Grand unification and proton stability near the Peccei-Quinn scale

We show that in an SU(2)circle timesU(1) model with a Dine-Fischler-Srednicki-like invisible axion it is possible to obtain (i) the convergence of the three gauge coupling constants at an energy scale near the Peccei-Quinn scale; (ii) the correct value for sin(2)theta<^>(W)(M-Z); (iii) the stabilization of the proton by the cyclic Z(13)circle timesZ(3) symmetries which also stabilize the axion as a solution to the strong CP problem. Concerning the convergence of the three coupling constants and the prediction of the weak mixing angle at the Z peak, this model is as good as the minimal supersymmetric standard model with mu(SUSY)=M-Z. We also consider the standard model with six and seven Higgs doublets. The main calculations were done in the 1-loop approximation but we briefly consider the 2-loop contributions.

Superfluid Fermi-Fermi mixture: Phase diagram, stability, and soliton formation

We study the phase diagram for a dilute Bardeen-Cooper-Schrieffer superfluid Fermi-Fermi mixture (of distinct mass) at zero temperature using energy densities for the superfluid fermions in one (1D), two (2D), and three (3D) dimensions. We also derive the dynamical time-dependent nonlinear Euler-Lagrange equation satisfied by the mixture in one dimension using this energy density. We obtain the linear stability conditions for the mixture in terms of fermion densities of the components and the interspecies Fermi-Fermi interaction. In equilibrium there are two possibilities. The first is that of a uniform mixture of the two components, the second is that of two pure phases of two components without any overlap between them. In addition, a mixed and a pure phase, impossible in 1D and 2D, can be created in 3D. We also obtain the conditions under which the uniform mixture is stable from an energetic consideration. The same conditions are obtained from a modulational instability analysis of the dynamical equations in 1D. Finally, the 1D dynamical equations for the system are solved numerically and by variational approximation (VA) to study the bright solitons of the system for attractive interspecies Fermi-Fermi interaction in 1D. The VA is found to yield good agreement to the numerical result for the density profile and chemical potential of the bright solitons. The bright solitons are demonstrated to be dynamically stable. The experimental realization of these Fermi-Fermi bright solitons seems possible with present setups.

Synchronization: Stability and duration time

We consider the problem of stability and duration of the synchronization process between self-excited oscillators, both in their regular and chaotic states. Making use of the properties of Hill equation describing the deviation between the slave and the master, we derive the stability conditions and expressions of the synchronization time. A fairly good agreement is obtained between the analytical and numerical results.

Formation of bright solitons and soliton trains in a fermion-fermion mixture by modulational instability

We employ a time- dependent mean- field- hydrodynamic model to study the generation of bright solitons in a degenerate fermion - fermion mixture in a cigar- shaped geometry using variational and numerical methods. Due to a strong Pauli- blocking repulsion among identical spin- polarized fermions at short distances there cannot be bright solitons for repulsive interspecies interactions. Employing a linear stability analysis we demonstrate the formation of stable solitons due to modulational instability of a constant-amplitude solution of the model equations for a sufficiently attractive interspecies interaction. We perform a numerical stability analysis of these solitons and also demonstrate the formation of soliton trains by jumping the effective interspecies interaction from repulsive to attractive. These fermionic solitons can be formed and studied in laboratory with present technology.

Binding three-particles at the edge of stability

The stability threshold for an Efimov state is determined as a function of the physical scales of the system. Light exotic nuclei and triatomic molecules are investigated. Scaling, universality, and renormalization-group invariance properties are discussed in this context.

Stability of atomic condensed systems with attractive two-body interactions

In the present report, we review recent investigations that we have conducted on the stability of atomic condensed systems, when the two-body interaction is attractive. In particular, the dynamics that occurs in the condensate due to nonconservative terms is considered in the context of an extension of the mean-field Gross-Pitaevskii approximation. Considering the relative intensity of the nonconservative parameters, chaotic and solitonic solutions are verified. Also discussed is the possibility of a liquid-gas phase transition in the presence of positive three-body elastic collisions.

On negative flows of the AKNS hierarchy and a class of deformations of a bihamiltonian structure of hydrodynamic type

A deformation parameter of a bihamiltonian structure of hydrodynamic type is shown to parametrize different extensions of the AKNS hierarchy to include negative flows. This construction establishes a purely algebraic link between, on the one hand, two realizations of the first negative flow of the AKNS model and, on the other, two-component generalizations of Camassa-Holmand Dym-type equations. The two-component generalizations of Camassa-Holm- and Dym-type equations can be obtained from the negative-order Hamiltonians constructed from the Lenard relations recursively applied on the Casimir of the first Poisson bracket of hydrodynamic type. The positive-order Hamiltonians, which follow froth the Lenard scheme applied on the Casimir of the second Poisson bracket of hydrodynamic type, are shown to coincide with the Hamiltonians of the AKNS model. The AKNS Hamiltonians give rise to charges conserved with respect to equations of motion of two-component Camassa-Holm- and two-component Dym-type equations.

