The stability of the spectator, Dirac, and Salpeter equations for mesons

Mesons are made of quark-antiquark pairs held together by the strong force. The one channel spectator, Dirac, and Salpeter equations can each be used to model this pairing. We look at cases where the relativistic kernel of these equations corresponds to a time-like vector exchange, a scalar exchange, or a linear combination of the two. Since the model used in this paper describes mesons which cannot decay physically, the equations must describe stable states. We find that this requirement is not always satisfied, and give a complete discussion of the conditions under which the various equations give unphysical, unstable solutions

Two-pion exchange potential and the πN\pi N amplitude

We discuss the two-pion exchange potential which emerges from a box diagram with one nucleon (the spectator) restricted to its mass shell, and the other nucleon line replaced by a subtracted, covariant $\pi N$ scattering amplitude which includes $\Delta$, Roper, and $D_{13}$ isobars, as well as contact terms and off-shell (non-pole) dressed nucleon terms. The $\pi N$ amplitude satisfies chiral symmetry constraints and fits $\pi N$ data below $\sim$ 700 MeV pion energy. We find that this TPE potential can be well approximated by the exchange of an effective sigma and delta meson, with parameters close to the ones used in one-boson-exchange models that fit $NN$ data below the pion production threshold.Comment: 9 pages (RevTex) and 7 postscript figures, in one uuencoded gzipped tar fil

Pathway from condensation via fragmentation to fermionization of cold bosonic systems

For small scattering lengths, cold bosonic atoms form a condensate the density profile of which is smooth. With increasing scattering length, the density {\it gradually} acquires more and more oscillations. Finally, the number of oscillations equals the number of bosons and the system becomes {\it fermionized}. On this pathway from condensation to fermionization intriguing phenomena occur, depending on the shape of the trap. These include macroscopic fragmentation and {\it coexistence} of condensed and fermionized parts that are separated in space.Comment: 12 pages, 2 figure

Beyond Mean-Field Theory for Attractive Bosons under Transverse Harmonic Confinement

We study a dilute gas of attractive bosons confined in a harmonic cylinder, i.e. under cylindric confinement due to a transverse harmonic potential. We introduce a many-body wave function which extends the Bethe ansatz proposed by McGuire (J. Math. Phys. {\bf 5}, 622 (1964)) by including a variational transverse Gaussian shape. We investigate the ground state properties of the system comparing them with the ones of the one-dimensional (1D) attractive Bose gas. We find that the gas becomes ultra 1D as a consequence of the attractive interaction: the transverse width of the Bose gas reduces by increasing the number of particles up to a critical width below which there is the collapse of the cloud. In addition, we derive a simple analytical expression for the simmetry-breaking solitonic density profile of the ground-state, which generalize the one deduced by Calogero and Degasperis (Phys. Rev. A {\bf 11}, 265 (1975)). This bright-soliton analytical solution shows near the collapse small deviations with respect to the 3D mean-field numerical solution. Finally, we show that our variational Gauss-McGuire theory is always more accurate than the McGuire theory. In addition, we prove that for small numbers of particles the Gauss-McGuire theory is more reliable than the mean-field theory described by the 3D Gross-Pitaevskii equation.Comment: To be published in J. Phys. B.: At. Mol. Opt. Phy

Bimodality as a signal of Liquid-Gas phase transition in nuclei?

We use the HIPSE (Heavy-Ion Phase-Space Exploration) Model to discuss the origin of the bimodality in charge asymmetry observed in nuclear reactions around the Fermi energy. We show that it may be related to the important angular momentum (spin) transferred into the quasi-projectile before secondary decay. As the spin overcomes the critical value, a sudden opening of decay channels is induced and leads to a bimodal distribution for the charge asymmetry. In the model, it is not assigned to a liquid-gas phase transition but to specific instabilities in nuclei with high spin. Therefore, we propose to use these reactions to study instabilities in rotating nuclear droplets.Comment: 4 pages, 4 figures Accepted to PR

Rigorous Derivation of the Gross-Pitaevskii Equation

The time dependent Gross-Pitaevskii equation describes the dynamics of initially trapped Bose-Einstein condensates. We present a rigorous proof of this fact starting from a many-body bosonic Schroedinger equation with a short scale repulsive interaction in the dilute limit. Our proof shows the persistence of an explicit short scale correlation structure in the condensate.Comment: 4 pages, 1 figur

Fragmentation Phase Transition in Atomic Clusters II - Coulomb Explosion of Metal Clusters -

We discuss the role and the treatment of polarization effects in many-body systems of charged conducting clusters and apply this to the statistical fragmentation of Na-clusters. We see a first order microcanonical phase transition in the fragmentation of $Na^{Z+}_{70}$ for Z=0 to 8. We can distinguish two fragmentation phases, namely evaporation of large particles from a large residue and a complete decay into small fragments only. Charging the cluster shifts the transition to lower excitation energies and forces the transition to disappear for charges higher than Z=8. At very high charges the fragmentation phase transition no longer occurs because the cluster Coulomb-explodes into small fragments even at excitation energy $\epsilon^* = 0$.Comment: 19 text pages +18 *.eps figures, my e-mail adress: [email protected] submitted to Z. Phys.

Solitary wave complexes in two-component mixture condensates

Axisymmetric three-dimensional solitary waves in uniform two-component mixture Bose-Einstein condensates are obtained as solutions of the coupled Gross-Pitaevskii equations with equal intracomponent but varying intercomponent interaction strengths. Several families of solitary wave complexes are found: (1) vortex rings of various radii in each of the components, (2) a vortex ring in one component coupled to a rarefaction solitary wave of the other component, (3) two coupled rarefaction waves, (4) either a vortex ring or a rarefaction pulse coupled to a localised disturbance of a very low momentum. The continuous families of such waves are shown in the momentum-energy plane for various values of the interaction strengths and the relative differences between the chemical potentials of two components. Solitary wave formation, their stability and solitary wave complexes in two-dimensions are discussed.Comment: 4 pages, 2 figures, 2 table

N-representability and stationarity in time-dependent density functional theory

To construct an N-representable time-dependent density-functional theory, a generalization to the time domain of the Levy-Lieb (LL) constrained search algorithm is required. That the action is only stationary in the Dirac-Frenkel variational principle eliminates the possibility of basing the search on the action itself. Instead, we use the norm of the partial functional derivative of the action in the Hilbert space of the wave functions in place of the energy of the LL search. The electron densities entering the formalism are $N$-representable, and the resulting universal action functional has a unique stationary point in the density at that corresponding to the solution of the Schr\"{o}dinger equation. The original Runge-Gross (RG) formulation is subsumed within the new formalism. Concerns in the literature about the meaning of the functional derivatives and the internal consistency of the RG formulation are allayed by clarifying the nature of the functional derivatives entering the formalism.Comment: 9 pages, 0 figures, Phys. Rev. A accepted. Introduction was expanded, subsections reorganized, appendix and new references adde