Infinite compressibility states in the Hierarchical Reference Theory of fluids. II. Numerical evidence

Continuing our investigation into the Hierarchical Reference Theory of fluids for thermodynamic states of infinite isothermal compressibility kappa[T] we now turn to the available numerical evidence to elucidate the character of the partial differential equation: Of the three scenarios identified previously, only the assumption of the equations turning stiff when building up the divergence of kappa[T] allows for a satisfactory interpretation of the data. In addition to the asymptotic regime where the arguments of part I (cond-mat/0308467) directly apply, a similar mechanism is identified that gives rise to transient stiffness at intermediate cutoff for low enough temperature. Heuristic arguments point to a connection between the form of the Fourier transform of the perturbational part of the interaction potential and the cutoff where finite difference approximations of the differential equation cease to be applicable, and they highlight the rather special standing of the hard-core Yukawa potential as regards the severity of the computational difficulties.Comment: J. Stat. Phys., in press. Minor changes to match published versio

Implementation of the Hierarchical Reference Theory for simple one-component fluids

Combining renormalization group theoretical ideas with the integral equation approach to fluid structure and thermodynamics, the Hierarchical Reference Theory is known to be successful even in the vicinity of the critical point and for sub-critical temperatures. We here present a software package independent of earlier programs for the application of this theory to simple fluids composed of particles interacting via spherically symmetrical pair potentials, restricting ourselves to hard sphere reference systems. Using the hard-core Yukawa potential with z=1.8/sigma for illustration, we discuss our implementation and the results it yields, paying special attention to the core condition and emphasizing the decoupling assumption's role.Comment: RevTeX, 16 pages, 2 figures. Minor changes, published versio

Effective wave-equations for the dynamics of cigar-shaped and disc-shaped Bose condensates

Starting from the 3D Gross-Pitaevskii equation and using a variational approach, we derive an effective 1D wave-equation that describes the axial dynamics of a Bose condensate confined in an external potential with cylindrical symmetry. The trapping potential is harmonic in the transverse direction and generic in the axial one. Our equation, that is a time-dependent non-polynomial nonlinear Schr\"odinger equation (1D NPSE), can be used to model cigar-shaped condensates, whose dynamics is essentially 1D. We show that 1D NPSE gives much more accurate results than all other effective equations recently proposed. By using 1D NPSE we find analytical solutions for bright and dark solitons, which generalize the ones known in the literature. We deduce also an effective 2D non-polynomial Schr\"odinger equation (2D NPSE) that models disc-shaped Bose condensates confined in an external trap that is harmonic along the axial direction and generic in the transverse direction. In the limiting cases of weak and strong interaction, our approach gives rise to Schr\"odinger-like equations with different polynomial nonlinearities.Comment: 7 pages, 5 figures, to be published in Phys. Rev.

Shell Effects and Phase Separation in a Trapped Multi-Component Fermi System

Shell effects in the coordinate space can be seen with degenerate Fermi vapors in non-uniform trapping potentials. In particular, below the Fermi temperature, the density profile of a Fermi gas in a confining harmonic potential is characterized by several local maxima. This effect is enhanced for "magic numbers" of particles and in quasi-1D (cigar-shaped) configurations. In the case of a multi-component Fermi vapor, the separation of Fermi components in different spatial shells (phase-separation) depends on temperature, number of particles and scattering length. We derive analytical formulas, based on bifurcation theory, for the critical density of Fermions and the critical chemical potential, which give rise to the phase-separation.Comment: to be published in the Proceedings of the VIII Meeting on Problems in Theoretical Nuclear Physics, Cortona, October 18-20, 2000, Ed. G. Pisent, A. Fabrocini and L. Canton (World Scientific

Approximating the ground state of fermion system by multiple determinant states: matching pursuit approach

We present a simple and stable numerical method to approximate the ground state of a quantum many-body system by multiple determinant states. This method searches these determinant states one by one according to the matching pursuit algorithm. The first determinant state is identical to that of the Hartree-Fock theory. Calculations for two-dimensional Hubbard model serve as a demonstration.Comment: 5 Pages, 1 figur

