, we find that although in principle, increasing (decreasing) tunneling strength (layer separation) could lead to a transition from the Abelian two-component Halperin 331 to non-Abelian one-component Moore-Read Pfaffian state, the FQHE excitation gap is relatively small in the lowest Landau level Pfaffian regime--we establish that all so far observed FQHE states in half-filled lowest Landau level bilayers are most likely described by the Abelian Halperin 331 state. In the second Landau level we make the prediction that bilayer structures would manifest two distinct branches of incompressible FQHE corresponding to the Abelian 331 state (at moderate to low tunneling and large layer separation) and the non-Abelian Moore-Read Pfaffian state (at large tunneling and small layer separation). The observation of these two FQHE branches and the possible quantum phase transition between them will be compelling evidence supporting the existence of the non-Abelian Moore-Read Pfaffian state in the second Landau level. We discuss our results in the context of existing experiments and theoretical works.
- We show how one can solve the problem of discriminating between qubit states. We use the quantum state discrimination duality theorem and the Bloch sphere representation of qubits which allows for an easy geometric and analytical representation of the optimal guessing strategies.
- Feb 24 2010 math.DG arXiv:1002.4387v1It is shown that the space of infinitesimal deformations of 2k-Einstein structures is finite dimensional at compact non-flat space forms. Moreover, spherical space forms are shown to be rigid in the sense that they are isolated in the corresponding moduli space.
- Feb 24 2010 q-bio.NC arXiv:1002.4368v1Primate visual system samples different parts of the world unevenly. The part of the visual scene corresponding to the eye center is represented densely, while away from the center the sampling becomes progressively sparser. Such distribution allows a more effective use of the limited transfer rate of the optic nerve, since animals can aim area centralis (AC) at the relevant position in the scene by performing saccadic eye movements. To locate a new saccade target the animal has to sample the corresponding region of the visual scene, away from AC. In this work we derive the sampling density away from AC, which optimizes the trajectory of saccadic eye movements. We obtain the scaling law for the sampling density as a function of eccentricity, which results from the evolutionary pressure to locate the target in the shortest time under the constraint of limited transfer rate of the optic nerve. In case of very small AC the visual scene is optimally represented by logarithmic conformal mapping, in which geometrically similar circular bands around AC are equally represented by the visual system. We also obtain corrections to the logarithmic scaling for the case of a larger AC and compare them to experimental findings.
- We analyze a finite element/boundary element procedure to solve a non-convex contact problem for the double-well potential. After relaxing the associated functional, the degenerate minimization problem is reduced to a boundary/domain variational inequality, a discretized saddle point formulation of which may then be solved numerically. The convergence of the Galerkin approximations to certain macroscopic quantities and a corresponding a posteriori estimate for the approximation error are discussed.
- Feb 24 2010 q-bio.PE arXiv:1002.4386v1Humans and chimpanzees are believed to have shared a common ancestor about 6 million years ago. Here using a new distance measure called the Jump distance, we calculate the number of base substitutions that might have occurred in the mitochondrial DNA during these 6 million years.
- Feb 24 2010 astro-ph.HE astro-ph.GA arXiv:1002.4383v1We report on gamma-ray observations in the off-pulse window of the Vela pulsar PSR B0833-45, using 11 months of survey data from the Fermi Large Area Telescope (LAT). This pulsar is located in the 8 degree diameter Vela supernova remnant, which contains several regions of non-thermal emission detected in the radio, X-ray and gamma-ray bands. The gamma-ray emission detected by the LAT lies within one of these regions, the 2*3 degrees area south of the pulsar known as Vela-X. The LAT flux is signicantly spatially extended with a best-fit radius of 0.88 +/- 0.12 degrees for an assumed radially symmetric uniform disk. The 200 MeV to 20 GeV LAT spectrum of this source is well described by a power-law with a spectral index of 2.41 +/- 0.09 +/- 0.15 and integral flux above 100 MeV of (4.73 +/- 0.63 +/- 1.32) * 10^-7 cm^-2 s^-1. The first errors represent the statistical error on the fit parameters, while the second ones are the systematic uncertainties. Detailed morphological and spectral analyses give strong constraints on the energetics and magnetic field of the pulsar wind nebula (PWN) system and favor a scenario with two distinct electron populations.
- Feb 24 2010 hep-ph arXiv:1002.4376v2A selection of the latest and most frequently used PDFs is incorporated in PYTHIA8, including the MC-adapted PDFs from the MSTW and CTEQ collaborations. This thesis examines the differences in PDFs as well as the effect they have on results of simulations. The results are also compared to data collected by the CDF experiment.
- Feb 24 2010 math.AG arXiv:1002.4382v2Let $C$ be an algebraic smooth complex genus $g>1$ curve. The object of this paper is the study of the birational structure of the coarse moduli space $U_C(r,0)$ of semi-stable rank r vector bundles on $C$ with degree 0 determinant and of its moduli subspace $SU_C(r)$ given by the vector bundles with trivial determinant. Notably we prove that $U_C(r,0)$ (resp. $SU_C(r)$) is birational to a fibration over the symmetric product $C^(rg)$ (resp. over $P^{(r-1)g}$) whose fibres are GIT quotients $(P^{r-1})^{rg}//PGL(r)$. In the cases of low rank and genus our construction produces families of classical modular varieties contained in the Coble hypersurfaces.
