Thermal field theory of bosonic gases with finite-range effective interaction

We study a dilute and ultracold Bose gas of interacting atoms by using an effective field theory which takes account finite-range effects of the inter-atomic potential. Within the formalism of functional integration from the grand canonical partition function we derive beyond-mean-field analytical results which depend on both scattering length and effective range of the interaction. In particular, we calculate the equation of state of the bosonic system as a function of these interaction parameters both at zero and finite temperature including one-loop Gaussian fluctuation. In the case of zero-range effective interaction we explicitly show that, due to quantum fluctuations, the bosonic system is thermodynamically stable only for very small values of the gas parameter. We find that a positive effective range above a critical threshold is necessary to remove the thermodynamical instability of the uniform configuration. Remarkably, also for relatively large values of the gas parameter, our finite-range results are in quite good agreement with recent zero-temperature Monte Carlo calculations obtained with hard-sphere bosons.Comment: 6 pages, 2 figures, added some equation

Finite-Range Corrections to the Thermodynamics of the One-Dimensional Bose Gas

The Lieb-Liniger equation of state accurately describes the zero-temperature universal properties of a dilute one-dimensional Bose gas in terms of the s-wave scattering length. For weakly-interacting bosons we derive non-universal corrections to this equation of state taking into account finite-range effects of the inter-atomic potential. Within the finite-temperature formalism of functional integration we find a beyond-mean-field equation of state which depends on scattering length and effective range of the interaction potential. Our analytical results, which are obtained performing dimensional regularization of divergent zero-point quantum fluctuations, show that for the one-dimensional Bose gas thermodynamic quantities like pressure and sound velocity are modified by changing the ratio between the effective range and the scattering length.Comment: 6 pages, 2 figures, accepted for publication in Physical Review

Condensation and superfluidity of dilute Bose gases with finite-range interaction

We investigate an ultracold and dilute Bose gas by taking into account a finite-range two-body interaction. The coupling constants of the resulting Lagrangian density are related to measurable scattering parameters by following the effective-field-theory approach. A perturbative scheme is then developed up to the Gaussian level, where both quantum and thermal fluctuations are crucially affected by finite-range corrections. In particular, the relation between spontaneous symmetry breaking and the onset of superfluidity is emphasized by recovering the renowned Landau's equation for the superfluid density in terms of the condensate one.Comment: 18 pages, 4 figures, invited contribution to New Journal of Physics Focus Issue on Quantum Transport in Ultracold Atom

Collisionless Dynamics in Two-Dimensional Bosonic Gases

We study the dynamics of dilute and ultracold bosonic gases in a quasi two-dimensional (2D) configuration and in the collisionless regime. We adopt the 2D Landau-Vlasov equation to describe a three-dimensional gas under very strong harmonic confinement along one direction. We use this effective equation to investigate the speed of sound in quasi 2D bosonic gases, i.e. the sound propagation around a Bose-Einstein distribution in collisionless 2D gases. We derive coupled algebraic equations for the real and imaginary parts of the sound velocity, which are then solved taking also into account the equation of state of the 2D bosonic system. Above the Berezinskii-Kosterlitz-Thouless critical temperature we find that there is rapid growth of the imaginary component of the sound velocity which implies a strong Landau damping. Quite remarkably, our theoretical results are in good agreement with very recent experimental data obtained with a uniform 2D Bose gas of $^{87}$Rb atoms.Comment: 5 pages, 2 figures, improved introduction and conclusions, accepted for publication in Physical Review

Nonequilibrium Kinetics of One-Dimensional Bose Gases

We study cold dilute gases made of bosonic atoms, showing that in the mean-field one-dimensional regime they support stable out-of-equilibrium states. Starting from the 3D Boltzmann-Vlasov equation with contact interaction, we derive an effective 1D Landau-Vlasov equation under the condition of a strong transverse harmonic confinement. We investigate the existence of out-of-equilibrium states, obtaining stability criteria similar to those of classical plasmas.Comment: 16 pages, 6 figures, accepted for publication in Journal of Statistical Mechanics: Theory and Experimen

The Generation and Dissipation of Interstellar Turbulence - Results from Large Scale High Resolution Simulations

We study, by means of adaptive mesh refinement hydro- and magnetohydrodynamical simulations that cover a wide range of scales (from kpc to sub-parsec), the dimension of the most dissipative structures and the injection scale of the turbulent interstellar gas, which we find to be about 75 pc, in agreement with observations. This is however smaller than the average size of superbubbles, but consistent with significant density and pressure changes in the ISM, which leads to the break-up of bubbles locally and hence to injection of turbulence. The scalings of the structure functions are consistent with log-Poisson statistics of supersonic turbulence where energy is dissipated mainly through shocks. Our simulations are different from previous ones by other authors as (i) we do not assume an isothermal gas, but have temperature variations of several orders of magnitude and (ii) we have no artificial forcing of the fluid with some ad hoc Fourier spectrum, but drive turbulence by stellar explosions at the Galactic rate, self-regulated by density and temperature thresholds imposed on the ISM gas.Comment: Five pages and three figures. Accepted for publication in Astrophysical Journal (Letters

