The unitary gas in an isotropic harmonic trap: symmetry properties and applications

We consider N atoms trapped in an isotropic harmonic potential, with s-wave interactions of infinite scattering length. In the zero-range limit, we obtain several exact analytical results: mapping between the trapped problem and the free-space zero-energy problem, separability in hyperspherical coordinates, SO(2,1) hidden symmetry, and relations between the moments of the trapping potential energy and the moments of the total energy

Teoría Económica y Desarrollo Social. Exclusión, desigualdad y democracia. Homenaje a Adolfo Figueroa

Los autores de los artículos de este libro de homenaje a Adolfo Figueroa abordan temas de desigualdad, exclusión y políticas para el desarrollo social y de la democraciadesigualdad, Brasil

Heteronuclear molecules in an optical lattice: Theory and experiment

We study properties of two different atoms at a single optical lattice site at a heteronuclear atomic Feshbach resonance. We calculate the energy spectrum, the efficiency of rf association and the lifetime as a function of magnetic field and compare the results with the experimental data obtained for K-40 and Rb-87 [C. Ospelkaus et al., Phys. Rev. Lett. 97, 120402 (2006)]. We treat the interaction in terms of a regularized delta function pseudopotential and consider the general case of particles with different trap frequencies, where the usual approach of separating center-of-mass and relative motion fails. We develop an exact diagonalization approach to the coupling between center-of-mass and relative motion and numerically determine the spectrum of the system. At the same time, our approach allows us to treat the anharmonicity of the lattice potential exactly. Within the pseudopotential model, the center of the Feshbach resonance can be precisely determined from the experimental data.Comment: 9 pages, 7 figures, revised discussion of transfer efficienc

Single-Particle Momentum Distribution of an Efimov trimer

Experimental progress in the study of strongly interacting ultracold atoms has recently allowed the observation of Efimov trimers. We study theoretically a non-conventional observable for these trimer states, that may be accessed experimentally, the momentum distribution n(k) of the constitutive bosonic particles. The large momentum part of the distribution is particularly intriguing: In addition to the expected 1/k^4 tail associated to contact interactions, it exhibits a subleading tail 1/k^5 which is a hall-mark of Efimov physics and leads to a breakdown of a previously proposed expression of the energy as a functional of the momentum distribution.Comment: This is a subpart of the (too long to be published) work arXiv:1001.0774. This subpart has 11 pages and 2 figures. Revised version correcting minor error

Resummation of diagrammatic series with zero convergence radius for strongly correlated fermions

We demonstrate that summing up series of Feynman diagrams can yield unbiased accurate results for strongly-correlated fermions even when the convergence radius vanishes. We consider the unitary Fermi gas, a model of non-relativistic fermions in three-dimensional continuous space. Diagrams are built from partially-dressed or fully-dressed propagators of single particles and pairs. The series is resummed by a conformal-Borel transformation that incorporates the large-order behavior and the analytic structure in the Borel plane, which are found by the instanton approach. We report highly accurate numerical results for the equation of state in the normal unpolarized regime, and reconcile experimental data with the theoretically conjectured fourth virial coefficient

Exact relations for quantum-mechanical few-body and many-body problems with short-range interactions in two and three dimensions

We derive relations between various observables for N particles with zero-range or short-range interactions, in continuous space or on a lattice, in two or three dimensions, in an arbitrary external potential. Some of our results generalise known relations between large-momentum behavior of the momentum distribution, short-distance behavior of the pair correlation function and of the one-body density matrix, derivative of the energy with respect to the scattering length or to time, and the norm of the regular part of the wavefunction; in the case of finite-range interactions, the interaction energy is also related to dE/da. The expression relating the energy to a functional of the momentum distribution is also generalised, and is found to break down for Efimov states with zero-range interactions, due to a subleading oscillating tail in the momentum distribution. We also obtain new expressions for the derivative of the energy of a universal state with respect to the effective range, the derivative of the energy of an efimovian state with respect to the three-body parameter, and the second order derivative of the energy with respect to the inverse (or the logarithm in the two-dimensional case) of the scattering length. The latter is negative at fixed entropy. We use exact relations to compute corrections to exactly solvable three-body problems and find agreement with available numerics. For the unitary gas, we compare exact relations to existing fixed-node Monte-Carlo data, and we test, with existing Quantum Monte Carlo results on different finite range models, our prediction that the leading deviation of the critical temperature from its zero range value is linear in the interaction effective range r_e with a model independent numerical coefficient.Comment: 51 pages, 5 figures. Split into three articles: Phys. Rev. A 83, 063614 (2011) [arXiv:1103.5157]; Phys. Rev. A 86, 013626 (2012) [arXiv:1204.3204]; Phys. Rev. A 86, 053633 (2012) [ arXiv:1210.1784

Virial theorems for trapped cold atoms

We present a general virial theorem for quantum particles with arbitrary zero-range or finite-range interactions in an arbitrary external potential. We deduce virial theorems for several situations relevant to trapped cold atoms: zero-range interactions with and without Efimov effect, hard spheres, narrow Feshbach resonances, and finite-range interactions. If the scattering length $a$ is varied adiabatically in the BEC-BCS crossover, we find that the trapping potential energy as a function of $1/a$ has an inflexion point at unitarity.Comment: A few small correction

Assembléia de peixes associados a ambientes consolidados no litoral do Paraná, Brasil: uma análise qualitativa com notas sobre sua bioecologia

Recently, reef fish studies have been receiving more attention from researchers. Five zoogeographical provinces were determined along the brazilian coast with the State of Paraná baing included within the south-southeast province. Reef fish fauna was accessed through underwater visual census at natural and artificial habitats. We observed that both sand matrix effect, which involves a artificial environment, and the attractor effect of these structures over the ichtyofauna, are evident on both sandy and pelagic species,respectively, and are the main responsible for differences found between natural and artificial assemblages. The apparent lower richness attributed to Paraná state when compared with other localities belonging to the same zoogeographic province could be a consequence of a local biological filter or just a outcome of regional studies absence.Recentemente, estudos com peixes recifais vêm recebendo cada vez mais atenção dos pesquisadores. Na costa brasileira cinco províncias zoogeográficas foram determinadas, sendo o Paraná incluído na província sul-sudeste. Utilizando-se do censo visual sub-aquático para acessar a fauna de peixes recifais, avaliou-se os ambientes naturais e artificiais. Observou-se que a heterogeneidade de ambientes na região configura diferenças na estrutura da ictiofauna influenciada pela matriz arenosa que envolve os ambientes artificiais e pelo efeito atrator destas estruturas evidenciado pela maior presença de espécies pelágicas, efeito diluído no entorno dos ambientes insulares avaliados. A aparente pobreza de espécies, quando comparado com outros locais pertencentes à mesma província, pode ser efeito de um filtro biológico local ou apenas um reflexo da inexistência de estudos na região