- Feb 24 2010 astro-ph.SR arXiv:1002.4381v1Absolute flux distributions for seven solar analog stars are measured from 0.3 to 2.5 \mu m by HST spectrophotometry.In order to predict the longer wavelength mid-IR fluxes that are required for JWST calibration, the HST SEDs are fit with Castelli & Kurucz model atmospheres; and the results are compared with fits from the MARCS model grid. The rms residuals in 10 broad band bins are all <0.5% for the best fits from both model grids. However, the fits differ systematically: The MARCS fits are 40-100 K hotter in T_eff, 0.25-0.80 higher in log g, 0.01-0.10 higher in log z, and 0.008-0.021 higher in the reddening E(B-V), probably because their specifications include different metal abundances. Despite these differences in the parameters of the fits, the predicted mid-IR fluxes differ by only ~1%; and the modeled flux distributions of these G stars have an estimated ensemble accuracy of 2% out to 30 \mu m.
- Feb 24 2010 cond-mat.other quant-ph arXiv:1002.4380v1Presented is a prediction, based on the Frenet-Serret differential geometry of space curves, that the wave number dependence of the average kinetic energy per unit length of two mutually interacting highly curved quantum vortex scales as k^-3. The interacting quantum vortices are helical in shape, supporting circularly polarized counter-propagating waves, with arbitrary curvature and torsion. This power-law spectrum agrees with the high-k spectrum found in precise quantum simulations of turbulent superfluidity with tangle of highly curved and excited quantum vortices.
- Feb 24 2010 math.DG arXiv:1002.4379v2The aim of this paper is to develop on the 1-jet space J^1(R,M^3) the Finsler-like geometry (in the sense of distinguished (d-) connection, d-torsions and d-curvatures) of the rheonomic Berwald-Moor metric of order three. Some natural geometrical field theories (gravitational and electromagnetic) produced by the preceding rheonomic Berwald-Moor metric of order three are also exposed.
- We present an analysis of the vacuum Einstein equations for a recently proposed extension of the Kerr-Schild ansatz that includes a spacelike vector field as well as the usual Kerr-Schild null vector. We show that many, although not all, of the simplifications that occur in the Kerr-Schild case continue to hold for the extended ansatz. In particular, we find a simple set of sufficient conditions on the vectors such that the vacuum field equations truncate beyond quadratic order in an expansion around a general vacuum background solution. We extend our analysis to the electrovac case with a related ansatz for the gauge field.
- We give an introduction to Joyce's construction of the motivic Hall algebra of coherent sheaves on a variety M. When M is a Calabi-Yau threefold we define a semi-classical integration map from a Poisson subalgebra of this Hall algebra to the ring of functions on a symplectic torus. This material will be used in arxiv:1002.4374 to prove some basic properties of Donaldson-Thomas curve-counting invariants on Calabi-Yau threefolds.
- We highlight a topological aspect of the graph limit theory. Graphons are limit objects for convergent sequences of dense graphs. We introduce the representation of a graphon on a unique metric space and we relate the dimension of this metric space to the size of regularity partitions. We prove that if a graphon has an excluded induced sub-bigraph then the underlying metric space is compact and has finite packing dimension. It implies in particular that such graphons have regularity partitions of polynomial size.
- Feb 24 2010 hep-ph arXiv:1002.4375v1We compute the resummed hadronic transverse energy (E_T) distribution due to initial-state QCD radiation in vector boson and Higgs boson production at hadron colliders. The resummed exponent, parton distributions and coefficient functions are treated consistently to next-to-leading order. The results are matched to fixed-order calculations at large E_T and compared with parton-shower Monte Carlo predictions at Tevatron and LHC energies.
- We use Joyce's theory of motivic Hall algebras to prove that reduced Donaldson-Thomas curve-counting invariants on Calabi-Yau threefolds coincide with stable pair invariants, and that the generating functions for these invariants are Laurent expansions of rational functions.
- Feb 24 2010 math.NT arXiv:1002.4373v2According to the Birch and Swinnerton-Dyer conjectures, if A/Q is an abelian variety then its L-function must capture substantial part of the arithmetic properties of A. The smallest number field L where A has all its endomorphisms defined must also have a role. This article deals with the relationship between these two objects in the specific case of modular abelian varieties A_f/Q associated to weight 2 newforms for the modular group Gamma_1(N). Specifically, our goal is to relate the order of L(A_f/Q,s) at s = 1 with Euler products cropped by the set of primes that split completely in L. The results we obtain for the case when f has complex multiplication are complete, while in the absence of CM, our results depend on the rate of convergence in Sato-Tate distributions.
- Feb 24 2010 physics.ins-det physics.bio-ph arXiv:1002.4237v1We propose a Zernike phase contrast electron microscope that uses an intense laser focus to convert a phase image into a visible image. We present the relativistic quantum theory of the phase shift caused by the laser-electron-interaction, study resonant cavities for enhancing the laser intensity, and discuss applications in biology, soft materials science, and atomic and molecular physics.
