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, $na^3 < 10^{-5}$, where $n = N/V$ and $a$ is the hard core diameter, the condensate is localized at the center of the trap. As $na^3$ increases, the condensate moves to the edges of the trap. At high density it is localized at the edges of the trap. At $na^3 \leq 10^{-4}$ the Gross-Pitaevskii theory of the condensate describes the whole system within 1%. At $na^3 \approx 10^{-3}$ corrections are 3% to the GP energy but 30% to the Bogoliubov prediction of the condensate depletion. At $na^3 \gtrsim 10^{-2}$, mean field theory fails. At $na^3 \gtrsim 0.1$, the Bosons behave more like a liquid $^4$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