Green's Functions and the Adiabatic Hyperspherical Method

Abstract

We address the few-body problem using the adiabatic hyperspherical representation. A general form for the hyperangular Green's function in $d$-dimensions is derived. The resulting Lippmann-Schwinger equation is solved for the case of three-particles with s-wave zero-range interactions. Identical particle symmetry is incorporated in a general and intuitive way. Complete semi-analytic expressions for the nonadiabatic channel couplings are derived. Finally, a model to describe the atom-loss due to three-body recombination for a three-component fermi-gas of ${}^6$Li atoms is presented.

14 pages, 8 figures, 2 tables

References in corpus (10)

• Observation of an Efimov spectrum in an atomic system
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• Universality in Three- and Four-Body Bound States of Ultracold Atoms
• Three-body recombination in a three-state Fermi gas with widely tunable interactions
• Observation of universality in ultracold 7Li three-body recombination
• Evidence for Universal Four-Body States Tied to an Efimov Trimer
• Low-energy three-body dynamics in binary quantum gases
• Scattering Length Scaling Laws for Ultracold Three-Body Collisions
• Ultracold three-body collisions near overlapping Feshbach resonances
• Magnetic Field Dependence and Efimov Resonance Broadening in Ultracold Three-Body Recombination

Cited by in corpus (34)

• Few-body physics with ultracold atomic and molecular systems in traps
• Universal three-body parameter in heteronuclear atomic systems
• Few-body physics in resonantly interacting ultracold quantum gases
• Three s-wave interacting fermions under anisotropic harmonic confinement: Dimensional crossover of energetics and virial coefficients
• Trimers in the resonant 2+1 fermionic problem on a narrow Feshbach resonance : Crossover from Efimovian to Hydrogenoid spectrum
• Thermodynamics of the two-component Fermi gas with unequal masses at unitarity
• Absence of a four-body Efimov effect in the 2 + 2 fermionic problem
• Universality of the unitary Fermi gas: A few-body perspective
• Trapped unitary two-component Fermi gases with up to ten particles
• Few-body resonances of unequal-mass systems with infinite interspecies two-body s-wave scattering length
• Few-body correlations in two-dimensional Bose and Fermi ultracold mixtures
• Non-universal bound states of two identical heavy fermions and one light particle
• Extension of the correlated Gaussian hyperspherical method to more particles and dimensions
• Harmonically trapped Fermi gas: Temperature dependence of the Tan contact
• Three-body Physics in Strongly Correlated Spinor Condensates
• A general T-matrix approach applied to two-body and three-body problems in cold atomic gases
• Three and four identical fermions near the unitary limit
• The interaction-sensitive states of a trapped two-component ideal Fermi gas and application to the virial expansion of the unitary Fermi gas
• Three-body rf association of Efimov trimers
• Ultracold heteronuclear three-body systems: How diabaticity limits the universality of recombination into shallow dimers
• Interferometry of Efimov states in thermal gases by modulated magnetic fields
• Dynamical excitation processes and correlations of three-body two-dimensional mixtures
• Hyperspherical approach to the three-bosons problem in 2D with a magnetic field
• Mass-imbalanced fermionic mixture in a harmonic trap
• Universal trimers with p-wave interactions and the faux-Efimov effect
• Three-Boson Bound States in Two Dimensions
• Asymmetric lineshapes of Efimov resonances in mass-imbalanced ultracold gases
• On the Appearance of Families of Efimov States in the Spinor Three-Body Problem
• Energetics of three interacting mass-imbalanced bodies in a three-dimensional spherical harmonic trap
• Fourth cluster and virial coefficients of a unitary Fermi gas for an arbitrary mass ratio
• Deformed Explicitly Correlated Gaussians
• Mechanisms of anomalous three-body loss in a population-imbalanced three-component Fermi gas
• Density effects on the interferometry of Efimov states by modulating magnetic fields
• Observable Resonances in Efimov-unfavored Systems