- Feb 24 2010 cond-mat.quant-gas arXiv:1002.4366v1Very recently Girardeau and Minguzzi [arXiv:0807.3366v2, Phys. Rev. A 79, 033610 (2009)] have studied an impurity in a one-dimensional gas of hard-core bosons. In particular they deal with the general case where the mass of the impurity is different from the mass of the bosons and the impurity-boson interaction is not necessarily infinitely repulsive. We show that one of their initial step is erroneous, contradicting both physical intuition and known exact results. Their results in the general case apply only actually when the mass of the impurity is infinite.
- Paper deals with the singular Sturm-Liouville expressions $$l(y) = -(py')' + qy$$ on a finite interval with coefficients $$q = Q', \quad 1/p, Q/p, Q^2/p ∈L_1,$$ where derivative of the function $Q$ is understood in the sense of distributions. Due to a new regularization corresponding operators are correctly defined as quasi-differential. Their resolvent approximation is investigated and all self-adjoint and maximal dissipative extensions and generalized resolvents are described in terms of homogeneous boundary conditions of the canonic form. Some results are new for the case $p(t)\equiv 1$ as well.
- Feb 24 2010 astro-ph.CO arXiv:1002.4370v1Photometric scaling relations are studied for S0 galaxies and compared with those for spirals. New 2D K_s-band multi-component decompositions are presented for 122 early-type disk galaxies. Combining with our previous decompositions, the final sample consists of 175 galaxies. As a comparison sample we use the Ohio State University Bright Spiral Galaxy Survey (OSUBSGS), for which similar decompositions have previously been made by us. Our main results are: (1) Important scaling relations are present, indicating that the formative processes of bulges and disks in S0s are coupled like has been previously found for spirals. (2) We obtain median r_eff/h_r = 0.20, 0.15 and 0.10 for S0, S0/a-Sa and Sab-Sc galaxies: these are smaller than predicted by simulation models in which bulges are formed by galaxy mergers. (3) The properties of bulges of S0s are different from the elliptical galaxies, which is manifested in the M_K(bulge) vs r_eff relation, in the photometric plane, and to some extent also in the Kormendy relation. The bulges of S0s are similar to bulges of spirals with M_K(bulge) < -20 mag. Some S0s have small bulges, but their properties are not compatible with the idea that they could evolve to dwarfs by galaxy harassment. (4) The relative bulge flux B/T for S0s covers the full range found in the Hubble sequence. (5) The values and relations of the parameters of the disks of the S0 galaxies in NIRS0S are similar to those obtained for spirals in the OSUBSGS. Overall, our results support the view that spiral galaxies with bulges brighter than -20 mag in the K-band can evolve directly into S0s, due to stripping of gas followed by truncated star formation.
- In this paper we investigate the vacuum polarization effects associated with a massive quantum scalar field in de Sitter spacetime in the presence of gravitational topological defects. Specifically we calculate the vacuum expectation value of the field square, $<\Phi^2>$. Because this investigation has been developed in a pure de Sitter space, here we are mainly interested on the effects induced by the presence of the defects.
- Feb 24 2010 cs.CG arXiv:1002.4364v1Higher order Delaunay triangulations are a generalization of the Delaunay triangulation which provides a class of well-shaped triangulations, over which extra criteria can be optimized. A triangulation is order-$k$ Delaunay if the circumcircle of each triangle of the triangulation contains at most $k$ points. In this paper we study lower and upper bounds on the number of higher order Delaunay triangulations, as well as their expected number for randomly distributed points. We show that arbitrarily large point sets can have a single higher order Delaunay triangulation, even for large orders, whereas for first order Delaunay triangulations, the maximum number is $2^{n-3}$. Next we show that uniformly distributed points have an expected number of at least $2^{\rho_1 n(1+o(1))}$ first order Delaunay triangulations, where $\rho_1$ is an analytically defined constant ($\rho_1 \approx 0.525785$), and for $k > 1$, the expected number of order-$k$ Delaunay triangulations (which are not order-$i$ for any $i < k$) is at least $2^{\rho_k n(1+o(1))}$, where $\rho_k$ can be calculated numerically.
- Feb 24 2010 cond-mat.str-el cond-mat.mes-hall arXiv:1002.4367v2Motivated by Resonant X-ray scattering experiments in cuprate ladder materials showing charge order modulation of period $\lambda=3$ and 5 at specific hole densities, we investigate models involving the electronic t-J ladders and bosonic chains coupled via screened Coulomb repulsion. Extensive density matrix renormalization group calculations applied to the ladders/chains supplemented by a self-consistent mean-field treatment of the inter-ladder/chain coupling provide quantitative estimates of the charge order for $\lambda=3,4$ and 5. As previously proposed, such patterns correspond to the emergence of pair density waves which stem from the strong electronic correlations. We comment on the existence of a $\lambda=4$ modulation not seen so far in experiment.
