Correlated Gaussian Hyperspherical Method for Few-Body Systems

Abstract

We develop an innovative numerical technique to describe few-body systems. Correlated Gaussian basis functions are used to expand the channel functions in the hyperspherical representation. The method is proven to be robust and efficient compared to other numerical techniques. The method is applied to few-body systems with short range interactions, including several examples for three- and four-body systems. Specifically, for the two-component, four-fermion system, we extract the coefficients that characterize its behavior at unitarity.

13 pages, 2 figures, 2 tables

References in corpus (20)

• Many-Body Physics with Ultracold Gases
• Vortices and Superfluidity in a Strongly Interacting Fermi Gas
• Observation of Bose-Einstein Condensation of Molecules
• Weakly bound dimers of fermionic atoms
• Double species condensate with tunable interspecies interactions
• Collisional stability of a three-component degenerate Fermi gas
• Three-body recombination in a three-state Fermi gas with widely tunable interactions
• Three-boson problem near a narrow Feshbach resonance
• Evidence for Universal Four-Body States Tied to an Efimov Trimer
• Universal properties of a trapped two-component Fermi gas at unitarity
• Four-body calculation of proton-3He scattering
• Association of ultracold double-species bosonic molecules
• Effective Theory for Trapped Few-Fermion Systems
• Energetics and Structural Properties of Trapped Two-Component Fermi Gases
• Unitary Fermi Gas in a Harmonic Trap
• Spectrum and Dynamics of the BCS-BEC crossover from a few-body perspective
• BEC-BCS Crossover of a Trapped Two-Component Fermi Gas with Unequal Masses
• Efimov Trimer Formation via Ultracold Four-body Recombination
• Dimer-dimer collisions at finite energies in two-component Fermi gases
• Stability of Inhomogeneous Multi-Component Fermi Gases

Cited by in corpus (31)

• Universal few-body physics and cluster formation
• Few-body physics with ultracold atomic and molecular systems in traps
• Natural and unnatural parity states of small trapped equal-mass two-component Fermi gases at unitarity and fourth-order virial coefficient
• Spectra of helium clusters with up to six atoms using soft core potentials
• Energy spectrum of harmonically trapped two-component Fermi gases: Three- and Four-Particle Problem
• The Hyperspherical Four-Fermion Problem
• Non-resonant Density of States Enhancement at Low Energies for Three or Four Neutrons
• The helium trimer with soft-core potentials
• Illustration of universal relations for trapped four-fermion system with arbitrary s-wave scattering length
• Efimov physics in heteronuclear four-body systems
• Unnuclear physics
• Accelerating the convergence of exact diagonalization with the transcorrelated method: Quantum gas in one dimension with contact interactions
• Universality of the unitary Fermi gas: A few-body perspective
• Trapped unitary two-component Fermi gases with up to ten particles
• A Comprehensive Study of the Three- and Four-Neutron Systems at Low Energies
• Extension of the correlated Gaussian hyperspherical method to more particles and dimensions
• General integral relations for the description of scattering states using the hyperspherical adiabatic basis
• Hyperspherical explicitly correlated Gaussian approach for few-body systems with finite angular momentum
• Convergence of a renormalization group approach to dimer-dimer scattering
• Broken scale-invariance in time-dependent trapping potentials
• Field-induced long-lived supermolecules
• Scattering properties of the $2e^{-}2e^{+}$ polyelectronic system
• Three and four identical fermions near the unitary limit
• Fate of Multiparticle Resonances: From $Q$-Balls to ${}^3$He Droplets
• Six-bodies calculations using the Hyperspherical Harmonics method
• Constrained correlated-Gaussians for hyperspherical calculations
• Hyperspherical asymptotics of a system of four charged particles
• Low-Energy Scattering Properties of Ground-State and Excited-State Positronium Collisions
• Orbital Variational Adiabatic Hyperspherical Method Applied to Bose-Einstein Condensates
• Observability of modified threshold behavior near unitarity
• Deformed Explicitly Correlated Gaussians