Felix Werner

Unitary gas in an isotropic harmonic trap : Symmetry properties and applications

We consider N atoms trapped in an isotropic harmonic potential, with s-wave interactions of infinite scattering length. In the zero-range limit, we obtain several exact analytical results: mapping between the trapped problem and the free-space zero-energy problem, separability in hyperspherical coordinates, SO(2,1) hidden symmetry, existence of a decoupled bosonic degree of freedom, and relations between the moments of the trapping potential energy and the moments of the total energy.

Shifted-action expansion and applicability of dressed diagrammatic schemes

While bare diagrammatic series are merely Taylor expansions in powers of interaction strength, dressed diagrammatic series, built on fully or partially dressed lines and vertices, are usually constructed by reordering the bare diagrams, which is an a priori unjustified manipulation, and can even lead to convergence to an unphysical result [E. Kozik, M. Ferrero, and A. Georges, Phys. Rev. Lett. 114, 156402 (2015)]. Here we show that for a broad class of partially dressed diagrammatic schemes, there exists an action

Polynomial complexity despite the fermionic sign

{S}^{(\ensuremath{\xi})}

Le troisième coefficient du viriel du gaz de Bose unitaire

depending analytically on an auxiliary complex parameter

Skeleton series and multivaluedness of the self-energy functional in zero space-time dimensions

\ensuremath{\xi}

Number of closed-channel molecules in the BEC-BCS crossover

, such that the Taylor expansion in

Feynman diagrams versus Fermi-gas Feynman emulator

\ensuremath{\xi}

Contact and Momentum Distribution of the Unitary Fermi Gas by Bold Diagrammatic Monte Carlo

of correlation functions reproduces the original diagrammatic series. The resulting applicability conditions are similar to the bare case. For fully dressed skeleton diagrammatics, analyticity of

Bold diagrammatic Monte Carlo for the resonant Fermi gas

{S}^{(\ensuremath{\xi})}

Equation of State of a Strongly Interacting Atomic Fermi Gas

is not granted, and we formulate a sufficient condition for converging to the correct result.