We derive an energy density functional for non-relativistic spin one-half fermions in the limit of a divergent two-body scattering length. Using an epsilon expansion around d=4-epsilon spatial dimensions we compute the coefficient of the leading correction beyond the local density approximation (LDA). In the case of N fermionic atoms trapped in a harmonic potential this correction has the form E=E_(LDA)(1+c_s (3N)^(-2/3)), where E_(LDA) is the total energy in LDA approximation. At next-to-leading order in the epsilon expansion we find c_s=1.68, which is significantly larger than the result for non-interacting fermions, c_s=0.5.
We consider a polarized Fermi gas in the unitarity limit. Results are calculated analytically up to next-to-leading order in an expansion about d=4 spatial dimensions. We find a first order transition from superfluid to normal phase. The critical chemical potential asymmetry for this phase transition is delta_mu_c= 2/(mu epsilon)*(1-0.467ε), where epsilon=4-d is the expansion parameter and 'mu' is the average chemical potential of the two fermion species. Stability of the superfluid phase in the presence of supercurrents is also studied.
We extract the shear viscosity to entropy density ratio η/s of cold fermionic atoms in the unitarity limit from experimental data on the damping of collective excitations. We find that near the critical temperature η/s is roughly equal to 1/2 in units of \hbar/k_B. With the possible exception of the quark gluon plasma, this value is closer to the conjectured lower bound 1/(4π) than any other known liquid.
The Interacting Boson Model of nuclear structure is introduced to the unitarity limit. Non relativistic conformal symmetry creates a scale invariant state from which the stationary states of atomic nuclei are obtained. A brief discussion of the nature of the conformal field theory is included along with the BCS-BEC crossover and hydrodynamic properties.
We consider two-component fermions on the lattice in the unitarity limit. This is an idealized limit of attractive fermions where the range of the interaction is zero and the scattering length is infinite. Using Euclidean time projection, we compute the ground state energy using four computationally different but physically identical auxiliary-field methods. The best performance is obtained using a bounded continuous auxiliary field and a non-local updating algorithm called hybrid Monte Carlo. With this method we calculate results for 10 and 14 fermions at lattice volumes 4^3, 5^3, 6^3, 7^3, 8…
We investigate fermion pairing in the unitary regime for a mass ratio corresponding to a 6Li-40K mixture using Quantum Monte Carlo methods. The ground-state energy and the average light and heavy particle excitation spectrum for the unpolarized superfluid state are nearly independent of the mass ratio. In the majority light system, the polarized superfluid is close to the energy of a phase separated mixture of nearly fully polarized normal and unpolarized superfluid. For a majority of heavy particles, we find an energy minimum for a normal state with a ratio of ~ 3:1 heavy to light particles. …
We examine the physics of two, three, and four heavy fermions interacting with a single light fermion via short-range interactions. Four-particle bosonic Efimov states have proven important experimentally and also been the subject of significant theoretical effort. Similar fermionic systems are just now being investigated. We find that with some simple interactions the four- and five-particle states collapse to the interaction range at smaller mass ratios than the three-body state, and also before larger clusters can collapse. These states and their excitations can be studied in cold atom expe…
We construct systematic expansions around four and two spatial dimensions for a Fermi gas near the unitarity limit. Near four spatial dimensions such a Fermi gas can be understood as a weakly interacting system of fermionic and bosonic degrees of freedom. To the leading and next-to-leading orders in the expansion over epsilon=4-d, with d being the dimensionality of space, we calculate the thermodynamic quantities and the fermion quasiparticle spectrum, both at unitarity and around the unitarity point. Then the phase structure of the polarized Fermi gas in the unitary regime is studied in the e…
Two methodologies have been presented in the literature which connect relativistic three-particle scattering amplitudes with lattice QCD spectra -- the ``relativistic effective field theory'' approach and the ``finite-volume unitarity'' method. While both methods have been shown to be equivalent in various works, it has not been shown how to arrive at the relativistic effective field theory results directly from $S$ matrix unitarity. In this work, we provide a simple proof of the relativistic effective field theory form of the scattering equations directly from unitarity. Motivated by the fini…
We investigate a two-species Fermi gas with a large mass ratio interacting by an interspecies short-range interaction. Using the Born-Oppenheimer approximation, we determine the interaction energy of two heavy fermions immersed in the Fermi sea of light fermions as a function of the s-wave scattering length. In the BCS limit, we recover the perturbative calculation of the effective interaction between heavy fermions. The p-wave projection of the effective interaction is attractive in the BCS limit while it turns out to be repulsive near the unitarity limit. We find that the p-wave attraction r…
