57 research outputs found
Properties of two - dimensional dusty plasma clusters
Two-dimensional classical cluster of particles interacting through a screened
Coulomb potential is studied. This system can be used as a model for "dusty
particles" in high-frequency discharge plasma. For systems consisting of N = 2
- 40 particles and confined by a harmonic potential we find ground-state
configurations, eigenfrequencies and eigenvectors for the normal modes as a
function of the Debye screening length R_D in plasma. Variations in R_D cause
changes in the ground-state structure of clusters, each structural
rearrangement can be considered as a phase transition of first or second order
(with respect to parameter R_D). Monte Carlo and molecular dynamics are used to
study in detail the melting of the clusters as the temperature is increased. By
varying the density and the temperature of plasma, to which the particles are
immersed, one can modulate thermodynamical properties of the system,
transforming it in a controllable way to an ordered (crystal-like),
orientationaly disordered or totally disordered (liquid-like) states. The
possibility of dynamical coexistence phenomena in small clusters is discussed.Comment: 5 pages, 6 Postscript figures; to appear in Phys.Lett.
Distinguibility, degeneracy, and correlations in three harmonically trapped bosons in one dimension
We study a system of two bosons of one species and a third atom of a second species in a one-dimensional parabolic trap at zero temperature. We assume contact repulsive inter- and intraspecies interactions. By means of an exact diagonalization method we calculate the ground and excited states for the whole range of interactions. We use discrete group theory to classify the eigenstates according to the symmetry of the interaction potential. We also propose and validate analytical Ansätze gaining physical insight over the numerically obtained wave functions. We show that, for both approaches, it is crucial to take into account that the distinguishability of the third atom implies the absence of any restriction over the wave function when interchanging this boson with any of the other two. We find that there are degeneracies in the spectra in some limiting regimes, that is, when the interspecies and/or the intraspecies interactions tend to infinity. This is in contrast with the three-identical boson system, where no degeneracy occurs in these limits. We show that, when tuning both types of interactions through a protocol that keeps them equal while they are increased towards infinity, the systems's ground state resembles that of three indistinguishable bosons. Contrarily, the systems's ground state is different from that of three-identical bosons when both types of interactions are increased towards infinity through protocols that do not restrict them to be equal. We study the coherence and correlations of the system as the interactions are tuned through different protocols, which permit us to build up different correlations in the system and lead to different spatial distributions of the three atoms
Correlation functions and momentum distribution of one-dimensional Bose systems
The ground-state correlation properties of a one-dimensional Bose system
described by the Lieb-Liniger Hamiltonian are investigated by using exact
quantum Monte Carlo techniques. The pair distribution function, static
structure factor, one-body density matrix and momentum distribution of a
homogeneous system are calculated for different values of the gas parameter
ranging from the Tonks-Girardeau to the mean-field regime. Results for the
momentum distribution of a harmonically trapped gas in configurations relevant
to experiments are also presented.Comment: 4 pages, 5 figure
Ewald method for polytropic potentials in arbitrary dimensionality
The Ewald summation technique is generalised to power-law 1/|r|^k potentials
in three-, two- and one-dimensional geometries with explicit formulae for all
the components of the sums. The cases of short-range, long-range and "marginal"
interactions are treated separately. The jellium model, as a particular case of
a charge-neutral system, is discussed and the explicit forms of the Ewald sums
for such system are presented. A generalised form of the Ewald sums for a
noncubic (nonsquare) simulation cell for three- (two-) dimensional geometry is
obtained and its possible field of application is discussed. A procedure for
the optimisation of the involved parameters in actual simulations is developed
and an example of its application is presented.Comment: 41 pages, 3 figure
Molecular regimes in ultracold Fermi gases
The use of Feshbach resonances for tuning the interparticle interaction in
ultracold Fermi gases has led to remarkable developments, in particular to the
creation and Bose-Einstein condensation of weakly bound diatomic molecules of
fermionic atoms. These are the largest diatomic molecules obtained so far, with
a size of the order of thousands of angstroms. They represent novel composite
bosons, which exhibit features of Fermi statistics at short intermolecular
distances. Being highly excited, these molecules are remarkably stable with
respect to collisional relaxation, which is a consequence of the Pauli
exclusion principle for identical fermionic atoms. The purpose of this review
is to introduce theoretical approaches and describe the physics of molecular
regimes in two-component Fermi gases and Fermi-Fermi mixtures, focusing
attention on quantum statistical effects.Comment: Chapter of the book: "Cold Molecules: Theory, Experiment,
Applications" edited by R. V. Krems, B. Friedrich and W. C. Stwalley
(publication expected in March 2009
Hydrodynamic modes of a 1D trapped Bose gas
We consider two regimes where a trapped Bose gas behaves as a one-dimensional
system. In the first one the Bose gas is microscopically described by 3D mean
field theory, but the trap is so elongated that it behaves as a 1D gas with
respect to low frequency collective modes. In the second regime we assume that
the 1D gas is truly 1D and that it is properly described by the Lieb-Liniger
model. In both regimes we find the frequency of the lowest compressional mode
by solving the hydrodynamic equations. This is done by making use of a method
which allows to find analytical or quasi-analytical solutions of these
equations for a large class of models approaching very closely the actual
equation of state of the Bose gas. We find an excellent agreement with the
recent results of Menotti and Stringari obtained from a sum rule approach.Comment: 15 pages, revtex, 1 figure
Natural Orbitals and BEC in traps, a diffusion Monte Carlo analysis
We investigate the properties of hard core Bosons in harmonic traps over a
wide range of densities. Bose-Einstein condensation is formulated using the
one-body Density Matrix (OBDM) which is equally valid at low and high
densities. The OBDM is calculated using diffusion Monte Carlo methods and it is
diagonalized to obtain the "natural" single particle orbitals and their
occupation, including the condensate fraction. At low Boson density, , where and is the hard core diameter, the condensate is
localized at the center of the trap. As increases, the condensate moves
to the edges of the trap. At high density it is localized at the edges of the
trap. At the Gross-Pitaevskii theory of the condensate
describes the whole system within 1%. At corrections are
3% to the GP energy but 30% to the Bogoliubov prediction of the condensate
depletion. At , mean field theory fails. At , the Bosons behave more like a liquid He droplet than a trapped Boson
gas.Comment: 13 pages, 14 figures, submitted Phys. Rev.
Three strongly correlated charged bosons in a one-dimensional harmonic trap: natural orbital occupancies
We study a one-dimensional system composed of three charged bosons confined
in an external harmonic potential. More precisely, we investigate the
ground-state correlation properties of the system, paying particular attention
to the strong-interaction limit. We explain for the first time the nature of
the degeneracies appearing in this limit in the spectrum of the reduced density
matrix. An explicit representation of the asymptotic natural orbitals and their
occupancies is given in terms of some integral equations.Comment: 6 pages, 4 figures, To appear in European Physical Journal
Persistent currents in a Bose-Einstein condensate in the presence of disorder
We examine bosonic atoms that are confined in a toroidal,
quasi-one-dimensional trap, subjected to a random potential. The resulting
inhomogeneous atomic density is smoothened for sufficiently strong, repulsive
interatomic interactions. Statistical analysis of our simulations show that the
gas supports persistent currents, which become more fragile due to the
disorder.Comment: 5 pages, RevTex, 3 figures, revised version, to appear in JLT
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