Towards a construction of inclusive collision cross-sections in the massless Nelson model

The conventional approach to the infrared problem in perturbative quantum electrodynamics relies on the concept of inclusive collision cross-sections. A non-perturbative variant of this notion was introduced in algebraic quantum field theory. Relying on these insights, we take first steps towards a non-perturbative construction of inclusive collision cross-sections in the massless Nelson model. We show that our proposal is consistent with the standard scattering theory in the absence of the infrared problem and discuss its status in the infrared-singular case.Comment: 23 pages, LaTeX. As appeared in Ann. Henri Poincar\'

Two Photon Radiation in W and Z Boson Production at the Tevatron Collider

We present a calculation of two photon radiation in W and Z boson production in hadronic collisions, based on the complete matrix elements for the processes q\bar q'\to\ell^\pm\nu\gamma\gamma and q\bar q\to\ell^+\ell^-\gamma\gamma, including finite charged lepton masses. In order to achieve stable numerical results over the full phase space, multiconfiguration Monte Carlo techniques are used to map the peaks in the differential cross section. Numerical results are presented for the Fermilab Tevatron.Comment: Revtex, 28 pages, 3 figure

Finite temperature phase diagram of spin-1/2 bosons in two-dimensional optical lattice

We study a two-species bosonic Hubbard model on a two-dimensional square lattice by means of quantum Monte Carlo simulations and focus on finite temperature effects. We show in two different cases, ferro- and antiferromagnetic spin-spin interactions, that the phase diagram is composed of solid Mott phases, liquid phases and superfluid phases. In the antiferromagnetic case, the superfluid (SF) is polarized while the Mott insulator (MI) and normal Bose liquid (NBL) phases are not. On the other hand, in the ferromagnetic case, none of the phases is polarized. The superfluid-liquid transition is of the Berezinsky-Kosterlitz-Thouless type whereas the solid-liquid passage is a crossover.Comment: 9 pages, 13 figure

Metal-insulator transitions in cyclotron resonance of periodic nanostructures due to avoided band crossings

A recently found metal-insulator transition in a model for cyclotron resonance in a two-dimensional periodic potential is investigated by means of spectral properties of the time evolution operator. The previously found dynamical signatures of the transition are explained in terms of avoided band crossings due to the change of the external electric field. The occurrence of a cross-like transport is predicted and numerically confirmed

Identifying topological edge states in 2D optical lattices using light scattering

We recently proposed in a Letter [Physical Review Letters 108 255303] a novel scheme to detect topological edge states in an optical lattice, based on a generalization of Bragg spectroscopy. The scope of the present article is to provide a more detailed and pedagogical description of the system - the Hofstadter optical lattice - and probing method. We first show the existence of topological edge states, in an ultra-cold gas trapped in a 2D optical lattice and subjected to a synthetic magnetic field. The remarkable robustness of the edge states is verified for a variety of external confining potentials. Then, we describe a specific laser probe, made from two lasers in Laguerre-Gaussian modes, which captures unambiguous signatures of these edge states. In particular, the resulting Bragg spectra provide the dispersion relation of the edge states, establishing their chiral nature. In order to make the Bragg signal experimentally detectable, we introduce a "shelving method", which simultaneously transfers angular momentum and changes the internal atomic state. This scheme allows to directly visualize the selected edge states on a dark background, offering an instructive view on topological insulating phases, not accessible in solid-state experiments.Comment: 17 pages, 10 figures. Revised and extended version, to appear in EJP Special Topic for the special issue on "Novel Quantum Phases and Mesoscopic Physics in Quantum Gases". Extended version of arXiv:1203.124

Efimov Trimers near the Zero-crossing of a Feshbach Resonance

Near a Feshbach resonance, the two-body scattering length can assume any value. When it approaches zero, the next-order term given by the effective range is known to diverge. We consider the question of whether this divergence (and the vanishing of the scattering length) is accompanied by an anomalous solution of the three-boson Schr\"odinger equation similar to the one found at infinite scattering length by Efimov. Within a simple zero-range model, we find no such solutions, and conclude that higher-order terms do not support Efimov physics.Comment: 8 pages, no figures, final versio

