Predictions on the couplings of f- and ϱ- trajectories to mesons from chiral symmetry

We employ a chiral saturation scheme involving 15, $\text{L = 0,}\text{and}\text{15}\text{, L = 1}$ mesons in a classification according to SU(4) ? O(3) (i.e. the mesonns π, ?, ω, A₁, A₂, f, A₀ (δ), B, D and σ) and calculate all f and ? Regge couplings between these mesons via a matrix version of finite-energy sum rules. In addition the size of exotic exchanges is evaluated and found to be small. The results are compared with experimental numbers and other models as far as available.     

Two axisymmetric black holes cannot be in static equilibrium

No static equilibrium configuration of two black holes can exist in an axisymmetric asymptotically flat vacuum space-time.Work partly supported by the Deutsche Forschungsgemeinschaft.For a definition of axisymmetry see Carter (1972).     

Electronic structure and dynamics of optically excited single-wall carbon nanotubes

We have studied the electronic structure and charge-carrier dynamics of individual single-wall carbon nanotubes (SWNTs) and nanotube ropes using optical and electron–spectroscopic techniques. The electronic structure of semiconducting SWNTs in the band-gap region is analyzed using near-infrared absorption spectroscopy. A semi-empirical expression for E₁₁^S transition energies, based on tight-binding calculations is found to give striking agreement with experimental data. Time-resolved PL from dispersed SWNT-micelles shows a decay with a time constant of about 15 ps. Using time-resolved photoemission we also find that the electron–phonon (e–ph) coupling in metallic tubes is characterized by a very small e–ph mass-enhancement of 0.0004. Ultrafast electron–electron scattering of photo-excited carriers in nanotube ropes is finally found to lead to internal thermalization of the electronic system within about 200 fs. PACS 78.47.+p; 81.07.De; 78.67.Ch; 87.64.Ni     

Quantum electrodynamics in 2 + 1 dimensions, confinement, and the stability of U(1) spin liquids

Compact quantum electrodynamics in 2 + 1 dimensions often arises as an effective theory for a Mott insulator, with the Dirac fermions representing the low-energy spinons. An important and controversial issue in this context is whether a deconfinement transition takes place. We perform a renormalization group analysis to show that deconfinement occurs when N > Nc = 36/pi3 approximately to 1.161, where N is the number of fermion replica. For N < Nc, however, there are two stable fixed points separated by a line containing a unstable nontrivial fixed point: a fixed point corresponding to the scaling limit of the noncompact theory, and another one governing the scaling behavior of the compact theory. The string tension associated with the confining interspinon potential is shown to exhibit a universal jump as N --> Nc-. Our results imply the stability of a spin liquid at the physical value N = 2 for Mott insulators.     

Fast chain contraction during protein folding: "foldability" and collapse dynamics

Theory indicates that at least some proteins will undergo a rapid and unimpeded collapse, like a disorganized hydrophobic chain, prior to folding. Yet experiments continue to find signs of an organized, or barrier-limited, collapse in even the fastest (approximately mus) folding proteins. Does the kinetic barrier represent a signature of the equilibrium "foldability" of these molecules? We have measured the rate of chain contraction in two nonfolding analogs of a very fast-collapsing protein. We find that these chains contract on the same time scale (approximately 10(-5)s) as the natural protein, and both pass over an energetic barrier at least as large as that encountered by the protein. The equilibrium foldability of the native structure therefore does not alone determine the dynamics of collapse; even the disordered chains contract approximately 1000x slower than expected for an ideal chain.     

Accretive perturbations and error estimates for the Trotter product formula

We study the operator-norm error bound estimate for the exponential Trotter product formula in the case of accretive perturbations. LetA be a semibounded from below self-adjoint operator in a separable Hilbert space. LetB be a closed maximal accretive operator such that, together withB ^*, they are Kato-small with respect toA with relative bounds less than one. We show that in this case the operator-norm error bound estimate for the exponential Trotter product formula is the same as for the self-adjointB [12]: