Integral equation for inhomogeneous condensed bosons generalizing the Gross-Pitaevskii differential equation

We give here the derivation of a Gross-Pitaevskii--type equation for inhomogeneous condensed bosons. Instead of the original Gross-Pitaevskii differential equation, we obtain an integral equation that implies less restrictive assumptions than are made in the very recent study of Pieri and Strinati [Phys. Rev. Lett. 91 (2003) 030401]. In particular, the Thomas-Fermi approximation and the restriction to small spatial variations of the order parameter invoked in their study are avoided.Comment: Phys. Rev. A (accepted

Sharp crossover from composite fermionization to phase separation in mesoscopic mixtures of ultracold bosons

We show that a two-component mixture of a few repulsively interacting ultracold atoms in a one-dimensional trap possesses very different quantum regimes and that the crossover between them can be induced by tuning the interactions in one of the species. In the composite fermionization regime, where the interactions between both components are large, none of the species show large occupation of any natural orbital. Our results show that by increasing the interaction in one of the species, one can reach the phase-separated regime. In this regime, the weakly interacting component stays at the center of the trap and becomes almost fully phase coherent, while the strongly interacting component is displaced to the edges of the trap. The crossover is sharp, as observed in the in the energy and the in the largest occupation of a natural orbital of the weakly interacting species. Such a transition is a purely mesoscopic effect which disappears for large atom numbers.Comment: 5 pages, 3 figure

Quantum correlations and spatial localization in one-dimensional ultracold bosonic mixtures

We present the complete phase diagram for one-dimensional binary mixtures of bosonic ultracold atomic gases in a harmonic trap. We obtain exact results with direct numerical diagonalization for small number of atoms, which permits us to quantify quantum many-body correlations. The quantum Monte Carlo method is used to calculate energies and density profiles for larger system sizes. We study the system properties for a wide range of interaction parameters. For the extreme values of these parameters, different correlation limits can be identified, where the correlations are either weak or strong. We investigate in detail how the correlation evolve between the limits. For balanced mixtures in the number of atoms in each species, the transition between the different limits involves sophisticated changes in the one- and two-body correlations. Particularly, we quantify the entanglement between the two components by means of the von Neumann entropy. We show that the limits equally exist when the number of atoms is increased, for balanced mixtures. Also, the changes in the correlations along the transitions among these limits are qualitatively similar. We also show that, for imbalanced mixtures, the same limits with similar transitions exist. Finally, for strongly imbalanced systems, only two limits survive, i.e., a miscible limit and a phase-separated one, resembling those expected with a mean-field approach.Comment: 18 pages, 8 figure

Information entropy and nucleon correlations in nuclei

The information entropies in coordinate and momentum spaces and their sum ($S_r$, $S_k$, $S$) are evaluated for many nuclei using "experimental" densities or/and momentum distributions. The results are compared with the harmonic oscillator model and with the short-range correlated distributions. It is found that $S_r$ depends strongly on $\ln A$ and does not depend very much on the model. The behaviour of $S_k$ is opposite. The various cases we consider can be classified according to either the quantity of the experimental data we use or by the values of $S$, i.e., the increase of the quality of the density and of the momentum distributions leads to an increase of the values of $S$. In all cases, apart from the linear relation $S=a+b\ln A$, the linear relation $S=a_V+b_V \ln V$ also holds. V is the mean volume of the nucleus. If $S$ is considered as an ensemble entropy, a relation between $A$ or $V$ and the ensemble volume can be found. Finally, comparing different electron scattering experiments for the same nucleus, it is found that the larger the momentum transfer ranges, the larger the information entropy is. It is concluded that $S$ could be used to compare different experiments for the same nucleus and to choose the most reliable one.Comment: 14 pages, 4 figures, 2 table

A Brief Review on Dark Matter Annihilation Explanation for e±e^\pm Excesses in Cosmic Ray