Abelian gauge potentials on cubic lattices

The study of the properties of quantum particles in a periodic potential subject to a magnetic field is an active area of research both in physics and mathematics; it has been and it is still deeply investigated. In this review we discuss how to implement and describe tunable Abelian magnetic fields in a system of ultracold atoms in optical lattices. After discussing two of the main experimental schemes for the physical realization of synthetic gauge potentials in ultracold set-ups, we study cubic lattice tight-binding models with commensurate flux. We finally examine applications of gauge potentials in one-dimensional rings.Comment: To appear on: "Advances in Quantum Mechanics: Contemporary Trends and Open Problems", G. Dell'Antonio and A. Michelangeli eds., Springer-INdAM series 201

The Gribov-Zwanziger action in the presence of the gauge invariant, nonlocal mass operator Tr∫d4xFμν(D2)−1FμνTr \int d^4x F_{\mu\nu} (D^2)^{-1} F_{\mu\nu} in the Landau gauge

We prove that the nonlocal gauge invariant mass dimension two operator $F_{\mu\nu} (D^2)^{-1} F_{\mu\nu}$ can be consistently added to the Gribov-Zwanziger action, which implements the restriction of the path integral's domain of integration to the first Gribov region when the Landau gauge is considered. We identify a local polynomial action and prove the renormalizability to all orders of perturbation theory by employing the algebraic renormalization formalism. Furthermore, we also pay attention to the breaking of the BRST invariance, and to the consequences that this has for the Slavnov-Taylor identity.Comment: 30 page

Artificial gauge fields for the Bose-Hubbard model on a checkerboard superlattice and extended Bose-Hubbard model

We study the effects of an artificial gauge field on the ground-state phases of the Bose-Hubbard model on a checkerboard superlattice in two dimensions, including the superfluid phase and the Mott and alternating Mott insulators. First, we discuss the single-particle Hofstadter problem, and show that the presence of a checkerboard superlattice gives rise to a magnetic flux-independent energy gap in the excitation spectrum. Then, we consider the many-particle problem, and derive an analytical mean-field expression for the superfluid-Mott and superfluid--alternating-Mott insulator phase transition boundaries. Finally, since the phase diagram of the Bose-Hubbard model on a checkerboard superlattice is in many ways similar to that of the extended Bose-Hubbard model, we comment on the effects of magnetic field on the latter model, and derive an analytical mean-field expression for the superfluid-insulator phase transition boundaries as well.Comment: 8 pages, 5 figures and 1 table; to appear in EPJ

A Solvable Regime of Disorder and Interactions in Ballistic Nanostructures, Part I: Consequences for Coulomb Blockade

We provide a framework for analyzing the problem of interacting electrons in a ballistic quantum dot with chaotic boundary conditions within an energy $E_T$ (the Thouless energy) of the Fermi energy. Within this window we show that the interactions can be characterized by Landau Fermi liquid parameters. When $g$, the dimensionless conductance of the dot, is large, we find that the disordered interacting problem can be solved in a saddle-point approximation which becomes exact as $g\to\infty$ (as in a large-N theory). The infinite $g$ theory shows a transition to a strong-coupling phase characterized by the same order parameter as in the Pomeranchuk transition in clean systems (a spontaneous interaction-induced Fermi surface distortion), but smeared and pinned by disorder. At finite $g$, the two phases and critical point evolve into three regimes in the $u_m-1/g$ plane -- weak- and strong-coupling regimes separated by crossover lines from a quantum-critical regime controlled by the quantum critical point. In the strong-coupling and quantum-critical regions, the quasiparticle acquires a width of the same order as the level spacing $\Delta$ within a few $\Delta$'s of the Fermi energy due to coupling to collective excitations. In the strong coupling regime if $m$ is odd, the dot will (if isolated) cross over from the orthogonal to unitary ensemble for an exponentially small external flux, or will (if strongly coupled to leads) break time-reversal symmetry spontaneously.Comment: 33 pages, 14 figures. Very minor changes. We have clarified that we are treating charge-channel instabilities in spinful systems, leaving spin-channel instabilities for future work. No substantive results are change