Topology and pion correlators -- a study in the N_f=2 Schwinger model

I readdress the issue whether the topological charge of the gauge background has an influence on a hadronic observable. To this end pion correlators in the Schwinger model with 2 dynamical flavours are determined on subensembles with a fixed topological charge. It turns out that the answer depends on a specific function of the sea-quark mass and the box volume which is in close analogy to the Leutwyler-Smilga parameter in full QCD.Comment: Lattice2001(confinement), 3 pages, 2 figure

A comparative study of overlap and staggered fermions in QCD

We perform a comparative study of the infrared properties of overlap and staggered fermions in QCD. We observe that the infrared spectrum of the APE/HYP improved staggered Dirac operator develops a four-fold near-degeneracy and is in quantitative agreement with the infrared spectrum of the overlap operator. The near-degeneracy allows us to identify the zero modes of the staggered operator and we find that the number of zero modes is in line with the topological index of the overlap operator.Comment: Talk presented at Lattice2004(chiral), Fermilab, June 21-26, 2004, 3 pages, 2 figure

A microscopic derivation of the quantum mechanical formal scattering cross section

We prove that the empirical distribution of crossings of a "detector'' surface by scattered particles converges in appropriate limits to the scattering cross section computed by stationary scattering theory. Our result, which is based on Bohmian mechanics and the flux-across-surfaces theorem, is the first derivation of the cross section starting from first microscopic principles.Comment: 28 pages, v2: Typos corrected, layout improved, v3: Typos corrected. Accepted for publication in Comm. Math. Phy

Bohmian Mechanics and Quantum Field Theory

We discuss a recently proposed extension of Bohmian mechanics to quantum field theory. For more or less any regularized quantum field theory there is a corresponding theory of particle motion, which in particular ascribes trajectories to the electrons or whatever sort of particles the quantum field theory is about. Corresponding to the nonconservation of the particle number operator in the quantum field theory, the theory describes explicit creation and annihilation events: the world lines for the particles can begin and end.Comment: 4 pages, uses RevTeX4, 2 figures; v2: shortened and with minor addition

Atom-molecule Rabi oscillations in a Mott insulator

We observe large-amplitude Rabi oscillations between an atomic and a molecular state near a Feshbach resonance. The experiment uses 87Rb in an optical lattice and a Feshbach resonance near 414 G. The frequency and amplitude of the oscillations depend on magnetic field in a way that is well described by a two-level model. The observed density dependence of the oscillation frequency agrees with the theoretical expectation. We confirmed that the state produced after a half-cycle contains exactly one molecule at each lattice site. In addition, we show that for energies in a gap of the lattice band structure, the molecules cannot dissociate

Collisional decay of 87Rb Feshbach molecules at 1005.8 G

We present measurements of the loss-rate coefficients K_am and K_mm caused by inelastic atom-molecule and molecule-molecule collisions. A thermal cloud of atomic 87Rb is prepared in an optical dipole trap. A magnetic field is ramped across the Feshbach resonance at 1007.4 G. This associates atom pairs to molecules. A measurement of the molecule loss at 1005.8 G yields K_am=2 10^-10 cm^3/s. Additionally, the atoms can be removed with blast light. In this case, the measured molecule loss yields K_mm=3 10^-10 cm^3/s

User's guide to Monte Carlo methods for evaluating path integrals

We give an introduction to the calculation of path integrals on a lattice, with the quantum harmonic oscillator as an example. In addition to providing an explicit computational setup and corresponding pseudocode, we pay particular attention to the existence of autocorrelations and the calculation of reliable errors. The over-relaxation technique is presented as a way to counter strong autocorrelations. The simulation methods can be extended to compute observables for path integrals in other settings

Observations on staggered fermions at non-zero lattice spacing

We show that the use of the fourth-root trick in lattice QCD with staggered fermions corresponds to a non-local theory at non-zero lattice spacing, but argue that the non-local behavior is likely to go away in the continuum limit. We give examples of this non-local behavior in the free theory, and for the case of a fixed topologically non-trivial background gauge field. In both special cases, the non-local behavior indeed disappears in the continuum limit. Our results invalidate a recent claim that at non-zero lattice spacing an additive mass renormalization is needed because of taste-symmetry breaking.Comment: 17 pages, two refs. and a note adde