Superfluidity and perturbation expansion in a large fermi system

Rashmiraj Balkrishna Prabhu

Simeon Hellerman, Daniil Krichevskiy, Domenico Orlando +3 more

We study the unitary Fermi gas in a harmonic trapping potential starting from a microscopic theory in the limit of large charge and large number of fermion flavors N. In this regime, we present an algorithmic procedure for extracting data from perturbation theory, order-by-order, without the need for other assumptions. We perform a gradient expansion in the interior of the particle cloud, sufficiently far from the cloud edge where the particle density drops rapidly to zero. In this latter region we present the first microscopic computation characterizing the contribution of the edge terms. The microscopic theory reproduces the predictions of the superfluid EFT, including the action, the form of the gap equation, and the energy of the system in a harmonic trap (which maps, via the non-relativistic state-operator correspondence, to the scaling dimension of the lowest operator of charge Q). We additionally give the Wilsonian coefficients at leading order in N up to NNLO in the large-charge expansion.

Simeon Hellerman, Daniil Krichevskiy, Domenico Orlando +3 more

A bstract We study the unitary Fermi gas in a harmonic trapping potential starting from a microscopic theory in the limit of large charge and large number of fermion flavors N . In this regime, we present an algorithmic procedure for extracting data from perturbation theory, order-by-order, without the need for other assumptions. We perform a gradient expansion in the interior of the particle cloud, sufficiently far from the cloud edge where the particle density drops rapidly to zero. In this latter region we present the first microscopic computation characterizing the contribution of the edge terms. The microscopic theory reproduces the predictions of the superfluid eft , including the action, the form of the gap equation, and the energy of the system in a harmonic trap (which maps, via the non-relativistic state-operator correspondence, to the scaling dimension of the lowest operator of charge Q ). We additionally give the Wilsonian coefficients at leading order in N up to nnlo in the large-charge expansion.

M. S. Mar’enko, M. Yu. Kagan, Dmitri V. Efremov +1 more

Shinji Koshida, Yusuke Kato

A perturbative way to investigate superfluid properties of various systems under nonuniform potential is presented. We derive the perturbation expansion of the superfluid fraction, which indicates how liquid exhibits nonclassical rotational inertia, in terms of the strength of nonuniform potential and find that the coefficient of the leading term reflects the density fluctuation of the system. Our formulation does not assume anything about Bose-Einstein condensation and thus is applicable to wide variety of systems. Superfluid properties of some examples including (non-)interacting Bose systems, especially Bose gas in the mean field limit, (non-)interacting Fermi sytems, Tomonaga-Luttinger liquid and spinless chiral $p$-wave superfluid are investigated.

Красильников Владимир Владимирович, S.V. Peletminskij, A. A. Yatsenko