Recently data from PAMELA, ATIC, FERMI-LAT and HESS show that there are $e^{\pm}$ excesses in the cosmic ray energy spectrum. PAMELA observed excesses only in $e^+$, but not in anti-proton spectrum. ATIC, FERMI-LAT and HESS observed excesses in $e^++e^-$ spectrum, but the detailed shapes are different which requires future experimental observations to pin down the correct data set. Nevertheless a lot of efforts have been made to explain the observed $e^\pm$ excesses, and also why PAMELA only observed excesses in $e^+$ but not in anti-proton. In this brief review we discuss one of the most popular mechanisms to explain the data, the dark matter annihilation. It has long been known that about 23% of our universe is made of relic dark matter. If the relic dark matter was thermally produced, the annihilation rate is constrained resulting in the need of a large boost factor to explain the data. We will discuss in detail how a large boost factor can be obtained by the Sommerfeld and Briet-Wigner enhancement mechanisms. Some implications for particle physics model buildings will also be discussed.Comment: 22 pages, 6 figures. Several typoes corrected and some references added. Published in Mod. Phys. Lett. A, Vol. 24, No. 27 (2009) pp. 2139-216

A topological charge selection rule for phase singularities

We present an study of the dynamics and decay pattern of phase singularities due to the action of a system with a discrete rotational symmetry of finite order. A topological charge conservation rule is identified. The role played by the underlying symmetry is emphasized. An effective model describing the short range dynamics of the vortex clusters has been designed. A method to engineer any desired configuration of clusters of phase singularities is proposed. Its flexibility to create and control clusters of vortices is discussed.Comment: 4 pages, 3 figure

Confining Flux Tubes in a Current Algebra Approach

We describe flux tubes and their interactions in a low energy sigma model induced by $SU({N_f}) \rightarrow SO({N_f})$ flavor symmetry breaking in $SO(N_c)$ QCD. Unlike standard QCD, this model allows gauge confinement to manifest itself in the low energy theory, which has unscreened spinor color sources and global $Z_2$ flux tubes. We construct the flux tubes and show how they mediate the confinement of spinor sources. We further examine the flux tubes' quantum stability, spectrum and interactions. We find that flux tubes are Alice strings, despite ambiguities in defining parallel transport. Furthermore, twisted loops of flux tube support skyrmion number, just as gauged Alice strings form loops that support monopole charge. This model, while phenomenologically nonviable, thus affords a perspective on both the dynamics of confinement and on subtleties which arise for global Alice strings.Comment: 29 pages (REVTEX) plus 6 figures, two corrections in the final section and added reference

Energy gaps in quantum first-order mean-field-like transitions: The problems that quantum annealing cannot solve

We study first-order quantum phase transitions in models where the mean-field traitment is exact, and the exponentially fast closure of the energy gap with the system size at the transition. We consider exactly solvable ferromagnetic models, and show that they reduce to the Grover problem in a particular limit. We compute the coefficient in the exponential closure of the gap using an instantonic approach, and discuss the (dire) consequences for quantum annealing.Comment: 6 pages, 3 figure

Power, norms and institutional change in the European Union: the protection of the free movement of goods

How do institutions of the European Union change? Using an institutionalist approach, this article highlights the interplay between power, cognitive limits, and the normative order that underpins institutional settings and assesses their impact upon the process of institutional change. Empirical evidence from recent attempts to reinforce the protection of the free movement of goods in the EU suggests that, under conditions of uncertainty, actors with ambiguous preferences assess attempts at institutional change on the basis of the historically defined normative order which holds a given institutional structure together. Hence, path dependent and incremental change occurs even when more ambitious and functionally superior proposals are on offer

Higgs bosons near 125 GeV in the NMSSM with constraints at the GUT scale

We study the NMSSM with universal Susy breaking terms (besides the Higgs sector) at the GUT scale. Within this constrained parameter space, it is not difficult to find a Higgs boson with a mass of about 125 GeV and an enhanced cross section in the diphoton channel. An additional lighter Higgs boson with reduced couplings and a mass <123 GeV is potentially observable at the LHC. The NMSSM-specific Yukawa couplings lambda and kappa are relatively large and tan(beta) is small, such that lambda, kappa and the top Yukawa coupling are of order 1 at the GUT scale. The lightest stop can be as light as 105 GeV, and the fine-tuning is modest. WMAP constraints can be satisfied by a dominantly higgsino-like LSP with substantial bino, wino and singlino admixtures and a mass of ~60-90 GeV, which would potentially be detectable by XENON100.Comment: 20 pages, 14 figure