Luca Salasnich

Modulational instability and complex dynamics of confined matter-wave solitons.

We study the formation of bright solitons in a Bose-Einstein condensate of 7Li atoms induced by a sudden change in the sign of the scattering length from positive to negative, as reported in a recent experiment [Nature (London) 417, 150 (2002)]]. The numerical simulations are performed by using the Gross-Pitaevskii equation with a dissipative three-body term. We show that a number of bright solitons is produced and this can be interpreted in terms of the modulational instability of the time-dependent macroscopic wave function of the Bose condensate. In particular, we derive a simple formula for the number of solitons that is in good agreement with the numerical results. We find that during the motion of the soliton train in an axial harmonic potential the number of solitonic peaks changes in time and the density of individual peaks shows an intermittent behavior.

Bulk and collective properties of a dilute Fermi gas in the BCS-BEC crossover

We investigate the zero-temperature properties of a dilute two-component Fermi gas with attractive interspecies interaction in the BCS-BEC crossover. We build an efficient parametrization of the energy per particle based on Monte Carlo data and asymptotic behavior. This parametrization provides, in turn, analytical expressions for several bulk properties of the system such as the chemical potential, the pressure, and the sound velocity. In addition, by using a time-dependent density functional approach, we determine the collective modes of the Fermi gas under harmonic confinement. The calculated collective frequencies are compared to experimental data on confined vapors of {sup 6}Li atoms and with other theoretical predictions.

Finite-element modelling of simple shear flow in Newtonian and non-Newtonian fluids around a circular rigid particle

Abstract The flow perturbation around a circular rigid particle during simple shear deformation has been investigated for both Newtonian and non-Newtonian (power-law) fluids by finite-element modelling. If the particle is rotating under the applied shear couple and no-slip occurs at the particle–fluid interface, a ‘bow-tie-shaped’ streamline pattern results for both Newtonian and power-law fluids and the shape of streamlines does not change noticeably if the stress exponent ( n ) is changed. In contrast, if the fluid is allowed to separate from the particle, a ‘double-bulge-shaped’ flow develops in the case of Newtonian fluids, and the type of streamline pattern is influenced by n . We suggest that both stair-stepping and non-stair-stepping geometries of porphyroclast tails may be produced in mylonites, depending on the degree of coherence between the porphyroclasts and the embedding matrix. A different behaviour of the fluid–particle interface may occur as the result of changing fluid rheology, owing to the contrasting stress fields developed for Newtonian and non-Newtonian fluids.

Condensate bright solitons under transverse confinement

Istituto Nazionale per la Fisica della Materia, Unit`a di ComoDipartimento di Scienze Fisiche, Universit`a dell’Insubria,Via Valeggio 11, 23100 Como, ItalyWe investigate the dynamics of Bose-condensed bright solitons made of alkali-metal atoms withnegative scattering length and under harmonic confinement in the transverse direction. Contrary tothe 1D case, the 3D bright soliton exists only below a critical attractive interaction which dependson the extent of confinement. Such a behavior is also found in multi-soliton condensates with boxboundary conditions. We obtain numerical and analytical estimates of the critical strength beyondwhich the solitons do not exist. By using an effective 1D nonpolynomial nonlinear Schr¨odinger equa-tion (NPSE), which accurately takes into account the transverse dynamics of cigar-like condensates,we numerically simulate the dynamics of the ”soliton train” reported in a recent experiment (Nature417 150 (2002)). Then, analyzing the macroscopic quantum tunneling of the bright soliton on aGaussian barrier we find that its interference in the tunneling region is strongly suppressed withrespect to non-solitonic case; moreover, the tunneling through a barrier breaks the solitonic natureof the matter wave. Finally, we show that the collapse of the soliton is induced by the scattering onthe barrier or by the collision with another matter wave when the density reaches a critical value,for which we derive an accurate analytical formula.03.75.Fi; 32.80.Pj; 42.50.VkI. INTRODUCTION

STRUCTURE AND STABILITY OF BOSONIC CLOUDS : ALKALI-METAL ATOMS WITH NEGATIVE SCATTERING LENGTH

We investigate the form and stability of a cloud of atoms confined in a harmonic trap when the scattering length is negative. We find that, besides the known low-density metastable solution, a different branch of Bose condensate appears at higher density when nonlocality effects in the attractive part are taken into account. The transition between the two classes of solutions as a function of the number

Ideal quantum gases in D-dimensional space and power-law potentials

N

Condensate fraction of a Fermi gas in the BCS-BEC crossover

of atoms can be either sharp or smooth according to the strength and range of the attractive interaction. Use of tight traps is favorable for investigating the evolution of the system, as the strength of the effective interaction increases with

Extended Thomas-Fermi density functional for the unitary Fermi gas

N

OSCILLATION FREQUENCIES FOR A BOSE CONDENSATE IN A TRIAXIAL MAGNETIC TRAP

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Localized modes in dense repulsive and attractive Bose-Einstein condensates with spin-orbit and Rabi couplings

We investigate ideal quantum gases in D-dimensional space and confined in a generic external potential by using the semiclassical approximation. In particular, we derive density of states, density profiles and critical temperatures for Fermions and Bosons trapped in isotropic power-law potentials. From such results, one can easily obtain those of quantum gases in a rigid box and in a harmonic trap. Finally, we show that the Bose–Einstein condensation can set up in a confining power-law potential if and only if D/2+D/n>1, where D is the space dimension and n is the power-law exponent.