The Hyperspherical Four-Fermion Problem

Abstract

The problem of a few interacting fermions in quantum physics has sparked intense interest, particularly in recent years owing to connections with the behavior of superconductors, fermionic superfluids, and finite nuclei. This review addresses recent developments in the theoretical description of four fermions having finite-range interactions, stressing insights that have emerged from a hyperspherical coordinate perspective. The subject is complicated, so we have included many detailed formulas that will hopefully make these methods accessible to others interested in using them. The universality regime, where the dominant length scale in the problem is the two-body scattering length, is particularly stressed, including its implications for the famous BCS-BEC crossover problem Derivations and relevant formulas are also included for the calculation of challenging few-body processes such as recombination.

66 pages, 33 figures

References in corpus (28)

• Theory of ultracold Fermi gases
• Weakly bound dimers of fermionic atoms
• Generalized Virial Theorem and Pressure Relation for a strongly correlated Fermi gas
• Observation of an Efimov spectrum in an atomic system
• Evidence for Universal Four-Body States Tied to an Efimov Trimer
• Universal Properties of the Four-Body System with Large Scattering Length
• Scattering Length Scaling Laws for Ultracold Three-Body Collisions
• Analytical solution of the bosonic three-body problem
• Universal properties of a trapped two-component Fermi gas at unitarity
• Adiabatic association of ultracold molecules via magnetic field tunable interactions
• Diatomic molecules in ultracold Fermi gases - Novel composite bosons
• Energetics and Structural Properties of Trapped Two-Component Fermi Gases
• Efimov physics in bosonic atom-trimer scattering
• 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
• Excited Thomas-Efimov levels in ultracold gases
• Quantum calculations of H2-H2 collisions: from ultracold to thermal energies
• Correlated Gaussian Hyperspherical Method for Few-Body Systems
• Efimov effect from functional renormalization
• Ultracold three-body collisions near overlapping Feshbach resonances
• Collisional properties of weakly bound heteronuclear dimers
• Pair correlations of an expanding superfluid Fermi gas
• Illustration of universal relations for trapped four-fermion system with arbitrary s-wave scattering length
• Efimov Trimer Formation via Ultracold Four-body Recombination
• Dimer-dimer collisions at finite energies in two-component Fermi gases
• New Calculations of Recombination Rates for Cold ${}^4$He Atoms and Determination of Universal Scaling Functions
• Hyperspherical Description of the Degenerate Fermi Gas: S-wave Interactions
• Four-quark stability

Cited by in corpus (30)

• Universal few-body physics and cluster formation
• Few-body physics with ultracold atomic and molecular systems in traps
• Virial expansion for a strongly correlated Fermi system and its application to ultracold atomic Fermi gases
• Comparison of classical and quantal calculations of helium three-body recombination
• Natural and unnatural parity states of small trapped equal-mass two-component Fermi gases at unitarity and fourth-order virial coefficient
• Universal four-body states in heavy-light mixtures with positive scattering length
• The quest for light multineutron systems
• Non-resonant Density of States Enhancement at Low Energies for Three or Four Neutrons
• Low energy structures in nuclear reactions with 4n in the final state
• Integrable families of hard-core particles with unequal masses in a one-dimensional harmonic trap
• 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
• Multichannel quantum-defect theory for ion-atom interactions
• Hyperspherical explicitly correlated Gaussian approach for few-body systems with finite angular momentum
• Microscopic derivation of multi-channel Hubbard models for ultracold nonreactive molecules in an optical lattice
• Renormalized contact interaction in degenerate unitary Bose gases
• Scattering properties of the $2e^{-}2e^{+}$ polyelectronic system
• Modelling double charge exchange response function for tetraneutron system
• Three and four identical fermions near the unitary limit
• Ultracold heteronuclear three-body systems: How diabaticity limits the universality of recombination into shallow dimers
• Hyperspherical theory of the quantum Hall effect: the role of exceptional degeneracy
• Coupled pair approach for strongly-interacting trapped fermionic atoms
• Universal trimers with p-wave interactions and the faux-Efimov effect
• 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
• Asymmetric lineshapes of Efimov resonances in mass-imbalanced ultracold gases
• Few-body collective excitations beyond Kohn's theorem in quantum Hall systems
• Resonances and collisional properties of neutron-rich helium isotopes in the adiabatic hyperspherical representation
• Hyperspherical Slater determinant approach to few-body fractional quantum Hall states