Third virial coefficient of the unitary Bose gas

Abstract

By unitary Bose gas we mean a system composed of spinless bosons with s-wave interaction of infinite scattering length and almost negligible (real or effective) range. Experiments are currently trying to realize it with cold atoms. From the analytic solution of the three-body problem in a harmonic potential, and using methods previously developed for fermions, we determine the third cumulant (or cluster integral) b_3 and the third virial coefficient a_3 of this gas, in the spatially homogeneous case, as a function of its temperature and the three-body parameter R_t characterizing the Efimov effect. A key point is that, converting series into integrals (by an inverse residue method), and using an unexpected small parameter (the three-boson mass angle nu=pi/6), one can push the full analytical estimate of b_3 and a_3 up to an error that is in practice negligible. ----- Nous entendons par gaz de Bose unitaire un systeme compose de bosons sans spin interagissant dans l'onde s par un potentiel de longueur de diffusion infinie et de portee (reelle ou effective) presque negligeable, systeme pour l'instant abstrait mais dont la tentative de realisation avec des atomes froids est en cours. A partir de la solution analytique connue du probleme a trois corps dans un piege harmonique, et de methodes precedemment developpees pour des fermions, nous determinons le troisieme cumulant b_3, puis le troisieme coefficient du viriel a_3 de ce gaz, dans le cas spatialement homogene, en fonction de sa temperature et du parametre a trois corps R_t caracterisant l'effet Efimov. Un point marquant est qu'en convertissant des series en des integrales (par une methode des residus inverse), puis en utilisant un petit parametre inattendu, l'angle de masse nu=pi/6 des trois bosons, on peut pousser l'estimation completement analytique de b_3 et de a_3 jusqu'a une erreur en pratique negligeable.

9 pages, one figure; problem with cross-referencing of footnotes solved; french version added

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Cited by in corpus (27)

• Efimov Physics: a review
• Universal few-body physics and cluster formation
• Stability of a unitary Bose gas
• Supplementary information to "Efimov-driven phase transitions of the unitary Bose gas"
• Efimov-driven phase transitions of the unitary Bose gas
• Strongly correlated Bose gases
• High-temperature limit of the resonant Fermi gas
• Efimov correlations in strongly interacting Bose gases
• Absence of a four-body Efimov effect in the 2 + 2 fermionic problem
• Path integral Monte Carlo determination of the fourth-order virial coefficient for unitary two-component Fermi gas with zero-range interactions
• The third virial coefficient of a two-component unitary Fermi gas across an Efimov-effect threshold
• Pairing and the spin susceptibility of the polarized unitary Fermi gas in the normal phase
• Fisher zeros of a unitary Bose gas
• Momentum distribution of a dilute unitary Bose gas with three-body losses
• The fourth- and fifth-order virial coefficients from weak-coupling to unitarity
• High Temperature Virial Expansion to Universal Quench Dynamics
• A liquid-gas transition for bosons with attractive interaction in one dimension
• The interaction-sensitive states of a trapped two-component ideal Fermi gas and application to the virial expansion of the unitary Fermi gas
• Momentum distribution in the unitary Bose gas from first principles
• Fourth- and fifth-order virial expansion of harmonically trapped fermions at unitarity
• Lee-Yang cluster expansion approach to the BCS-BEC crossover: BCS and BEC limits
• Thermodynamics of one-dimensional SU(4) and SU(6) fermions with attractive interactions
• Equation of state and contact of a strongly interacting Bose gas in the normal state
• Virial coefficients for Bose and Fermi trapped gases beyond the unitary limit: an S-Matrix approach
• Second-order virial expansion for an atomic gas in a harmonic waveguide
• 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