Swift reveals the eclipsing nature of the high mass X-ray binary IGR~J16195-4945

IGR J16195-4945 is a hard X-ray source discovered by INTEGRAL during the Core Program observations performed in 2003. We analyzed the X-ray emission of this source exploiting the Swift-BAT survey data from December 2004 to March 2015, and all the available Swift-XRT pointed observations. The source is detected at a high significance level in the 123-month BAT survey data, with an average 15-150 keV flux of the source of ~1.6 mCrab. The timing analysis on the BAT data reveals with a significance higher than 6 standard deviations the presence of a modulated signal with a period of 3.945 d, that we interpret as the orbital period of the binary system. The folded light curve shows a flat profile with a narrow full eclipse lasting ~3.5% of the orbital period. We requested phase-constrained XRT observations to obtain a more detailed characterization of the eclipse in the soft X-ray range. Adopting resonable guess values for the mass and radius of the companion star, we derive a semi-major orbital axis of ~31 R_sun, equivalent to ~1.8 times the radius of the companion star. From these estimates and from the duration of the eclipse we derive an orbital inclination between 55 and 60 degrees. The broad band time-averaged XRT+BAT spectrum is well modeled with a strongly absorbed flat power law, with absorbing column N_H=7x 10^22 cm^(-2) and photon index Gamma=0.5, modified by a high energy exponential cutoff at E_cut=14 keV.Comment: 5 pages, 5 figures, 2 tables. Published on MNRA

Recent developments of the Hierarchical Reference Theory of Fluids and its relation to the Renormalization Group

The Hierarchical Reference Theory (HRT) of fluids is a general framework for the description of phase transitions in microscopic models of classical and quantum statistical physics. The foundations of HRT are briefly reviewed in a self-consistent formulation which includes both the original sharp cut-off procedure and the smooth cut-off implementation, which has been recently investigated. The critical properties of HRT are summarized, together with the behavior of the theory at first order phase transitions. However, the emphasis of this presentation is on the close relationship between HRT and non perturbative renormalization group methods, as well as on recent generalizations of HRT to microscopic models of interest in soft matter and quantum many body physics.Comment: 17 pages, 5 figures. Review paper to appear in Molecular Physic

Spin-lattice coupling in frustrated antiferromagnets

We review the mechanism of spin-lattice coupling in relieving the geometrical frustration of pyrochlore antiferromagnets, in particular spinel oxides. The tetrahedral unit, which is the building block of the pyrochlore lattice, undergoes a spin-driven Jahn-Teller instability when lattice degrees of freedom are coupled to the antiferromagnetism. By restricting our considerations to distortions which preserve the translational symmetries of the lattice, we present a general theory of the collective spin-Jahn-Teller effect in the pyrochlore lattice. One of the predicted lattice distortions breaks the inversion symmetry and gives rise to a chiral pyrochlore lattice, in which frustrated bonds form helices with a definite handedness. The chirality is transferred to the spin system through spin-orbit coupling, resulting in a long-period spiral state, as observed in spinel CdCr2O4. We discuss explicit models of spin-lattice coupling using local phonon modes, and their applications in other frustrated magnets.Comment: 23 pages, 6 figures. Lecture notes for Trieste Summer School, August 2007. To appear as a chapter in "Highly Frustrated Magnetism", Eds. C. Lacroix, P. Mendels, F. Mil

Swift-XRT 6-year monitoring of the ultraluminous X-ray source M33-X8

The long term evolution of ULX with their spectral and luminosity variations in time give important clues on the nature of ULX and on the accretion process that powers them. We report here the results of a Swift-XRT 6-year monitoring campaign of the closest example of a persistent ULX, M33 X-8, that extends to 16 years the monitoring of this source in the soft X-rays. The luminosity of this source is a few 10^39 erg/s, marking the faint end of the ULX luminosity function. We analysed the set of 15 observations collected during the Swift monitoring. We searched for differences in the spectral parameters at different observing epochs, adopting several models commonly used to fit the X-ray spectra of ULX. The source exhibits flux variations of the order of 30%. No significant spectral variations are observed along the monitoring. The average 0.5-10 keV spectrum can be well described by a thermal model, either in the form of a slim disk, or as a combination of a Comptonized corona and a standard accretion disk.Comment: 6 pages, 4 figures, 2 tables. Paper published in A&