On Flux Quantization in F-Theory II: Unitary and Symplectic Gauge Groups

We study the quantization of the M-theory G-flux on elliptically fibered Calabi-Yau fourfolds with singularities giving rise to unitary and symplectic gauge groups. We seek and find its relation to the Freed-Witten quantization of worldvolume fluxes on 7-branes in type IIB orientifold compactifications on Calabi-Yau threefolds. By explicitly constructing the appropriate four-cycles on which to calculate the periods of the second Chern class of the fourfolds, we find that there is a half-integral shift in the quantization of G-flux whenever the corresponding dual 7-brane is wrapped on a non-spin submanifold. This correspondence of quantizations holds for all unitary and symplectic gauge groups, except for SU(3), which behaves mysteriously. We also perform our analysis in the case where, in addition to the aforementioned gauge groups, there is also a 'flavor' U(1)-gauge group.Comment: 33 pages, 4 figure

Aperiodic Ising Quantum Chains

Some years ago, Luck proposed a relevance criterion for the effect of aperiodic disorder on the critical behaviour of ferromagnetic Ising systems. In this article, we show how Luck's criterion can be derived within an exact renormalisation scheme for Ising quantum chains with coupling constants modulated according to substitution rules. Luck's conjectures for this case are confirmed and refined. Among other outcomes, we give an exact formula for the correlation length critical exponent for arbitrary two-letter substitution sequences with marginal fluctuations of the coupling constants.Comment: 27 pages, LaTeX, 1 Postscript figure included, using epsf.sty and amssymb.sty (one error corrected, some minor changes

Surface Properties of Aperiodic Ising Quantum Chains

We consider Ising quantum chains with quenched aperiodic disorder of the coupling constants given through general substitution rules. The critical scaling behaviour of several bulk and surface quantities is obtained by exact real space renormalization.Comment: 4 pages, RevTex, reference update

The spin-1/2 XXZ Heisenberg chain, the quantum algebra U_q[sl(2)], and duality transformations for minimal models

The finite-size scaling spectra of the spin-1/2 XXZ Heisenberg chain with toroidal boundary conditions and an even number of sites provide a projection mechanism yielding the spectra of models with a central charge c<1 including the unitary and non-unitary minimal series. Taking into account the half-integer angular momentum sectors - which correspond to chains with an odd number of sites - in many cases leads to new spinor operators appearing in the projected systems. These new sectors in the XXZ chain correspond to a new type of frustration lines in the projected minimal models. The corresponding new boundary conditions in the Hamiltonian limit are investigated for the Ising model and the 3-state Potts model and are shown to be related to duality transformations which are an additional symmetry at their self-dual critical point. By different ways of projecting systems we find models with the same central charge sharing the same operator content and modular invariant partition function which however differ in the distribution of operators into sectors and hence in the physical meaning of the operators involved. Related to the projection mechanism in the continuum there are remarkable symmetry properties of the finite XXZ chain. The observed degeneracies in the energy and momentum spectra are shown to be the consequence of intertwining relations involving U_q[sl(2)] quantum algebra transformations.Comment: This is a preprint version (37 pages, LaTeX) of an article published back in 1993. It has been made available here because there has been recent interest in conformal twisted boundary conditions. The "duality-twisted" boundary conditions discussed in this paper are particular examples of such boundary conditions for quantum spin chains, so there might be some renewed interest in these result

Structure of the solar photosphere studied from the radiation hydrodynamics code ANTARES

The ANTARES radiation hydrodynamics code is capable of simulating the solar granulation in detail unequaled by direct observation. We introduce a state-of-the-art numerical tool to the solar physics community and demonstrate its applicability to model the solar granulation. The code is based on the weighted essentially non-oscillatory finite volume method and by its implementation of local mesh refinement is also capable of simulating turbulent fluids. While the ANTARES code already provides promising insights into small-scale dynamical processes occurring in the quiet-Sun photosphere, it will soon be capable of modeling the latter in the scope of radiation magnetohydrodynamics. In this first preliminary study we focus on the vertical photospheric stratification by examining a 3-D model photosphere with an evolution time much larger than the dynamical timescales of the solar granulation and of particular large horizontal extent corresponding to $25\!" \!\! \times \, 25\!"$ on the solar surface to smooth out horizontal spatial inhomogeneities separately for up- and downflows. The highly resolved Cartesian grid thereby covers $\sim 4~\mathrm{Mm}$ of the upper convection zone and the adjacent photosphere. Correlation analysis, both local and two-point, provides a suitable means to probe the photospheric structure and thereby to identify several layers of characteristic dynamics: The thermal convection zone is found to reach some ten kilometers above the solar surface, while convectively overshooting gas penetrates even higher into the low photosphere. An $\approx 145\,\mathrm{km}$ wide transition layer separates the convective from the oscillatory layers in the higher photosphere.Comment: Accepted for publication in Astrophysics and Space Science; 18 pages, 12 figures, 2 tables; typos correcte

