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Fedorov, D. V., E-mail: fedorov@phys.au.dk

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[en] Within the Correlated Gaussian Method the parameters of the Gaussian basis functions are often chosen stochastically using pseudo-random sequences. We show that alternative low-discrepancy sequences, also known as quasi-random sequences, provide bases of better quality. (author)

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Ludwig Faddeev Memorial Issue

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Fedorov, D. V., E-mail: fedorov@phys.au.dk

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[en] Matrix elements between shifted correlated Gaussians of various potentials with several form-factors are shown to be analytic. Their gradients with respect to the non-linear parameters of the Gaussians are also analytic. Analytic matrix elements are of importance for the correlated Gaussian method in quantum few-body physics. (author)

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[en] The quantum- mechanical three-body problem is reformulated in two dimensions by use of hyperspherical coordinates and an adiabatic expansion of the Faddeev equations. The effective radial potentials are calculated and their large-distance asymptotic behavior is derived analytically for short-range two-body interactions. Energies and wave functions are computed numerically for various potentials. An infinite series of Efirnov states does not exist in two dimensions. Borromean systems, i.e. bound three-body systems without bound binary subsystems, can only appear when a short-range repulsive barrier at finite distance is present in the two-body interaction. The corresponding Borromean state is never spatially extended. For a system of three weakly interacting identical bosons we find two bound states with both binding energies proportional to the two-body binding energy. In the limit of small binding these states are spatially located at the very large distances characterized by the scattering length. Their properties are universal and independent of the details of the potential. We compare throughout with the corresponding properties in three dimensions. (author)

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Few-Body Systems; ISSN 0177-7963; ; v. 27; p. 15-55

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Fedorov, D. V.; Mikkelsen, M.; Jensen, A. S.; Zinner, N. T., E-mail: fedorov@phys.au.dk

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[en] We investigate three-body recombination rates into deep dimers in cold atomic gases with large scattering length within hyper-spherical adiabatic zero-range approach. We derive closed analytic expressions for the rates for one- and two-species gases. Although the deep dimers are beyond the zero-range theory the latter can still describe the recombination into deep dimers by use of one additional short-range absorption parameter. The recombination rate, as function of the scattering length, retains the known universal behavior—the fourth power trend with characteristic log-periodic peaks—however increasing the short-range absorption broadens the peaks until they are eventually completely smeared out. Increasing the heavy-to-light mass ratio in a two-species system with two identical bosons and a third particle decreases the distance between the peaks and increases the overall scale of the recombination rate. (author)

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[en] We investigate two-component boson systems consisting of atoms and binary bound molecules of the same atoms. We assume that a coherent superposition of atomic and molecular Bose-Einstein condensates is formed in a non-stationary state leading to oscillations between the two condensates. To facilitate the formulation, we first give analogies in neutrino oscillations applicable for two states of one particle. We then extend to many non-interacting particles in an external field treated in the mean-field approximation as for collective motion of finite systems. We then go beyond the mean field and provide a framework for interacting particles and correlated wavefunctions. The atom-molecule oscillation frequency is dominated by the molecular binding energy when the atom-atom scattering length is substantially smaller than the oscillator trap length. Comparable scattering lengths can completely change the oscillation frequency. The damping time of the oscillations decreases with atom number and scattering lengths, although a large increase can occur for special combinations of the different interactions

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S0953-4075(05)99995-1; Available online at http://stacks.iop.org/0953-4075/38/2979/b5_16_010.pdf or at the Web site for the Journal of Physics. B, Atomic, Molecular and Optical Physics (ISSN 1361-6455) http://www.iop.org/; Country of input: International Atomic Energy Agency (IAEA)

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Journal of Physics. B, Atomic, Molecular and Optical Physics; ISSN 0953-4075; ; CODEN JPAPEH; v. 38(16); p. 2979-2997

