Bright and dark breathers in Fermi-Pasta-Ulam lattices

In this paper we study the existence and linear stability of bright and dark breathers in one-dimensional FPU lattices. On the one hand, we test the range of validity of a recent breathers existence proof [G. James, {\em C. R. Acad. Sci. Paris}, 332, Ser. 1, pp. 581 (2001)] using numerical computations. Approximate analytical expressions for small amplitude bright and dark breathers are found to fit very well exact numerical solutions even far from the top of the phonon band. On the other hand, we study numerically large amplitude breathers non predicted in the above cited reference. In particular, for a class of asymmetric FPU potentials we find an energy threshold for the existence of exact discrete breathers, which is a relatively unexplored phenomenon in one-dimensional lattices. Bright and dark breathers superposed on a uniformly stressed static configuration are also investigated.Comment: 11 pages, 16 figure

Equilibrium Phases of Tilted Dipolar Lattice Bosons

The recent advances in creating nearly degenerate quantum dipolar gases in optical lattices are opening the doors for the exploration of equilibrium physics of quantum systems with anisotropic and long-range dipolar interactions. In this paper we study the zero- and finite-temperature phase diagrams of a system of hard-core dipolar bosons at half-filling, trapped in a two-dimensional optical lattice. The dipoles are aligned parallel to one another and tilted out of the optical lattice plane by means of an external electric field. At zero-temperature, the system is a superfluid at all tilt angles $\theta$ provided that the strength of dipolar interaction is below a critical value $V_c(\theta)$. Upon increasing the interaction strength while keeping $\theta$ fixed, the superfluid phase is destabilized in favor of a checkerboard or a stripe solid depending on the tilt angle. We explore the nature of the phase transition between the two solid phases and find evidence of a micro-emulsion phase, following the Spivak-Kivelson scenario, separating these two solid phases. Additionally, we study the stability of these quantum phases against thermal fluctuations and find that the stripe solid is the most robust, making it the best candidate for experimental observation.Comment: 7 pages, 6 figure

Breathers in FPU systems, near and far from the phonon band

There exists a recent mathematical proof on the existence of small amplitude breathers in FPU systems near the phonon band, which includes a prediction of their amplitude and width. In this work we obtain numerically these breathers, and calculate the range of validity of the predictions, which extends relatively far from the phonon band. There exist also large amplitude breathers with the same frequency, with the consequence that there is an energy gap for breather creation in these systems.Comment: 3 pages, 2 figures, proceeding of the conference on Localization and to and Energy Transfer in Nonlinear Systems, June 17-21, 2002, San Lorenzo de El Escorial, Madrid, Spain. To be published by World Scientifi

The Axion and the Goldstone Higgs

We consider the renormalizable $SO(5)/SO(4)$ $\sigma$-model, in which the Higgs particle has a pseudo-Nambu-Goldstone boson character, and explore what the minimal field extension required to implement the Peccei-Quinn symmetry (PQ) is, within the partial compositeness scenario. It turns out that the minimal model does not require the enlargement of the exotic fermionic sector, but only the addition of a singlet scalar: it is sufficient that the exotic fermions involved in partial compositeness and the singlet scalar become charged under Peccei-Quinn transformations. We explore the phenomenological predictions for photonic signals in axion searches for all models discussed. Because of the constraints imposed on the exotic fermion sector by the Standard Model fermion masses, the expected range of allowed axion-photon couplings turns out to be generically narrowed with respect to that of standard invisible axion models, impacting the experimental quest.Comment: 31 pages, 2 Figures. Description improved, results unchange

Collective Coordinates Theory for Discrete Soliton Ratchets in the sine-Gordon Model

A collective coordinate theory is develop for soliton ratchets in the damped discrete sine-Gordon model driven by a biharmonic force. An ansatz with two collective coordinates, namely the center and the width of the soliton, is assumed as an approximated solution of the discrete non-linear equation. The evolution of these two collective coordinates, obtained by means of the Generalized Travelling Wave Method, explains the mechanism underlying the soliton ratchet and captures qualitatively all the main features of this phenomenon. The theory accounts for the existence of a non-zero depinning threshold, the non-sinusoidal behaviour of the average velocity as a function of the difference phase between the harmonics of the driver, the non-monotonic dependence of the average velocity on the damping and the existence of non-transporting regimes beyond the depinning threshold. In particular it provides a good description of the intriguing and complex pattern of subspaces corresponding to different dynamical regimes in parameter space

Theory of correlations between ultra-cold bosons released from an optical lattice

In this paper we develop a theoretical description of the correlations between ultra-cold bosons after free expansion from confinement in an optical lattice. We consider the system evolution during expansion and give criteria for a far field regime. We develop expressions for first and second order two-point correlations based on a variety of commonly used approximations to the many-body state of the system including Bogoliubov, meanfield decoupling, and particle-hole perturbative solution about the perfect Mott-insulator state. Using these approaches we examine the effects of quantum depletion and pairing on the system correlations. Comparison with the directly calculated correlation functions is used to justify a Gaussian form of our theory from which we develop a general three-dimensional formalism for inhomogeneous lattice systems suitable for numerical calculations of realistic experimental regimes.Comment: 18 pages, 11 figures. To appear in Phys. Rev. A. (few minor changes made and typos fixed

Non-renormalization of two and three Point Correlators of N=4 SYM in N=1 Superspace

Certain two and three point functions of gauge invariant primary operators of ${\cal N}=4$ SYM are computed in ${\cal N}=1$ superspace keeping all the $\th$-components. This allows one to read off many component descendent correlators. Our results show the only possible $g^2_{YM}$ corrections to the free field correlators are contact terms. Therefore they vanish for operators at separate points, verifying the known non-renormalization theorems. This also implies the results are consistent with ${\cal N}=4$ supersymmetry even though the Lagrangian we use has only ${\cal N}=1$ manifest supersymmetry. We repeat some of the calculations using supersymmetric Landau gauge and obtain, as expected, the same results as those of supersymmetric Feynman gauge.Comment: 10 pages, 20 eps figures, references adde