Four types of special functions of G_2 and their discretization

Properties of four infinite families of special functions of two real variables, based on the compact simple Lie group G2, are compared and described. Two of the four families (called here C- and S-functions) are well known, whereas the other two (S^L- and S^S-functions) are not found elsewhere in the literature. It is shown explicitly that all four families have similar properties. In particular, they are orthogonal when integrated over a finite region F of the Euclidean space, and they are discretely orthogonal when their values, sampled at the lattice points F_M \subset F, are added up with a weight function appropriate for each family. Products of ten types among the four families of functions, namely CC, CS, SS, SS^L, CS^S, SS^L, SS^S, S^SS^S, S^LS^S and S^LS^L, are completely decomposable into the finite sum of the functions. Uncommon arithmetic properties of the functions are pointed out and questions about numerous other properties are brought forward.Comment: 18 pages, 4 figures, 4 table

Ramping fermions in optical lattices across a Feshbach resonance

We study the properties of ultracold Fermi gases in a three-dimensional optical lattice when crossing a Feshbach resonance. By using a zero-temperature formalism, we show that three-body processes are enhanced in a lattice system in comparison to the continuum case. This poses one possible explanation for the short molecule lifetimes found when decreasing the magnetic field across a Feshbach resonance. Effects of finite temperatures on the molecule formation rates are also discussed by computing the fraction of double-occupied sites. Our results show that current experiments are performed at temperatures considerably higher than expected: lower temperatures are required for fermionic systems to be used to simulate quantum Hamiltonians. In addition, by relating the double occupancy of the lattice to the temperature, we provide a means for thermometry in fermionic lattice systems, previously not accessible experimentally. The effects of ramping a filled lowest band across a Feshbach resonance when increasing the magnetic field are also discussed: fermions are lifted into higher bands due to entanglement of Bloch states, in good agreement with recent experiments.Comment: 9 pages, 7 figure

Magnetically Controlled Exchange Process in an Ultracold Atom-Dimer Mixture

We report on the observation of an elementary exchange process in an optically trapped ultracold sample of atoms and Feshbach molecules. We can magnetically control the energetic nature of the process and tune it from endoergic to exoergic, enabling the observation of a pronounced threshold behavior. In contrast to relaxation to more deeply bound molecular states, the exchange process does not lead to trap loss. We find excellent agreement between our experimental observations and calculations based on the solutions of three-body Schr\"odinger equation in the adiabatic hyperspherical representation. The high efficiency of the exchange process is explained by the halo character of both the initial and final molecular states.Comment: 4 pages, 4 figure

Cruising through molecular bound state manifolds with radio frequency

The emerging field of ultracold molecules with their rich internal structure is currently attracting a lot of interest. Various methods have been developed to produce ultracold molecules in pre-set quantum states. For future experiments it will be important to efficiently transfer these molecules from their initial quantum state to other quantum states of interest. Optical Raman schemes are excellent tools for transfer, but can be involved in terms of equipment, laser stabilization and finding the right transitions. Here we demonstrate a very general and simple way for transfer of molecules from one quantum state to a neighboring quantum state with better than 99% efficiency. The scheme is based on Zeeman tuning the molecular state to avoided level crossings where radio-frequency transitions can then be carried out. By repeating this process at different crossings, molecules can be successively transported through a large manifold of quantum states. As an important spin-off of our experiments, we demonstrate a high-precision spectroscopy method for investigating level crossings.Comment: 5 pages, 5 figures, submitted for publicatio

Gauge Fluxes in F-theory and Type IIB Orientifolds

We provide a detailed correspondence between G_4 gauge fluxes in F-theory compactifications with SU(n) and SU(n)x(1) gauge symmetry and their Type IIB orientifold limit. Based on the resolution of the relevant F-theory Tate models we classify the factorisable G_4-fluxes and match them with the set of universal D5-tadpole free U(1)-fluxes in Type IIB. Where available, the global version of the universal spectral cover flux corresponds to Type IIB gauge flux associated with a massive diagonal U(1). In U(1)-restricted Tate models extra massless abelian fluxes exist which are associated with specific linear combinations of Type IIB fluxes. Key to a quantitative match between F-theory and Type IIB is a proper treatment of the conifold singularity encountered in the Sen limit of generic F-theory models. We also shed further light on the brane recombination process relating generic and U(1)-restricted Tate models.Comment: 53 pages, 3 figures; v2: Refs added; v3: minor corrections to match version published in JHE