The interaction-sensitive states of a trapped two-component ideal Fermi gas and application to the virial expansion of the unitary Fermi gas

Abstract

We consider a two-component ideal Fermi gas in an isotropic harmonic potential. Some eigenstates have a wavefunction that vanishes when two distinguishable fermions are at the same location, and would be unaffected by s-wave contact interactions between the two components. We determine the other, interaction-sensitive eigenstates, using a Faddeev ansatz. This problem is nontrivial, due to degeneracies and to the existence of unphysical Faddeev solutions. As an application we present a new conjecture for the fourth-order cluster or virial coefficient of the unitary Fermi gas, in good agreement with the numerical results of Blume and coworkers.

arXiv commentUpdated augmented version in English (33 pages) and in French (35 pages)

References in corpus (23)

• Revealing the Superfluid Lambda Transition in the Universal Thermodynamics of a Unitary Fermi Gas
• Exploring the Thermodynamics of a Universal Fermi Gas
• Deterministic Preparation of a Tunable Few-Fermion System
• Three-body problem in Fermi gases with short-range interparticle interaction
• Breathing Modes and Hidden Symmetry of Trapped Atoms in 2D
• The unitary gas in an isotropic harmonic trap: symmetry properties and applications
• Quantum Hall fractions in rotating Bose-Einstein condensates
• Atom interferometry with a weakly-interacting Bose Einstein condensate
• Virial expansion for a strongly correlated Fermi gas
• A Composite Fermion Description of Rotating Bose-Einstein Condensates
• Diatomic molecules in ultracold Fermi gases - Novel composite bosons
• Four-body Efimov effect
• Natural and unnatural parity states of small trapped equal-mass two-component Fermi gases at unitarity and fourth-order virial coefficient
• Universal Fermi Gas with Two- and Three-Body Resonances
• Energy spectrum of harmonically trapped two-component Fermi gases: Three- and Four-Particle Problem
• Green's Functions and the Adiabatic Hyperspherical Method
• Isotropic contact forces in arbitrary representation: heterogeneous few-body problems and low dimensions
• Trimers in the resonant 2+1 fermionic problem on a narrow Feshbach resonance : Crossover from Efimovian to Hydrogenoid spectrum
• High-temperature limit of the resonant Fermi gas
• Third virial coefficient of the unitary Bose gas
• Absence of a four-body Efimov effect in the 2 + 2 fermionic problem
• Renormalisation-group analysis of repulsive three-body systems
• The third virial coefficient of a two-component unitary Fermi gas across an Efimov-effect threshold

Cited by in corpus (8)

• Resummation of diagrammatic series with zero convergence radius for strongly correlated fermions
• Universality of the unitary Fermi gas: A few-body perspective
• Pairing and the spin susceptibility of the polarized unitary Fermi gas in the normal phase
• The fourth- and fifth-order virial coefficients from weak-coupling to unitarity
• Fourth- and fifth-order virial expansion of harmonically trapped fermions at unitarity
• Mass-imbalanced fermionic mixture in a harmonic trap
• Fourth cluster and virial coefficients of a unitary Fermi gas for an arbitrary mass ratio
• Toward an automated-algebra framework for high orders in the virial expansion of quantum matter