The one-dimensional Hubbard model for large or infiniteU

The magnetic properties of the one-dimensional Hubbard model with a hardcore interaction on a ring (periodic boundary conditions) are investigated. At finite temperatures it is shown to behave up to exponentially small corrections as a pure paramagnet. An explicit expression for the ground-state degeneracies is derived. The eigenstates of this model are used to perform a perlurbational treatment for large but finite interactions. In first order inU ¹ an effective Hamiltonian for the one-dimensional Hubbard model is derived. It is the Hamiltonian of the one-dimensional Hcisenberg model with antiferromagnetic couplings between nearest neighbor spins. An asymptotic expansion for the ground-state energy is given. The results are valid for arbitrary densities of electrons.     

Electrical and infrared dielectrical properties of silica aerogels and of silica-aerogel-based composites

In this contribution we have studied the key electrical parameters of silica aerogels and of silica-aerogel-based composites, namely the dielectric constants , the dielectric losses tan (at 1 kHz), and the breakdown fields E _b (at 50 Hz). For low-density bulk silica aerogels we find =1.25 and tan =0.0005. E _b is about 500 kV/cm in quasi-homogeneous fields, and of the order of MV/cm in strongly inhomogeneous fields. The dielectric constants of partially densified aerogels increase linearly with density; their dielectric losses are relatively large and their breakdown fields are comparativiely low. The same results are found for aerogels in the form of settled materials, i.e. aerogel granules and powders in air. Acrylate-based aerogel composites with volume fractions larger than 70% have low dielectric constants but their losses are at least 10 times higher than those of low-density aerogels. These materials sustain high local fields in the MV/cm region, while in quasihomogeneous fields, breakdown occurs at about 100 kV/cm. Based on the present results and the interplay with other physical properties (low mechanical resistance, low thermal conductivity, adsorption of water, etc.), silica aerogels and silica aerogel-acrylate-based composites are predicted to have a low potential for electrical insulation.     

Knot wormholes in geometrodynamics?

The familiar wormhole model of geometrodynamics is extended to allow for knotted embeddings of the initial hypersurface. It is shown that topology change is not only a means to modify the connectivity of the space, but also the knot invariants of its embedding. In a probabilistic framework the process of wormhole scattering can be expressed by creation and annihilation operators acting on the wave function of quantum geometrodynamics. Implications concerning Wheeler's exciton model of elementary particles, thef-gravity approach to hadronic matter, and interrelations with Jehle's flux quantization program are discussed.Work supported by a grant of the Studienstiftung des deutschen Volkes and in part by National Science Foundation grant No. GP 30799 X to Princeton University.     

Variational reactive scattering calculations: computational optimization strategies

Summary We have developed efficient and accurate techniques for the calculation of quantum mechanical reaction probabilities of atom-diatom exchange reactions in the gas phase, and we have optimized a computer code employing these techniques and applied it sucessfully to several systems. In this paper we consider further strategies for improving the algorithm to allow even more demanding applications. In this context, improvement means that equivalent results can be obtained using fewer computational resources (computer time or storage) or that an equivalent expenditure of resources can yield higher accuracy. The new strategies discussed here lead to improvement in both of these areas. Two areas of special focus in the present paper are (i) the finite difference boundary value method used for calculating distorted wave Green's functions and regular solutions for scattering by the distortion potential and (ii) the choice of the distortion potential itself. Among other results included here is the first application of the outgoing wave or scattered wave variational principle to reactive scattering.     

Infrared matrix isolation and quantum chemical studies of the nitrous acid complexes with water

The 1:1 and 2:1 complexes between water and trans- and cis-isomers of nitrous acid have been isolated in argon matrices and studied using FTIR spectroscopy and DFT(B3LYP) calculations with a 6-311++G(2d,2p) basis set. The analysis of the experimental spectra indicate that 1:1 complexes trapped in solid argon involve very strong hydrogen bond in which acid acts as the proton donor and water as the proton acceptor. The perturbed OH stretches are −248, −228 cm⁻¹ red shifted from their free-molecules values in complexes formed by trans- and cis-HONO isomers, respectively. The calculated spectral parameters for the two complexes are in good agreement with experimental data. The calculations also predict stability of two more 1:1 weakly bound complexes formed by each isomer. In these the water acts as the proton donor and one of the two oxygen atoms of the acid as the acceptor. The experimental spectra demonstrate also formation of 2:1 complex between water and trans-HONO isomer in an argon matrix. The performed calculations indicate that the complex involves a seven-membered ring in which OH group of HONO forms very strong hydrogen bond with the oxygen atom of one water molecule and nitrogen atom acts as a weak proton acceptor for the hydrogen atom of the second water molecule of the water dimer. The observed perturbations of the OH stretch of trans-HONO (750 cm⁻¹ red shift) is much larger than that predicted by calculations (556 cm⁻¹ red shift); this difference is attributed to strong solvation effect of argon matrix on very strong hydrogen bond.     

Fermi surface of CeIn3 above the Néel critical field

We report measurements of the de Haas-van Alphen effect in CeIn(3) in magnetic fields extending to approximately 90 T, well above the Néel critical field of mu(0)H(c) approximately 61 T. The unreconstructed Fermi surface a sheet is observed in the high magnetic field polarized paramagnetic limit, but with its effective mass and Fermi surface volume strongly reduced in size compared to that observed in the low magnetic field paramagnetic regime under pressure. The spheroidal topology of this sheet provides an ideal realization of the transformation from a "large Fermi surface" accommodating f electrons to a "small Fermi surface" when the f-electron moments become polarized.     

Boson Stars: Rotation, Formation, and Evolution

Boson stars are descendants of the so-calledgeons of Wheeler, except that they are built from scalarparticles instead of electromagnetic fields. If scalarfields exist in nature, such localized configurations kept together by their self-generatedgravitational field can form within Einstein's generalrelativity. In the case of complex scalar fields, anabsolutely stable branch of such non-topologicalsolitons with conserved particle number exists. Thepresent surge of interest stems from the speculativepossibility that these compact objects could provide aconsiderable fraction of the non-baryonic part of dark matter. In any case, they may serve as aconvenient laboratory for studyingnumerically rapidly rotating bodies in generalrelativity and the generation of gravitational waves.Furthermore, we mention how to detect boson stars by gravitationallensing or gravitational redshift. Finally, we explorethe evolution of boson stars within scalar-tensortheories.     

Are Axidilaton Stars Massive Compact Halo Objects?

Boson stars built from a very light Kalb–Ramond axion, the dilaton or other moduli fields of effective string models could provide a considerable fraction of the non-baryonic part of dark matter. Gravitational microlensing of 0.5 M MACHOs within the halo of galaxies may indirectly "weighing" the mass of the constituent scalar particle, resulting in 10^–10 eV/c².