332 research outputs found
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
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.
Bosonic clouds with attractive interaction beyond the local interaction approximation
We study the properties of a Bose-Einstein condensed cloud of atoms with
negative scattering length confined in a harmonic trap. When a realistic non
local (finite range) effective interaction is taken into account, we find that,
besides the known low density metastable solution, a new branch of Bose
condensate appears at higher density. This state is self-bound but its density
can be quite low if the number of atoms is not too big. The transition
between the two classes of solutions as a function of can be either sharp
or smooth according to the ratio between the range of the attractive
interaction and the length of the trap. A tight trap leads to a smooth
transition. In addition to the energy and the shape of the cloud we study also
the dynamics of the system. In particular, we study the frequencies of
collective oscillation of the Bose condensate as a function of the number of
atoms both in the local and in the non local case. Moreover, we consider the
dynamics of the cloud when the external trap is switched off.Comment: Latex, 6 pages, 2 figure, 1 table, presented to the International
Symposium of Quantum Fluids and Solids 98, Amherst (USA), 9-14 June 199
Fluctuations and Pattern Formation in Fluids with Competing Interactions
One of the most interesting phenomena in the soft-matter realm consists in
the spontaneous formation of super-molecular structures (microphases) in
condition of thermodynamic equilibrium. A simple mechanism responsible for this
self-organization or pattern formation is based on the competition between
attractive and repulsive forces with different length scales in the microscopic
potential, typically, a short-range attraction against a longer-range
repulsion.
We analyse this problem by simulations in 2D fluids. We find that, as the
temperature is lowered, liquid-vapor phase separation is inhibited by the
competition between attraction and repulsion, and replaced by a transition to
non-homogeneous phases. The structure of the fluid shows well defined
signatures of the presence of both intra- and inter-cluster correlations.
Even when the competition between attraction and repulsion is not so strong
as to cause microphase formation, it still induces large density fluctuations
in a wide region of the temperature-density plane. In this large-fluctuation
regime, pattern formation can be triggered by a weak external modulating field.Comment: To appear in the proceedings of the "International workshop on
collective phenomena in macroscopic systems", 2006 Villa Olmo (Como), Ital
Thermodynamics of Bose-Condensed Atomic Hydrogen
We study the thermodynamics of the Bose-condensed atomic hydrogen confined in
the Ioffe-Pritchard potential. Such a trapping potential, that models the
magnetic trap used in recent experiments with hydrogen, is anharmonic and
strongly anisotropic. We calculate the ground-state properties, the condensed
and non-condensed fraction and the Bose-Einstein transition temperature. The
thermodynamics of the system is strongly affected by the anharmonicity of this
external trap. Finally, we consider the possibility to detect Josephson-like
currents by creating a double-well barrier with a laser beam.Comment: 11 pages, 4 figures, to be published in European Physical Journal
Thermodynamics of a trapped Bose condensate with negative scattering length
We study the Bose-Einstein condensation (BEC) for a system of atoms,
which have negative scattering length (attractive interaction), confined in a
harmonic potential. Within the Bogoliubov and Popov approximations, we
numerically calculate the density profile for both condensate and
non-condensate fractions and the spectrum of elementary excitations. In
particular, we analyze the temperature and number-of-boson dependence of these
quantities and evaluate the BEC transition temperature . We calculate
the loss rate for inelastic two- and three-body collisions. We find that the
total loss rate is strongly dependent on the density profile of the condensate,
but this density profile does not appreciably change by increasing the thermal
fraction. Moreover, we study, using the quasi-classical Popov approximation,
the temperature dependence of the critical number of condensed bosons,
for which there is the collapse of the condensate. There are different regimes
as a function of the total number of atoms. For the condensate is
always metastable but for the condensate is metastable only for
temperatures that exceed a critical value .Comment: RevTex, 7 postscript figures, to be published in Journal of Low
Temperature Phsyic
Phase diagram of symmetric binary mixtures at equimolar and non-equimolar concentrations: a systematic investigation
We consider symmetric binary mixtures consisting of spherical particles with
equal diameters interacting via a hard-core plus attractive tail potential with
strengths epsilon_{ij}, i,j=1,2, such that epsilon_{11} = epsilon_{22} >
epsilon_{12}. The phase diagram of the system at all densities and
concentrations is investigated as a function of the unlike-to-like interaction
ratio delta = epsilon_{12}/epsilon_{11} by means of the hierarchical reference
theory (HRT). The results are related to those of previous investigations
performed at equimolar concentration, as well as to the topology of the
mean-field critical lines. As delta is increased in the interval 0 < delta < 1,
we find first a regime where the phase diagram at equal species concentration
displays a tricritical point, then one where both a tricritical and a
liquid-vapor critical point are present. We did not find any clear evidence of
the critical endpoint topology predicted by mean-field theory as delta
approaches 1, at least up to delta=0.8, which is the largest value of delta
investigated here. Particular attention was paid to the description of the
critical-plus-tricritical point regime in the whole density-concentration
plane. In this situation, the phase diagram shows, in a certain temperature
interval, a coexistence region that encloses an island of homogeneous,
one-phase fluid.Comment: 27 pages + 20 figure
Thermodynamics of Solitonic Matter Waves in a Toroidal Trap
We investigate the thermodynamic properties of a Bose-Einstein condensate
with negative scattering length confined in a toroidal trapping potential. By
numerically solving the coupled Gross-Pitaevskii and Bogoliubov-de Gennes
equations, we study the phase transition from the uniform state to the
symmetry-breaking state characterized by a bright-soliton condensate and a
localized thermal cloud. In the localized regime three states with a finite
condensate fraction are present: the thermodynamically stable localized state,
a metastable localized state and also a metastable uniform state. Remarkably,
the presence of the stable localized state strongly increases the critical
temperature of Bose-Einstein condensation.Comment: 4 pages, 4 figures, to be published in Physical Review A as a Rapid
Communication. Related papers can be found at
http://www.padova.infm.it/salasnich/tdqg.htm
Transition from 3D to 1D in Bose Gases at Zero Temperature
We investigate the effects of dimensional reduction in Bose gases induced by
a strong harmonic confinement in the transverse cylindric radial direction. By
using a generalized Lieb-Liniger theory, based on a variational treatment of
the transverse width of the Bose gas, we analyze the transition from a 3D
Bose-Einstein condensate to the 1D Tonks-Girardeau gas. The sound velocity and
the frequency of the lowest compressional mode give a clear signature of the
regime involved. We study also the case of negative scattering length deriving
the phase diagram of the Bose gas (uniform, single soliton, multi soliton and
collapsed) in toroidal confinement.Comment: 5 pages, 5 figures, to be published in Phys. Rev.
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