3D relativistic hydrodynamic computations using lattice-QCD-inspired equations of state

In this communication, we report results of three-dimensional hydrodynamic computations, by using equations of state with a critical end Point as suggested by the lattice QCD. Some of the results are an increase of the multiplicity in the mid-rapidity region and a larger elliptic-flow parameter nu(2). We discuss also the effcts of the initial-condition fluctuations and the continuous emission.

Stability and collapse of a coupled Bose-Einstein condensate

The dynamics of a coupled Bose-Einstein condensate involving trapped atoms in two quantum states is studied using the time-dependent Gross-Pitaevskii equation including an interaction which can transform atoms from one state to the other. We find interesting oscillation of the number of atoms in each of the states. For all repulsive interactions, stable condensates are formed. When some of the atomic interactions are attractive, the possibility of collapse is studied by including an absorptive contact interaction and a quartic three-body recombination term. One or both components of the condensate may undergo collapse when one or more of the nonlinear terms are attractive in nature. (C) 2001 Elsevier B.V. B.V. All rights reserved.

Stability of the trapped nonconservative Gross-Pitaevskii equation with attractive two-body interaction

The dynamics of a nonconservative Gross-Pitaevskii equation for trapped atomic systems with attractive two-body interaction is numerically investigated, considering wide variations of the nonconservative parameters, related to atomic feeding and dissipation. We study the possible limitations of the mean-field description for an atomic condensate with attractive two-body interaction, by defining the parameter regions, where stable or unstable formation can be found. The present study is useful and timely considering the possibility of large variations of attractive two-body scattering lengths, which may be feasible in recent experiments.

Dynamical collapse in a degenerate binary fermion mixture using a hydrodynamic model

We use a time-dependent dynamical hydrodynamic model to study a collapse in a degenerate fermion-fermion mixture ( DFFM) of different atoms. Due to a strong Pauli-blocking repulsion among identical spin-polarized fermions at short distances, there cannot be a collapse for repulsive interspecies fermion fermion interaction. However, there can be a collapse for a sufficiently attractive interspecies fermion-fermion interaction in a DFFM of different atoms. Using a variational analysis and numerical solution of the hydrodynamic model, we study different aspects of collapse in such a DFFM initiated by a jump in the interspecies fermion-fermion interaction ( scattering length) to a large negative ( attractive) value using a Feshbach resonance. Suggestion for experiments of collapse in a DFFM of distinct atoms is made.

Bright solitons and soliton trains in a fermion-fermion mixture

We use a time-dependent dynamical mean-field-hydrodynamic model to predict and study bright solitons in a degenerate fermion-fermion mixture in a quasi-one-dimensional cigar-shaped geometry using variational and numerical methods. Due to a strong Pauli-blocking repulsion among identical spin-polarized fermions at short distances there cannot be bright solitons for repulsive interspecies fermion-fermion interactions. However, stable bright solitons can be formed for a sufficiently attractive interspecies interaction. We perform a numerical stability analysis of these solitons and also demonstrate the formation of soliton trains. These fermionic solitons can be formed and studied in laboratory with present technology.

Stability analysis of the D-dimensional nonlinear Schrodinger equation with trap and two- and three-body interactions

Considering the static solutions of the D-dimensional nonlinear Schrodinger equation with trap and attractive two-body interactions, the existence of stable solutions is limited to a maximum critical number of particles, when D greater than or equal to 2. In case D = 2, we compare the variational approach with the exact numerical calculations. We show that, the addition of a positive three-body interaction allows stable solutions beyond the critical number. In this case, we also introduce a dynamical analysis of the conditions for the collapse. (C) 2000 Published by Elsevier B.V. B.V. All rights reserved.

Stability and collapse of a hybrid Bose-Einstein condensate of atoms and molecules

The dynamics of stability and collapse of a trapped atomic Bose-Einstein condensate (BEC) coupled to a molecular one is studied using the time-dependent Gross-Pitaevskii (GP) equation including a nonlinear interaction term which can transform two atoms into a molecule and vice versa. We find an interesting oscillation of the number of atoms and molecules for a BEC of fixed mass. This oscillation is a consequence of continuous transformation in the condensate of two atoms into a molecule and vice versa. For the study of collapse an absorptive contact interaction and an imaginary quartic three-body recombination term are included in the GP equation. It is possible to have a collapse of one or both components when one or more of the nonlinear terms in the GP equation are attractive in nature, respectively.