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[en] We calculate energies, condensate fractions and two-body correlation functions for a system of N identical bosons in a trap. Both attractive and repulsive finite-range interactions with a large range of positive scattering lengths are used. At small scattering lengths the system is model independent. When the scattering length is comparable to the trap length the properties of the system depend on the details of the interaction

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Joint physics/mathematics workshop on quantum few-body systems; Arhus (Denmark); 19-20 Mar 2007; (c) 2008 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

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[en] We investigate systems of identical bosons with the focus on two-body correlations. We apply a Faddeev type of decomposition of the wavefunction. At large scattering length a series of spatially extended many-body bound states appears, analogously to the three-body Efimov states. We discuss a recombination process with these many-body Efimov states as intermediate states

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Wigner centennial conference; Pecs (Hungary); 8-12 Jul 2002; S1464-4266(03)59497-6; Available online at http://stacks.iop.org/1464-4266/5/S388/ob3374.pdf or at the Web site for the Journal of Optics. B, Quantum and Semiclassical Optics (Print) (ISSN 1464-4266) http://www.iop.org/; Country of input: International Atomic Energy Agency (IAEA)

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Journal of Optics. B, Quantum and Semiclassical Optics (Print); ISSN 1464-4266; ; v. 5(3); p. S388-S391

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[en] We investigate systems of identical bosons with the focus on two-body correlations. We use the hyperspherical adiabatic method and a decomposition of the wavefunction in two-body amplitudes. An analytic parametrization is used for the adiabatic effective radial potential. We discuss the structure of a condensate for arbitrary scattering length. Stability and timescales for various decay processes are estimated. The previously predicted Efimov-like states are found to be very narrow. We discuss the validity conditions and formal connections between the zero- and finite-range mean-field approximations, Faddeev-Yakubovskii formulation, Jastrow ansatz and the present method. We compare numerical results from the present work with mean-field calculations and discuss qualitatively the connection with measurements

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S0953-4075(04)65311-9; Available online at http://stacks.iop.org/0953-4075/37/93/b4_1_006.pdf or at the Web site for the Journal of Physics. B, Atomic, Molecular and Optical Physics (ISSN 1361-6455) http://www.iop.org/; Country of input: International Atomic Energy Agency (IAEA)

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Journal of Physics. B, Atomic, Molecular and Optical Physics; ISSN 0953-4075; ; CODEN JPAPEH; v. 37(1); p. 93-116

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Fedorov, D. V.; Armstrong, J. R.; Zinner, N. T.; Jensen, A. S., E-mail: fedorov@phys.au.dk

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[en] We investigate a system of two polarized molecules in a layered trap. Themolecules reside in adjacent layers and interact purely via the dipole-dipole interaction. We determine the properties of the ground state of the system as a function of the dipole moment and polarization angle. A bound state is always present in the system and in the weak binding limit the bound state extends to a very large distance and shows universal behavior. (author)

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21st European Conference on Few-Body Problems in Physics (Salamanca 2010)

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[en] The effective potential is computed for two boson systems in one trap as a function of their two individual hyperadii and the distance between their centres. Zero-range interactions are used and only relative s-states are included. Existence and properties of minima are investigated as a function of these three collective coordinates. For sufficiently strong repulsion stable structures are found at a finite distance between the centres. The relative centre-of-mass motion corresponds to the lowest normal mode. The highest normal mode is essentially the breathing mode where the subsystems vibrate by scaling their radii in phase. The intermediate normal mode corresponds to isovector motion where the subsystems vibrate by scaling their radii in opposite phase. Stability conditions are established as substantially more restrictive than in mean-field computations

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S0953-4075(04)77060-1; Available online at http://stacks.iop.org/0953-4075/37/2145/b4_10_011.pdf or at the Web site for the Journal of Physics. B, Atomic, Molecular and Optical Physics (ISSN 1361-6455) http://www.iop.org/; Country of input: International Atomic Energy Agency (IAEA)

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Journal of Physics. B, Atomic, Molecular and Optical Physics; ISSN 0953-4075; ; CODEN JPAPEH; v. 37(10); p. 2145-2164

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