Detection of a light echo from SN1998bu

About 500d after explosion the light curve of the Type Ia SN1998bu suddenly flattened and at the same time the spectrum changed from the typical nebular emission to a blue continuum with broad absorption and emission features reminiscent of the SN spectrum at early phases. We show that in analogy to SN1991Tbu (Schmidt et al. 1994), this can be explained by the emergence of a light echo from a foreground dust cloud. Based on a simple model we argue that the amount of dust required can consistently explain the extinction which has been estimated by completely independent methods. Because of the similar echo luminosity but much higher optical depth of the dust in SN1998bu compared with SN1991T, we expect that the echo ring size of SN1998bu grows faster than in SN1991T. HST observations have indeed confirmed this prediction.Comment: 5 pages (including 3 figures) - Accepted for pubblication in ApJ Letter

The Rates of Hypernovae and Gamma-Ray Bursts: Implications for their Progenitors

A critical comparison of estimates for the rates of hypernovae (HNe) and gamma-ray bursts (GRBs) is presented. Within the substantial uncertainties, the estimates are shown to be quite comparable and give a Galactic rate of $10^{-6}$ -- $10^{-5}$yr$^{-1}$ for both events. These rates are several orders of magnitude lower than the rate of core-collapse supernovae, suggesting that the evolution leading to a HN/GRB requires special circumstances, very likely due to binary interactions. Various possible binary channels are discussed, and it is shown that these are generally compatible with the inferred rates.Comment: Accepted by Astrophysical Journal Letters. 12 page

Nebular Spectra of SN 1998bw Revisited: Detailed Study by One and Two Dimensional Models

Refined one- and two-dimensional models for the nebular spectra of the hyper-energetic Type Ic supernova (SN) 1998bw, associated with the gamma-ray burst GRB980425, from 125 to 376 days after B-band maximum are presented. One dimensional, spherically symmetric spectrum synthesis calculations show that reproducing features in the observed spectra, i.e., the sharply peaked [OI] 6300\AA doublet and MgI] 4570\AA emission, and the broad [FeII] blend around 5200\AA, requires the existence of a high-density O-rich core expanding at low velocities (\lsim 8,000 km s$^{-1}$) and of Fe-rich material moving faster than the O-rich material. Synthetic spectra at late phases from aspherical (bipolar) explosion models are also computed with a two-dimensional spectrum synthesis code. The above features are naturally explained by the aspherical model if the explosion is viewed from a direction close to the axis of symmetry ($\sim 30^{\rm o}$), since the aspherical model yields a high-density O-rich region confined along the equatorial axis. By examining a large parameter space (in energy and mass), our best model gives following physical quantities: the kinetic energy $E_{51} \equiv E_{\rm K}/10^{51}$ ergs \gsim 8 - 12 and the main-sequence mass of the progenitor star M_{\rm ms} \gsim 30 - 35 \Msun. The temporal spectral evolution of SN 1998bw also indicates mixing among Fe-, O-, and C-rich regions, and highly clumpy structure.Comment: 38 pages, 22 figures. ApJ, 640 (01 April 2006 issue), in pres

Why Are Radio-Galaxies Prolific Producers of Type Ia Supernovae?

An analysis of SNIa events in early type galaxies from the Cappellaro et al (1999) database provides conclusive evidence that the rate of type Ia Supernovae (SNe) in radio-loud galaxies is about 4 times higher than the rate measured in radio-quiet galaxies, i.e. SNIa-rate$(radio-loud galaxies) = 0.43^{+0.19}_{-0.14}h^2_{75}$ SNu as compared to SNIa-rate$(radio-quiet galaxies) = 0.11^{+0.06}_{-0.03}h^2_{75}$ SNu. The actual value of the enhancement is likely to be in the range $\sim 2-7$ (P$\sim 10^{-4}$). This finding puts on robust empirical grounds the results obtained by Della Valle & Panagia (2003) on the basis of a smaller sample of SNe. We analyse the possible causes of this result and conclude that the enhancement of SNIa explosion rate in radio-loud galaxies has the same origin as their being strong radio sources, but there is no causality link between the two phenomena. We argue that repeated episodes of interaction and/or mergers of early type galaxies with dwarf companions, on times-scale of about 1 Gyr, are responsible for inducing both strong radio activity observed in $\sim$14% of early type galaxies and to supply an adequate number of SNIa progenitors to the stellar population of ellipticals.Comment: 26 pages+6 figures, ApJ, in pres