By generalizing our automated algebra approach from homogeneous space to harmonically trapped systems, we have calculated the fourth- and fifth-order virial coefficients of universal spin-1/2 fermions in the unitary limit, confined in an isotropic harmonic potential. We present results for said coefficients as a function of trapping frequency (or, equivalently, temperature), which compare favorably with previous Monte Carlo calculations (available only at fourth order) as well as with our previous estimates in the untrapped limit (high temperature, low frequency). We use our estimates of the v…
We present a lattice study of up to N=20 unitary fermions confined to a harmonic trap. Our preliminary results show better than 1% agreement with high precision solutions to the many-body Schrodinger equation for up to N=6. We are able to make predictions for larger N which were inaccessible by the Hamiltonian approach due to computational limitations. Harmonic traps are used experimentally to study cold atoms tuned to a Feshbach resonance. We show that they also provide certain benefits to numerical studies of many-body correlators on the lattice. In particular, we anticipate that the methods…
The self-consistent random phase approximation (RPA) approach with the residual interaction derived from a relativistic point-coupling energy functional is applied to evaluate the isospin symmetry-breaking corrections δc for the 0+\to0+ superallowed Fermi transitions. With these δc values, together with the available experimental ft values and the improved radiative corrections, the unitarity of the Cabibbo-Kobayashi-Maskawa (CKM) matrix is examined. Even with the consideration of uncertainty, the sum of squared top-row elements has been shown to deviate from the unitarity condition by 0.1% fo…
We study in a nonperturbative fashion the thermodynamics of a unitary Fermi gas over a wide range of temperatures and spin polarizations. To this end, we use the complex Langevin method, a first principles approach for strongly coupled systems. Specifically, we show results for the density equation of state, the magnetization, and the magnetic susceptibility. At zero polarization, our results agree well with state-of-the art results for the density equation of state and with experimental data. At finite polarization and low fugacity, our results are in excellent agreement with the third-order …
We present lattice results for spin-1/2 fermions at unitarity, where the effective range of the interaction is zero and the scattering length is infinite. We measure the spatial coherence of difermion pairs for a system of 6, 10, 14, 18, 22, 26 particles with equal numbers of up and down spins in a periodic cube. Using Euclidean time projection, we analyze ground state properties and transient behavior due to low-energy excitations. At asymptotically large values of t we see long-range order consistent with spontaneously broken U(1) fermion-number symmetry and a superfluid ground state. At int…
Motivated by applications to the study of ultracold atomic gases near the unitarity limit, we investigate the structure of the operator product expansion (OPE) in non-relativistic conformal field theories (NRCFTs). The main tool used in our analysis is the representation theory of charged (i.e. non-zero particle number) operators in the NRCFT, in particular the mapping between operators and states in a non-relativistic "radial quantization" Hilbert space. Our results include: a determination of the OPE coefficients of descendant operators in terms of those of the underlying primary state, a de…
We present analytic expressions for the vacuum polarization effects due to a light fermion with finite mass in the binding energy and in the wave function at the origin of QED and (weak coupling) QCD non-relativistic bound states. Applications to exotic atoms, Υ(1s) and t\bar{t} production near threshold are briefly discussed.
Large back-to-back correlations of observable fermion -- anti-fermion pairs are predicted to appear, if the mass of the fermions is modified in a thermalized medium. The back-to-back correlations of protons and anti-protons are experimentally observable in ultra-relativistic heavy ion collisions, similarly to the Andreev reflection of electrons off the boundary of a superconductor. While quantum statistics suppresses the probability of observing pairs of fermions with nearby momenta, the fermionic back-to-back correlations are positive and of similar strength to bosonic back-to-back correlatio…
It is usually believed that unlike the external magnetic field which one can set directly, vorticity is a property of the flow of particles, which is indirectly controlled by external fields and initial conditions. Using the curved-space technics it is shown that the influence of the vorticity on the relativistic chiral fermions can indeed be controlled directly.
With a non-unitary transformation, the Lagrangian of a Dirac fermion is decomposed into two decoupled sectors. We propose to describe massive relativistic fermions in gauge theories in a two-component form. All relations between the Green's functions in this form and those in the conventional four-component form are derived. It is shown that the S-matrix elements in both forms are exactly the same. The description of the fermion in the new form simplifies significantly the gamma-matrix algebra in the four-component form. In particular, in perturbative calculations the propagator of the fermion…
In the Light-Front Dynamics, the wave function equations and their numerical solutions, for two fermion bound systems, are presented. Analytical expressions for the ladder one-boson exchange interaction kernels corresponding to scalar, pseudoscalar, pseudovector and vector exchanges are given. Different couplings are analyzed separately and each of them is found to exhibit special features. The results are compared with the non relativistic solutions.