- Feb 24 2010 math.KT arXiv:1002.4365v3We construct $C^\ast$-categories that are anologues of the categories used in controlled algebraic $K$-theory. We then show that the reduced $C^\ast$-algebra of a finitely presented group and an associated controlled $C^\ast$-category have equivalent $K$-theory spectra, and that, at least in certain special cases, the associated $C^\ast$-category depends functorially on the group. Thus in these cases the $K$-theory spectrum of the reduced group $C^\ast$-algebra is a functor.
- We propose a solution to the longstanding cosmological constant (CC) problem which is based on the fusion of two existing concepts. The first is the suggestion that the proper description of classical gravitational effects is the gauge theory of gravity in which the connection instead of the metric acts as the dynamical variable. The resulting field equation does not then contain the CC term. This removes the connection between the CC and the quantum vacuum energy, and therefore addresses the \it old CC problem of why quantum vacuum energy does not gravitate. The CC-equivalent in this approach arises from the constant of integration when reducing the field equation to the Einstein equation. The second is the assumption that the universe obeys de Sitter symmetry, with the observed accelerating expansion as its manifestation. We combine these ideas and identify the constant of integration with the inverse-square of the radius of curvature of the de Sitter space. The origin of dark energy (DE) is therefore associated with the inherent spacetime geometry, with the smallness of DE protected by symmetry. This addresses the \it new CC problem, or the DE puzzle. This approach, however, faces major challenges from quantum considerations. These are the ghost problem associated with higher order gravity theories and the quantum instability of the de Sitter spacetime. We discuss their possible remedies.
- In the recent past, there has been a concerted effort to develop mathematical models for real-world networks and to analyze various dynamics on these models. One particular problem of significant importance is to understand the effect of random edge lengths or costs on the geometry and flow transporting properties of the network. Two different regimes are of great interest, the weak disorder regime where optimality of a path is determined by the sum of edge weights on the path and the strong disorder regime where optimality of a path is determined by the maximal edge weight on the path. In the context of the stochastic mean-field model of distance, we provide the first mathematically tractable model of weak disorder and show that no transition occurs at finite temperature. Indeed, we show that for every finite temperature, the number of edges on the minimal weight path (i.e., the hopcount) is $\Theta(\log{n})$ and satisfies a central limit theorem with asymptotic means and variances of order $\Theta(\log{n})$, with limiting constants expressible in terms of the Malthusian rate of growth and the mean of the stable-age distribution of an associated continuous-time branching process. More precisely, we take independent and identically distributed edge weights with distribution $E^s$ for some parameter $s>0$, where $E$ is an exponential random variable with mean 1. Then the asymptotic mean and variance of the central limit theorem for the hopcount are $s\log{n}$ and $s^2\log{n}$, respectively. We also find limiting distributional asymptotics for the value of the minimal weight path in terms of extreme value distributions and martingale limits of branching processes.
- Feb 24 2010 cond-mat.stat-mech cond-mat.dis-nn arXiv:1002.4363v3Glauber dynamics of a bond-diluted Ising model on a Bethe lattice (a random graph with fixed connectivity) is investigated by an approximate theory which provides exact results for equilibrium properties. The time-dependent solutions of the dynamical system derived by this method are in good agreement with the results obtained by Monte Carlo simulations in almost all situations. Furthermore, the derived dynamical system exhibits a remarkable phenomenon that the magnetization shows multi-step relaxations at intermediate time scales in a low-temperature part of the Griffiths phase without bond percolation clusters.
- We establish the cutoff-dependent upper Higgs boson mass bound by means of direct lattice computations in the framework of a chirally invariant lattice Higgs-Yukawa model emulating the same chiral Yukawa coupling structure as in the Higgs-fermion sector of the Standard Model. As expected from the triviality picture of the Higgs sector, we observe the upper mass bound to decrease with rising cutoff parameter $\Lambda$. Moreover, the strength of the fermionic contribution to the upper mass bound is explored by comparing to the corresponding analysis in the pure $\Phi^4$-theory.
- We obtain new connections between permutation patterns and singularities of Schubert varieties, by giving a new characterization of Gorenstein varieties in terms of so called bivincular patterns. These are generalizations of classical patterns where conditions are placed on the location of an occurrence in a permutation, as well as on the values in the occurrence. This clarifies what happens when the requirement of smoothness is weakened to factoriality and further to Gorensteinness, extending work of Bousquet-Melou and Butler (2007), and Woo and Yong (2006). We also show how mesh patterns, introduced by Branden and Claesson (2011), subsume many other types of patterns and define an extension of them called marked mesh patterns. We use these new patterns to further simplify the description of Gorenstein Schubert varieties and give a new description of Schubert varieties that are defined by inclusions, introduced by Gasharov and Reiner (2002). We also give a description of 123-hexagon avoiding permutations, introduced by Billey and Warrington (2001), Dumont permutations and cycles in terms of marked mesh patterns.

Ill-posedness of basic equations of fluid dynamics in Besov spaces

serfati philippe Feb 16 2018 10:57 UTCserfati philippe Feb 16 2018 10:44 UTC

...(continued)+on (3 and more, 2008-13-14..) papers of bourgain etal (and their numerous descendants) on =1/ (t-static) illposednesses for the nd incompressible euler equations (and nse) and +- critical spaces, see possible counterexamples constructed on my nd shear flows, pressureless (shockless) solutions of in

serfati philippe Feb 15 2018 19:03 UTC

...(continued)+on (3 and more, 2008-13-14..) papers of bourgain etal (and their numerous descendants) on =1/ (t-static) illposednesses for the nd incompressible euler equations (and nse) and +- critical spaces, see possible counterexamples constructed on my nd shear flows, pressureless (shockless) solutions of in

serfati philippe Feb 15 2018 19:03 UTC

...(continued)+on (3 and more, 2008-13-14..) papers of bourgain etal (and their numerous descendants) on =1/ (t-static) illposednesses for the nd incompressible euler equations (and nse) and +- critical spaces, see possible counterexamples constructed on my nd shear flows, pressureless (shockless) solutions of in

serfati philippe Feb 15 2018 19:03 UTC

serfati philippe Feb 15 2018 13:29 UTC

...(continued)on transport and continuity equations with regular speed out of an hypersurface, and on it, having 2 relative normal components with the same punctual sign (possibly varying) and better unexpected results on solutions and jacobians etc, see (https://www.researchgate.net/profile/Philippe_Serfati), pa

serfati philippe Feb 15 2018 12:35 UTC

...(continued)on transport and continuity equations with regular speed out of an hypersurface, and on it, having 2 relative normal components with the same punctual sign (possibly varying) and better unexpected results on solutions and jacobians etc, see (https://www.researchgate.net/profile/Philippe_Serfati), pa

Beni Yoshida Feb 13 2018 19:53 UTC

...(continued)This is not a direct answer to your question, but may give some intuition to formulate the problem in a more precise language. (And I simplify the discussion drastically). Consider a static slice of an empty AdS space (just a hyperbolic space) and imagine an operator which creates a particle at some

Abhinav Deshpande Feb 10 2018 15:42 UTC

...(continued)I see. Yes, the epsilon ball issue seems to be a thorny one in the prevalent definition, since the gate complexity to reach a target state from any of a fixed set of initial states depends on epsilon, and not in a very nice way (I imagine that it's all riddled with discontinuities). It would be inte

Elizabeth Crosson Feb 10 2018 05:49 UTC

...(continued)Thanks for the correction Abhinav, indeed I meant that the complexity of |psi(t)> grows linearly with t.

Producing an arbitrary state |phi> exactly is also too demanding for the circuit model, by the well-known argument that given any finite set of gates, the set of states that can be reached i

- Supported by Silverpond.